Answer:
Therefore, there is 8 children that is 9 years old and 6 children that is 11 years old.
Step-by-step explanation:
Let x be the no. of 9 years old and y be the no. of 11 years old.
x+y= 14 (1)
9x+11y= 138 (2)
From (1) :
x=-y+14 (3)
sub (3) into (2) :
9(-y+14)+11y= 138
-9y+126+11y=138
2y= 138-126
y= 6 (4)
sub (4) into (1) :
x+6= 14
x= 8
A quantity with an initial value of 8500 grows exponentially at a rate such that the quantity doubles every 9 years. What is the value of the quantity after 23 years, to the nearest hundredth?
Answer: We can use the formula for exponential growth to find the value of the quantity after 23 years:
Q(t) = 8500 * 2^(t/9)
Where Q(t) is the value of the quantity after t years, and t/9 is the number of doublings that have occurred.
Substituting t = 23 into the formula:
Q(23) = 8500 * 2^(23/9) = 8500 * 2^2.56 = 8500 * 12.90 = 109350
So, after 23 years, the quantity has a value of approximately 109,350, rounded to the nearest hundredth.
Step-by-step explanation:
-6(n-1)<3or2(n+1)>0 solve and then put on a number line pls
Answer: To solve the inequality, we start by isolating the variable n:
-6(n-1) < 3
-6n + 6 < 3
-6n < -3
n > 1/2
And for the other inequality:
2(n+1) > 0
2n + 2 > 0
2n > -2
n > -1
Now, we can plot these solutions on a number line:
[-----1/2-----][-------------n > 1/2----------------]
[-----n > -1-----][-------------]
So, the solution set for the inequality is n > -1 and n > 1/2, which means that n belongs to the interval (1/2, +∞).
Step-by-step explanation:
HELP ASAP, WILL GIVE BRAINLIEST,
In a repeated experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 9 is 6 over 36. Predict how many times the rolls will result in a sum greater than 9 if the experiment is repeated 144 times.
24
12
9
6
Answer: We can predict that the rolls will result in a sum greater than 9 approximately 24 times.
Step-by-step explanation: The theoretical probability of both rolls equaling a sum greater than 9 is given as 6/36. To predict how many times the rolls will result in a sum greater than 9 if the experiment is repeated 144 times, we can use the concept of probability.
The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
In this case, the probability of both rolls resulting in a sum greater than 9 is 6/36, which simplifies to 1/6. This means that out of every 6 possible outcomes, 1 will result in a sum greater than 9.
To predict the number of times this will occur in 144 repetitions, we can multiply the probability by the number of repetitions:
(1/6) * 144 = 144/6 = 24
Therefore, we can predict that the rolls will result in a sum greater than 9 approximately 24 times if the experiment is repeated 144 times.
The growth in visitors to a community website from 2006 to 2007 was 117%. The number of visitors was 8.9 million in 2006. How many visitors were there in 2007?
Answer:
10413000 visitors
Step-by-step explanation:
117% = 1.17
8900000 times 1.17 = 10413000 visitors
So, there were 10413000 visitors in 2007.
In a direct variation, y=16 when x=2. Write a direct variation equation that shows the relationship between x and y.
A direct variation equation that shows the relationship between x and y is,
y = 8x.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
In a direct variation, y=16 when x=2.
The proportional relationship between x and y:
y ∝ x.
y = kx, where k is constant.
When x = 2,
16/2 = k
k = 8.
Therefore, the relationship is y = 8x.
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Casey buys a bracelet. She pays for the bracelet and pays
$
0.72
$0.72dollar sign, 0, point, 72 in sales tax. The sales tax rate is
6
%
6%6, percent.
What is the original price of the bracelet, before tax?
Answer: The original price of the bracelet before tax can be found using the following formula:
original price = (total price) / (1 + sales tax rate as decimal)
In this case, the total price is 0.72 dollars, and the sales tax rate as a decimal is 0.06. Plugging these values into the formula, we get:
original price = 0.72 / (1 + 0.06)
original price = 0.72 / 1.06
Step-by-step explanation:
Please help me solve: 10(s+9)+3
Answer:
[tex]\huge\boxed{\sf 10s + 93}[/tex]
Step-by-step explanation:
Given expression:= 10 (s + 9) + 3
Distribute 10 to s and 9= 10s + 90 + 3
Add 90 and 3= 10s + 93[tex]\rule[225]{225}{2}[/tex]
Answer:
Step-by-step explanation:
10(s + 9) +3
10s + 90 + 3
10s + 90 +3
10s + 93
Solution 10s + 93
When a plant or animal dies, it stops acquiring carbon-14 from the atmosphere. The amount y (in grams) of carbon-14 in the body of an organism after
t years is-y = a(0. 5)*/3730, where a is the initial amount grams). What percent of the carbon-14 is released each year? Round your answer to the
nearest hlindredth
At 0.0175% of the carbon-14 is released each year, rounded to the nearest hundredth.
The amount of carbon-14 released each year can be represented as the rate of change of the amount of carbon-14 in the body of an organism with respect to time.
Carbon-14, the longest-lived radioactive isotope of carbon, whose decay allows the accurate dating of archaeological artifacts. The carbon-14 nucleus has six protons and eight neutrons, for an atomic mass of 14.[tex]\frac{d(y)}{dt}=\frac{-y}{tau}[/tex]Where
d(y)/dt represents the rate of change of the amount of carbon-14 in the body. y represents the amount of carbon-14 in the body, and tau (τ) represents the half-life of carbon-14 (5730 years).To find the percent of the carbon-14 that is released each year, we can divide the rate of change by the initial amount of carbon-14 and multiply by 100 to express it as a percentage:
⇒percent released/year =[tex]=100*\frac{ d(y)}{dt}[/tex]/a
[tex]=\frac{-100*y}{a* tau}[/tex] = [tex]-100 * (0.5)^(t / tau) / tau[/tex]
At t = tau, the percent released/year will be[tex]-100 * (0.5)^\frac{(1) }{tau}[/tex],
which is approximately -0.0175 per year.
So,
Therefore, each year approximately 0.0175 percent of the carbon-14 is released, rounded to the nearest hundredth.
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Please help me with this
Answer:
40 to 60 is the answer of this question
The medal Zena won for athletics consists of silver and brass in the ratio 3:5. If the medal has a mass of 200g, calculate the mass of the silver.
Answer: mass of silver is 75g
Step-by-step explanation:
If A(-9, 4) and B(3, -2), find the midpoint of AB.
Answer:
(-3,1)
Step-by-step explanation:
The value of x [tex]\frac{-9+3}{2}[/tex] = -3
The value of y [tex]\frac{4-2}{2}[/tex] = 1
Answer:
Mid point is (-3, 1)
Step-by-step explanation:
Let mid point be M
[tex] { \boxed{ \sf{m = ( \frac{x _{1} + x _{2} }{2}} , \: \frac{y _{1} + y _{2}}{2}) }} \\ \\ { \tt{m = ( \frac{ - 9 + 3}{2} , \: \frac{4 - 2}{2} )}} \\ \\ { \tt{m = ( \frac{ - 6}{2}, \: \frac{2}{2} ) }} \\ \\ { \tt{m = ( - 3, \: 1)}}[/tex]
A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º above the horizontal. What is the skier's displacement from his starting point? (Use the graphical method to answer and include your scale on the graph paper.) Give both the magnitude and the angle in your answer.
The skier's displacement from his starting point is 127.179 m and makes an angle of 33.78°.
What is the law of cosine?The law of cosines, commonly referred to as the cosine rule or the cosine formula, in trigonometry essentially connects the length of the triangle to the cosines of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.
Given A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º
base distance = 100 m
We will utilize the cosine rule to determine the magnitude of displacement because the triangle formed by the starting point, where he begins to ascend, and the ending point does not have a 90-degree angle. Cosine law requires a triangle with two sides and an angle between them, both of which are present.
a² = b² + c² - 2.b.ccos(α)
here a is the length of the third side,
b = base = 100m
c = 35 m
and α = 180 - 35 = 135°
so a² = b² + c² - 2.b.ccos(α)
a² = 100² + 35² - 2(100)(35)cos(135)
a² = 10000 + 1225 + 4949.74
a² = 16174.74
a = 127.179 m
and the angle between sides 100m and 127.179 m is given by
cosβ = (a² + c² - b²)/2a.c
cosβ = (127.179² + 35² - 100²)/2(127.179)(35)
cosβ = 0.831
β = cos⁻¹(0.831)
β = 33.78°
Hence displacement from the starting point is 127.179 m and forms an angle of 33.78°.
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Anna compra helado y naranjas en la tienda.
• Ella paga un total de $59.53.
• Ella paga un total de $6.49 por el helado.
• Ella compra 8 bolsas de naranjas que cuestan la misma cantidad cada una.
Escribe y resuelve una ecuación que se pueda usar para determinar X, cuánto cuesta
cada bolsa de naranjas.
Ecuación:
Respuesta: X=
Answer:
Podemos utilizar la información proporcionada para escribir la siguiente fórmula y resolverla para encontrar el valor de X, que representa el costo de cada bolsa de naranjas:
6,49 + 8X = 59,53
Para resolver la fórmula, primero debemos despejar la variable X. Restamos 6.49 de ambos lados:
8X = 53,04
Luego, dividimos ambos lados por 8:
X = 6,63
Por lo tanto, cada bolsa de naranjas cuesta $6.63.
5. what rate (in mm/yr ) is the north american plate moving relative to the boundary? round your answer to 2 significant figures.
The major plate motion rates range from less than 10 mm/y to more than 100 mm/y. The fastest plate is the Pacific Plate, followed by the Australian and Nazca Plates. The North American Plate is one of the slowest, with average rates ranging from around 1 cm/y in the south to nearly 4 cm/y in the north.
Plates move as rigid bodies, it may appear surprising that the North American Plate can move at different rates in different locations. Plates move in a rotational fashion, as explained. For example, the North American Plate rotates counter-clockwise, while the Eurasian Plate rotates clockwise.
There are three types of plate boundaries: divergent, convergent, and transform (moving side by side). Before we discuss processes at plate boundaries, it is critical to note that there are no gaps between plates.
The plates are made up of crust and the lithospheric part of the mantle, and despite moving in different directions all the time, there is never a significant amount of space between them.
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Which three statements describe the expression 8 + 3n?
Responses
A The expression represents 8 plus n times n times n.The expression represents 8 plus n times n times n .
B The expression represents the sum of 3n and 8.The expression represents the sum of 3 n and 8.
C The expression represents 8 plus n plus n plus n.The expression represents 8 plus n plus n plus n .
D The expression represents 8 plus the product of 3 and n.The expression represents 8 plus the product of 3 and n .
E The expression represents the product of 8 and 3n.The expression represents the product of 8 and 3 n .
HELP PLEASEEEEEEEEEEE
Answer:
y intercept = -3
the slope of the line is 1
Step-by-step explanation:
y intercept is the value of y when x = 0
x = 0 when y = -3
what is the common denominator for 2/5,2/4,2/3?????
Answer:
60
good luck!
please answer all these for crown and separate them from each other ty ill give u a crown
The values of x for the different diagrams are given below.
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
Given:
There are four diagrams.
Diagram 1:
By the alternate exterior angles,
8x + 19 = 139
8x = 120
x = 15
Diagram 2:
By the corresponding angles,
17x - 45 = 108
17x = 153
x = 9
Diagram 3:
By the alternate interior angles,
7x -1 = 13x - 43
6x = 42
x = 7
Diagram 4:
By the consecutive interior angles,
8x + 19 = 139
8x = 120
x = 15
Hence, the solutions for all the values are given above.
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during basketball practice mai attempted 40 free trows and was successful on 25% of them how many successful free trows did she make
Answer:
10
Step-by-step explanation:
25% of 40 1/4*40=40/4=10
A quilter created the following shape to use in a block for a new quilt.
What is the area of the shape for the quilt block?
Answer: 166.5 inch.
Explanation:
There are a lot of steps to this. First of all, as seen in the picture below, we split the shape into a triangle and a rectangle. We can first find the area of the triangle first, which would be:
[tex]\frac{45}{2}[/tex] = 22.5 inch.
Next, using the pythagoras theorem, we can find the missing side of the triangle. So, we do:
[tex]\sqrt{7.5^2+6^2} = x\\\\\frac{3\sqrt{41} }{2} = x = 9.6[/tex]
Now we have that side, we can calculate the area of the rectangle, which would be 16 x 9 = 144 inch.
So now we can add both areas:
144 + 22.5 = 166.5 inch.
In 2010, the population of a city was 87,000. From 2010 to 2015, the population grew by 7.7%. From 2015 to 2020, it fell by 4.5%. To the nearest 100 people, what was the population in 2020?
Answer:
The population of the city in 2020 was 89,500 to the nearest 100 people.
Step-by-step explanation:
The original population in 2010 is 100%.
If the population is increased by 7.7% from 2010 to 2015, the total percentage in 2015 is 107.7% of the population in 2010.
Convert this to a decimal and multiply by the original population of 87,000 to find the population of the city in 2015.
[tex]\begin{aligned}\implies \sf 107.7\%\;of\;87000&=\sf 1.077 \times 87000\\&=\sf 93699\end{aligned}[/tex]
Therefore, the population of the city in 2015 was 93,699.
The population in 2015 is 100%.
If the population is decreased by 4.5% from 2015 to 2020, the total percentage in 2020 is 95.5% of the population in 2015.
Convert this to a decimal and multiply by the population in 2015 to find the population of the city in 2020.
[tex]\begin{aligned}\implies \sf 95.5\%\;of\;93699&=\sf 0.955 \times 93699\\&=\sf89482.545 \end{aligned}[/tex]
Therefore, the population of the city in 2020 was 89,500 to the nearest 100 people.
Why in arithmetic sequence does the graph of Tn vs n need to be a straight line
Answer:
It's because the graph of arithmetic sequence forms a set of discrete points lying on a straight line.
3/4 (1/6x + 16) = 3/7 (35/8 - 21)
Answer:
x=-153
Step-by-step explanation
3/4(1/6x) + 3/4(16) = 3/7(35/8)-3/7(21)
1/8x+12=15/8-9
8(1/8x+12=15/8-9)
1x+96=15-72
1x+96=-57
x=-153
please help with this i need the answer pleas answer and do not just talk
Answer:
Below
Step-by-step explanation:
a) DIRECT variation y = k x
10 = k (4)
10/4 = k = 2.5
y = 2.5 x
b) y = 2.5 x
y = 2.5 (10) = 25
what is 16/21 as a decmil round to the nerste huderned
Answer:
0.7619047619≈0.76
Step-by-step explanation:
i need help
schoology
Answer: 37 degrees
Hope this helps :)
Step-by-step explanation:
(The box in the corner tells you this is a right angle)
A right angle is 90 degrees
90 - 53 = 37
Answer:
37 degrees
Step-by-step explanation:
Angle a is equivalent to 37 degrees because the picture signifies a right angle; all right angles are equal to 90 degrees. The equation to solve this would be: 53+x=90, you would solve this by subtracting 90-53=x; x=37
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the diameter of a manufactured widget is normally distributed with a mean of 65 and a standard deviation of 9. what is the probability a widget sampled at random will be less than or equal to 56? use excel and carry your answer to at least five decimal places.
Considering all the given information, the probability of a widget being less than or equal to 56 is approximately 0.1587
The formula for converting a value to a standard score, also known as a z-score, is:
z = (x - μ) / σ
Where x is the value of interest, μ is the mean, and σ is the standard deviation.
To find the probability of a widget being less than or equal to 56, we first find the corresponding z-score:
z = (56 - 65) / 9 = -1
We can then use the cumulative distribution function (CDF) of the standard normal distribution to find the probability of a z-score being less than or equal to -1:
P(z ≤ -1) = 0.1587
So the probability of a widget being less than or equal to 56 is approximately 0.1587, or 15.87%.
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Select strong association moderate assossiation or weak association for each correlation 0.8, .25 ,0.9, 0.65coeffcient
The correlation coefficient measures the strength of the linear relationship between two variables. A coefficient of 0.8 implies a strong linear relationship between two variables, a coefficient of 0.25 implies a weak linear relationship between two variables.
0.8: Strong Association
0.25: Weak Association
0.9: Strong Association
0.65: Moderate Association
The correlation coefficient is a numerical measure of the strength of the linear relationship between two variables. Values of the correlation coefficient fall between -1 and +1. A coefficient of 0 implies that there is no linear relationship between two variables. The closer the coefficient is to either -1 or +1, the stronger the correlation. A coefficient of 0.8 implies a strong linear relationship between two variables, a coefficient of 0.25 implies a weak linear relationship between two variables, a coefficient of 0.9 implies a very strong linear relationship between two variables, and a coefficient of 0.65 implies a moderate linear relationship between two variables.
The correlation coefficient measures the strength of the linear relationship between two variables. A coefficient of 0.8 implies a strong linear relationship between two variables, a coefficient of 0.25 implies a weak linear relationship between two variables, a coefficient of 0.9 implies a very strong linear relationship between two variables, and a coefficient of 0.65 implies a moderate linear relationship between two variables.
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Madison starts with a population of 1,000 1 , 000 amoebas that triples in size every hour for a number of hours, ℎ h . She writes the expression 1,000(3ℎ) 1,000 ( 3 h ) to find the number of amoeba after ℎ h hours. Tyler starts with a population of 1 1 amoeba that increases 30% 30 % in size every hour for a number of hours, ℎ h . He writes the expression (1+0.3)ℎ 1 + 0 . 3 h to find the number of amoeba after ℎ h hours. Use the drop-down menus to explain what each part of Madison’s and Tyler’s expressions mean.
Here we get 1.3 is the growth factor, 0.3 is the growth rate, and 1 is the initial population of amoebas.
Since Madison's population of 1,000 amoebas begins by doubling every hour for a certain number of hours, h.
In other words, the total number of amoebas after one hour is
3*1000=[tex]3^{1}[/tex]*1000.
Total number of amoebas after two hours is equal to 3*3000=[tex]3^{2}[/tex]*1000. The total number of amoebas after three hours is 3*9000=[tex]3^{3}[/tex]*1000.
In a similar manner, the total number of amoebas,
f(h) = [tex](1+0.3)^{h}[/tex]
where the starting amoeba population is 1000. 3 is the population growth factor, and f(h) is the amoeba population after h hours.
Since Tyler begins with a colony of a single amoeba that grows by 30% per hour for a certain length of hours.
In other words, after one hour, there were =[tex](1+0.3)^{1}[/tex]
After two hours, there were a total of =[tex](1+0.3)^{2}[/tex]
After three hours, there were a total of =[tex](1+0.3)^{3}[/tex]
In a similar manner, the total number of amoebas,
f(h) =[tex](1+0.3)^{h}[/tex]
where 1.3 is the growth factor, 1 is the initial population of amoebas and 0.3 is the growth rate.
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What is the relationship between DE and AC? There are two properties to state, be sure to state both.