Answers
The simplified forms of the fractions are 3 and -5 repectively
How do you simplify a fraction?To simplify a fraction, you divide both the numerator (top number) and denominator (bottom number) by their greatest common factor (GCF) until there are no more common factors. The result will be the simplified form of the fraction.
We have to note that;
1 ) 1 + 1/2 = 3/2
Then we have;
3/2 * 2/1 = 6/2 = 3
2) 3/4 - 2 = -5/4
Then we have;
-5/4 * 4/1 = -5
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Related Questions
Identify the letter that represents the following numbers on the number line.
Answers
Letters which represent negative integers on a number line are present on the left side of zero and you can also identify them with the minus sign they carry.
What is number lines ?
Integers are arranged at equal intervals along horizontal, straight lines known as number lines. A number line can be used to visualize all the numbers in a succession. Both endpoints of this line continue indefinitely.
The number line is a straightforward straight line with divisions indicated at regular intervals, much like a scale. Any point can be selected as "0," and all positive and negative numbers are arranged to the right and left of the "0" respectively.
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The complete question is -
Identify the letter that represents the following number negative integers on a number line .
The points (4,2) and (5,r) fall on a line with a slope of
–7. What is the value of r?
Answers
Answer:
r = -5
Step-by-step explanation:
To find the value of 'r', use the slope formula.
(4, 2) ; x₁ = 4 and y₁ = 2
(5 , r ) ; x₂ = 5 and y₂= r
[tex]\boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\dfrac{r -2}{5 - 4 }= -7\\\\\dfrac{r -2}{1}=-7[/tex]
r - 2 = -7
r = -7 + 2
r = -5
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=
Answers
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.
42. Solve for y: 2(y - 4) > 0
Answers
Answer:
Step-by-step explanation:
if we divide each side with 2,
(2(y-4))/2>0/2
y-4>0
y>4
Answer:
y > 4
Step-by-step explanation:
2(y - 4) > 0
Solving the inequality:
Divide each side by 2.
2/2(y - 4) > 0/2
y - 4 > 0
Add 4 to each side.
y - 4+4 > 0+4
y > 4
A parabola can be drawn given a focus of
(5, -4) and a directrix of y=2. Write the equation of the parabola in any form.
Answers
Therefore , the solution of the given problem of equation comes out to be the equation of the parabola in standard form is x² - 10x - 12y + 13 = 0
Define equation.In arithmetic equations, the identical figure (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12.
Here,
The distance between the focus and vertex is the same as the distance between the vertex and directrix, which is |-4 - (-1)| = 3. This distance is also equal to the absolute value of the coefficient "a" in the equation of the parabola.
Therefore, the equation of the parabola in vertex form is:
(x - 5)² = 4p(y + 1)
where "p" is the distance between the vertex and the focus, which is 3. Substituting this value into the equation gives:
(x - 5)² = 4(3)(y + 1)
Simplifying:
(x - 5)² = 12y + 12
Expanding the left side:
x² - 10x + 25 = 12y + 12
Moving all the terms to one side:
x² - 10x - 12y + 13 = 0
So the equation of the parabola in standard form is:
x^2 - 10x - 12y + 13 = 0
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Probability: The answer i got was 0.2
this is my work:
Non-negativity: f(x) ≥ 0 for all x in the support of X.
normalization: The sum of f(x) over all x in the support of X must be equal to 1.
In this case, the support of X is {0, 1, 2, 3, 4}. So, for f(x) to be a valid probability distribution function, i should have:
0 ≤ f(x) for all x in {0, 1, 2, 3, 4}
and
f(0) + f(1) + f(2) + f(3) + f(4) = 1
so find the value of k such that:
0 ≤ k ≤ 1
and
f(x) = k for all x in {0, 1, 2, 3, 4}
since f(x) must be equal to k for all x in the support of X, we have:
k = f(0) = f(1) = f(2) = f(3) = f(4)
and
k * 5 = 1 so, k = 1/5
so,
f(x) = 1/5 for all x in {0, 1, 2, 3, 4}
is a valid probability distribution function for a discrete random variable X which can take on the values 0, 1, 2, 3, or 4.
so the answer is 0.2
Answers
The required [tex]f(x) = x/10[/tex] is a valid probability distribution function for a discrete random variable X which can take on the values 0, 1, 2, 3, or 4.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
For a function f(x) to be a valid probability distribution function (pdf) for a discrete random variable X, it must satisfy the following conditions:
Non-negativity: [tex]f(x) = x/k[/tex] is non-negative for all x when k > 0.
Normalization: We need to find the value of k such that the sum of the probabilities for x = 0, 1, 2, 3, 4 is equal to 1.
[tex]f(x) = x/k[/tex] for x = 0, 1, 2, 3, 4.
The sum of the probabilities is given by:
[tex](0/k) + (1/k) + (2/k) + (3/k) + (4/k) = 1[/tex]
[tex]10/k = 1[/tex]
So, k = 10.
Thus,[tex]f(x) = x/10[/tex] is a valid probability distribution function for a discrete random variable X which can take on the values 0, 1, 2, 3, or 4.
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If A(-9, 4) and B(3, -2), find the midpoint of AB.
Answers
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]
You can use the equation A = HW 1/2 to approximate a person's body surface area A (in 3600 square meters), where His height (in centimeters), and Wis weight (in kilograms). Approximate the body surface area to the nearest tenth of a person with a height of 160 centimeters and a weight of 64 kilograms. m²
Answers
The body surface area is 1.7 m²
How to determine the body surface areaFrom the question, we have the following parameters that can be used in our computation:
A = (HW/3600)^(1/2)
Where H is the height in cm and W is the weight in kg.
Substitute the known values in the above equation, so, we have the following representation
A = (160 * 64 / 3600)^(1/2)
Evaluate
A ≈ 1.69 m²
Rounding to the nearest tenth:
A ≈ 1.7 m²
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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?
Answers
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:
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?
Answers
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:
HELP PLEASEEEEEEEEEEE
Answers
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
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?
Answers
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.
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.
Answers
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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which of these data sets represent continuous data? a.) number of questions answered correctly in a multiple-choice quiz b.) numbers of tickets sold for a football game c.) heights of members of a baseball team d.) population of towns within a state
Answers
All four data which is number of questions answered correctly in a multiple-choice quiz and numbers of tickets sold for a football game and heights of members of a baseball team and population of towns within a state are continuous data.
Countable data is referred to as continuous data. The values in this data are not constant and can take on an endless number of different forms. You can also divide these measures up into smaller, independent components. Examples of continuous data include the following: A person's height or weight
in a) number of questions answered correctly in a multiple-choice quiz can be count
b.) numbers of tickets sold for a football game can be count and c.) heights of members of a baseball team can be measure and d.) population of towns within a state can be count .
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Select strong association moderate assossiation or weak association for each correlation 0.8, .25 ,0.9, 0.65coeffcient
Answers
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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Why in arithmetic sequence does the graph of Tn vs n need to be a straight line
Answers
Answer:
It's because the graph of arithmetic sequence forms a set of discrete points lying on a straight line.
How does Huck feel in the adventures of huckleberry finn
Answers
In Adventures of Huckleberry Finn, at first, Huck feels good about writing to Jim's owner.
What is adventures?Adventure is an exciting experience or undertaking that is usually daring, sometimes risky. Adventures can be dangerous activities such as travel, exploration, skydiving, mountain climbing, diving, rafting or other extreme sports.
here, we have,
Adventures are often undertaken for psychological excitement or to achieve a greater goal, such as the pursuit of knowledge that can only be obtained through such activities.
Adventure not only expands your mind, increasing courage, but also gives you the opportunity to grow and learn. New environments and cultures are full of meaningful lessons that you may not encounter in your everyday life. Adventures expand the way we see and interact with the world.
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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?
Answers
Answer:
10413000 visitors
Step-by-step explanation:
117% = 1.17
8900000 times 1.17 = 10413000 visitors
So, there were 10413000 visitors in 2007.
3/4 (1/6x + 16) = 3/7 (35/8 - 21)
Answers
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
What is the relationship between DE and AC? There are two properties to state, be sure to state both.
Answers
The first property is that Direct Current (DC) can be converted into Alternating Current (AC) through a device called an inverter. An inverter takes a DC voltage and converts it into a sinusoidal AC voltage of the desired frequency and magnitude.
The second property is that Alternating Current (AC) can be rectified or converted into Direct Current (DC) through a device called a rectifier. A rectifier converts an AC voltage into a pulsed DC voltage. This conversion process can be useful in applications where DC power is required but only AC power is available, such as in battery charging or power supply systems.
Calculate the slope based on the table below:
Answers
Answer:-1/2
Step-by-step explanation:
Take two points and use the formula (y2-y1)/(x2-x1). I used (0,4) and (4,2) as my set of coordinate pts.
Ned made the design at the right. Use a protractor. Find and write the measure of each of the 3 angles
Answers
The measures of the three angles are 60 degrees, 75 degrees and 45 degrees.
A semi-circle has a total angle measure of 180 degrees. The sum of the angles formed by the two arcs must equal the total angle measure of the semi-circle.
Let's call the angle formed by the first arc "angle A" and the angle formed by the second arc "angle B".
From the given information, we know that:
angle A = 60 degrees
angle B = 75 degrees
So, angle A + angle B = 60 degrees + 75 degrees = 135 degrees
Since the total angle measure of the semi-circle is 180 degrees, the measure of the remaining angle is:
180 degrees - 135 degrees = 45 degrees
Therefore, the measures of the three angles are:
angle A = 60 degrees
angle B = 75 degrees
angle C = 45 degrees
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Question: Ned made the design at the right. Use a protractor. Find and write the measure of the 3rd angle with given 60 and 75 degrees.
Find the volume of cuboid which is 9cm multiply 4cm multiply 5cm
Answers
The volume of cuboid is 180 cubic centimeters.
As we know the formula for the volume of the cuboid is given as:
V = l × w × h
where, V is the volume of the cuboid
l is the length of the cuboid
w is the width of the cuboid
and h is the height of the cuboid
Here, the dimensions of the cuboid are: 9cm × 4cm × 5cm
Let the length of the cuboid is l = 9 cm,
the width of the cuboid is w = 4 cm
and the height of the cuboid is h = 5 cm
Using above formula of volume of cuboid,
V = l × w × h
substitute values, l = 9, w = 4 and h = 5
⇒ V = 9 × 4 × 5
⇒ V = 180 cm³
Therefore, the volume of cuboid 180 cubic centimeters
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The function f(x) = 5x + 2,500 models the number of computer chips produced by a manufacturing plant each month during its first year. How many computer chips was the plant able to produce in month 3?
Answers
The number of computer chips produced in 3 months will be 2515.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the function f(x) = 5x + 2,500 models the number of computer chips produced by a manufacturing plant each month during its first year.
The number of chips will be calculated as:-
f(x) = 5x + 2,500
f(3) = 5 x 3 + 2500
f(3) = 15 + 2500
f(3) = 2515
Therefore, the number of chips will be 2515.
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on a blueprint, a rectangular kitchen has a length of 4 inches and a width of 3 inches. if the length of the kitchen is 6 feet, what is the perimeter of the kitchen?
Answers
21 feet is the perimeter of the kitchen .
In arithmetic, what is a perimeter?
The perimeter is the space surrounding a shape's edge. Discover how to calculate the perimeter of various forms by multiplying their side lengths. The whole distance that the sides or limits of a rectangle cover is known as its perimeter.
The perimeter of a rectangle will be equal to the sum of its four sides because rectangles have four sides.
on a blueprint, a rectangular kitchen has a length = 4 inches
a width = 3 inches
So it's width is equal to = 6/4 * 3
= 4.5 feet
the perimeter of this kitchen is = 2(6 + 4.5 )
= 2 * 10.5 = 21 feet
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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
Answers
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.
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?
Answers
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.
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.
Answers
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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during basketball practice mai attempted 40 free trows and was successful on 25% of them how many successful free trows did she make
Answers
Answer:
10
Step-by-step explanation:
25% of 40 1/4*40=40/4=10
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 .
Answers
Explanation: if you look at the equation and know the basics, the 3n will be multiplied by each other then you add the outcome of that to your 8.