Answer:
Because 435 divided by 35 equals 12 that means the most you can make is 12 because 855/20 equals 42 which means you dont have enough yellow beads so the most is 12
Step-by-step explanation:
The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
435÷35 = 12 that means the most you can make is 12 because 855/20 =42
What is probability and example?Probability = the number of ways of achieving success. the total number of possible outcomes.
For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .
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A magician has a magic trick that uses an 18" length of string that is cut into two pieces. One piece is two inches longer that the other. Find the length of each piece. Use algebraic equations.
The length of each piece is 10 in and 8 in.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The total length of the string = 18 in
One piece = x + 2
Another piece = x
Now,
Solve for x.
x + 2 + x = 18
2x + 2 = 18
2x = 18 - 2
2x = 16
x = 8
Now,
One piece = 8 + 2 = 10 in
Another piece = 8 in
Thus,
The length of each piece is 10 in and 8 in.
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1x-2y=18, 4x+3y=-16 what is this answer
Answer:
y = -8
x = 2
Step-by-step explanation:
1x-2y=18 / *(-4)
4x+3y=-16
11y =-88
y=-8
4x = 8
x = 2
With your team, create a piecewise-defined function with at least three “pieces.” The function does not need to be a step-function with horizontal line segments, but it needs to meet the definition of a function. Make a table and a graph for your function, and write an equation for each part. Be sure to state the domain for each part, as well as the domain for the whole function.
On solving the provided question we can say that The following is the data table of the function.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
here,
the provided functions that can be formed are
x -infinity < x < -10
f(x) = 2x + 10 -10 < x < 10
4X - 10 10 < x < infinty
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.
A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.
Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
The provided functions that can be formed are
\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
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Solve for m.
m+15<−123
Responses
m>−11315
m is greater than negative 1 and 13 over 15
m>−1715
m is greater than negative 1 and 7 over 15
m<−1715
m is less than negative 1 and 7 over 15
m<−11315
help
The solution to the value of m in the inequality m + 1/5 < - 1 2/3 is "m is less than negative 1 and 13 over 15".
The correct answer option is option D
How to solve inequality?Inequality is a statement that is of two quantities I'm which one is specifically less than (or greater than) another. The symbols of inequality are;
Greater than >Less than <Equal to =Greater than or equal toLess than or equal tom + 1/5 < - 1 2/3
substract 1/5 from both sides
m < -5/3 - 1/5
m < (-25-3) / 15
m < -28/15
Therefore, from the inequality m + 1/5 < - 1 2/3, m is less than negative 1 and 13 over 15.
Complete question:
m + 1/5 < -1 2/3
Responses
A. m > −1 13/15
m is greater than negative 1 and 13 over 15
B. m > −1 7/15
m is greater than negative 1 and 7 over 15
C. m < −1 7/15
m is less than negative 1 and 7 over 15
D. m < −1 13/15
m is less than negative 1 and 7 over 15
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differenciate the Function 1/ X3
Step-by-step explanation:
To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:
Write the function: f(x) = 1/x^3.
Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).
Differentiate the function: In our case, n = -3, so the derivative is:
f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.
Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.
Rami runs 3/4 mile on Monday, 7/8 mile on Tuesday, and 5/6 mile on Wednesday. How many miles did Rami run in all?
Answer:
2.45833333 miles (keystrokes)
The radioactive substance cesium-137 has a half-life of 30 years. The amount A (r) (in grams) of a sample of cesium-137 remaining after t years is
given by the following exponential function.
A (t)-266 6 (1) 10
Find the initial amount in the sample and the amount remaining after 50 years.
Round your answers to the nearest gram as necessary.
Initial amount:
Amount after 50 years:
The amount remaining after 50 years is approximately 45.5% of the Initial amount, A₀.
The given exponential function represents the amount A(t) (in grams) of cesium-137 remaining after t years:
A(t) = A₀ * (1/2)^(t/30)
We are asked to find the initial amount A₀ and the amount remaining after 50 years.
1. Initial amount:
The initial amount, A₀, is the amount of cesium-137 present at t = 0 years. To find A₀, we substitute t = 0 into the equation:
A(0) = A₀ * (1/2)^(0/30)
A(0) = A₀ * 1
Since anything raised to the power of zero is 1, we have A(0) = A₀ * 1, which simplifies to A(0) = A₀.
Therefore, the initial amount of the sample is A₀.
2. Amount after 50 years:
To find the amount remaining after 50 years, we substitute t = 50 into the equation:
A(50) = A₀ * (1/2)^(50/30)
Now we can calculate the amount using the given formula:
A(50) = A₀ * (1/2)^(5/3)
To round the answer to the nearest gram, we evaluate the expression and round the result to the nearest gram:
A(50) = A₀ * 0.455
A(50) ≈ A₀ * 0.455
Therefore, the amount remaining after 50 years is approximately 45.5% of the initial amount, A₀.
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4 lines extend from point B. A line extends straight up from B to point A. Another line extends up and to the right to point C. Another line extends slight up and to the right to point D. The other line extends slightly down and to the right to point E.
Given that ∠ABC ≅ ∠DBE, which statement must be true?
∠ABC ≅ ∠ABD
∠ABD ≅ ∠CBE
∠CBD ≅ ∠DBE
∠CBD ≅ ∠ABC
Answer:
The Correct Answer Is: ∠ABD ≅ ∠CBE
Step-by-step explanation:
I just took the test
∠ABD≅∠CBE is the true statement of congruent angles as per the given condition ∠ABC ≅∠DBE.
What are congruent angles?" Congruent angles are pair of such angles which are equal in their measurements."
According to the question,
Given,
∠ABC ≅∠DBE ________(1)
As shown in the diagram drawn as per the given conditions we have,
'D' is the interior point of angle ABC.
Therefore,
∠ABC = ∠ABD + ∠CBD ______(2)
'C' is the interior point of ∠DBE.
Therefore,
∠DBE = ∠CBD + ∠CBE ______(3)
Substitute (2) and (3) in (1) to represent congruent angles we get,
∠ABD + ∠CBD ≅ ∠CBD + ∠CBE
⇒∠ABD ≅ ∠CBE (∠CBD is common in both)
Hence, ∠ABD≅∠CBE is the true statement of congruent angles as per the given condition ∠ABC ≅∠DBE.
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Please solve this
∫ (log(1 + x ^ 2))/((x + 1) ^ 2) dx
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
We have,
To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.
Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:
∫ (log(1 + (u-1)²) / u²) du.
Expanding the numerator, we have:
∫ (log(1 + u² - 2u + 1) / u²) du
= ∫ (log(u² - 2u + 2) / u²) du.
Now, let's split the logarithm using the properties of logarithms:
∫ (log(u² - 2u + 2) - log(u²)) / u² du
= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.
We can simplify the second integral:
∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.
Using the power rule for integration, we can integrate both terms:
∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.
Now, let's focus on the second integral:
∫ (log(u) / u³) du.
This integral does not have a simple closed-form solution in terms of elementary functions.
It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).
Therefore,
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
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Find the geometric mean and arithmetic mean between 3 and 15.
Answer:
Geometric mean = 6.71
Arithmetic mean = 9
Step-by-step explanation:
\(geometric \: mean \\ = \sqrt{3 \times 15} \\ = \sqrt{45} \\ = 6.70820393 \\ = 6.71 \\ \\ arithmetic \: mean \\ \\ = \frac{3 + 15}{2} \\ \\ = \frac{18}{2} \\ \\ = 9\)
Brianna estimated that she would spend $60 shopping for school supplies before the start of the school year. She actually spent $55. What is the percent error for her estimate?
She spent $60 on school supplies before the start of the school year, thus the mistake percentage is 16.66666.
what is percentage ?A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it. There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage.
given
Percent Error = (Vobserved - Vtrue )/ Vtrue
= 55 - 66 / 66
= -11 / 66
= -16.666666666667%
= 16.666666666667% error
She spent $60 on school supplies before the start of the school year, thus the mistake percentage is 16.66666.
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please help me identify these!!!
tina is training for a biathlon. To train for the bicycle portion, she rides her bike 15 miles uphill and 15 miles back down. the complete trip takes her 2 hours. If her downhill speed is 20 miles per hour fadter than her uphill speed how fast does dhe ride uphill?
Answer:
Step-by-step explanation:
Tina is training for a biathlon. To train for the running portion of the race, she runs 7 miles each day over the same course. The first 4 miles of the course is on level ground, while the last 3 miles is downhill. She runs 3 miles per hour slower on level.
What is equivalent to a/b=c/d?
Answer:
wdre
Step-by-step explanation:
PLEASE HELP ASAP is this relationship linear, exponential, or neither?
Answer:
neither
gfhhhufkufjkg
A game card handed out at a grocery store states the probabilities of winning a prize: 0.2 for $10, 0.1 for $5, and 0.7 for $0. What is the probability of winning any amount of money?
Answer:
Step-by-step explanation:
To calculate the probability of winning any amount of money, we need to sum up the probabilities of winning each individual prize.
Given the probabilities stated on the game card:
Probability of winning $10 prize = 0.2
Probability of winning $5 prize = 0.1
Probability of winning $0 prize = 0.7
To find the probability of winning any amount of money, we add these probabilities together:
0.2 + 0.1 + 0.7 = 1
The sum of the probabilities is 1, which indicates that the total probability of winning any amount of money is 1 or 100%.
Therefore, the probability of winning any amount of money in this game is 100%.
Hope this answer your question
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PLEASE HELP ME IM LOSIN ALOT OF POINTS
Sixty-nine percent of U.S heads of household play video or computer games. Choose 4 heads of household at random. Find the probability that none play video or computer games.
Answer: 0.00923521
Step-by-step explanation:
Given : The probability U.S households play video or computer games=69%=0.69
here, the probability of each U.S household play video or computer games is fixed as 0.69
Then, the probability of each U.S household not play video or computer games= 1-0.69=0.31
For independent events the probability of their intersection is product of probability of each event.
Now, the probability that none play video/computer games will be :-
\((0.31)^4=0.00923521\)
find specified geometric series of the following geometric sequences of 3, 12, 48,... S7 with solution?
Answer:
Step-by-step explanation:
The formula for fundung the nth term of t geometeric series is expressed as;
Tn = ar^(n-1)
a is the first term
n is the number of term
r is the common ratio
Given
a = 3
r = 21/3 = 48/12 = 4
Substitute
Tn = 3(4)^(n-1)
Tn = 3(4^n/4)
Tn = 3/4(4^n)
Tn = 0.75(4^n)
Hence the nth term of the geometric series is Tn = 0.75(4^n)
To get any term, simply substitute the value of into the equation
Findr given y = 180(1305)
First, divide through by 180.
\(\frac{y}{180}\text{ = }\frac{180(1.305)^x}{180}\)\(\begin{gathered} 1.305^{x\text{ }}\text{ = }\frac{y}{180} \\ \text{Next, take the logarithm of both sides} \\ Log^{1.305^x}=Log^{\frac{y}{180}}\text{ } \\ \text{xLog}^{1.305}=Log^{\frac{y}{180}} \\ r\text{ = }\frac{Log^{\frac{y}{180}}}{Log^{1.305}^{}} \\ r\text{ = }\frac{Log^{\frac{y}{180}}}{0.11} \\ r=8.65Log^{\frac{y}{180}} \end{gathered}\)Ali went backpacking over the 3-day Labor Day weekend. On Saturday she hiked
one-fourth of the distance. On Sunday she hiked one-half of the remaining distance. On
Monday she hiked the remaining 12 miles. How long did Ali hike during the entire backpacking
trip?
On average, 24% of customers who buy shoes in a particular store buy two or more pairs. One weekend, 350 customers purchased shoes. How many can be predicted to buy two or more pairs? If 107 customers buy more than two pairs, did more customers than normal buy two or more pairs?
It is predicted that__________
customers bought two or more pairs out of 350 customers. There were customers than normal who bought two or ___ pairs.
3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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When we carry out a chi-square goodness-of-fit test for a normal distribution, the null hypothesis states that the population:________
a. Does not have a normal distribution
b. Has a normal distribution
c. Has a chi-square distribution
d. Does not have a chi-square distribution
e. Has k-3 degrees of freedom
Answer:
Option B
Step-by-step explanation:
The null hypothesis for a chi-square goodness of fit test states that the data are consistent with a specified distribution.
While the alternative hypothesis states that the data are not consistent with a specified distribution.
In this case study, the test is for a nose distribution. Thus the null hypothesis would be that the population has a normal distribution.
Minimise : 3x+2y
Subject to: 5x+y=10
X+y=6
X+4y= 12
Find this question?
This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:
5x + y = 10
x + y = 6
x + 4y = 12
The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.
To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.
For example, using the first and second equations, you can solve for x in terms of y as follows:
x = 6 - y (from the second equation)
y = 10 - 5x (from the first equation)
Substituting y = 10 - 5x into the third equation, you get:
x + 4(10 - 5x) = 12
Simplifying this equation, you get:
-19x + 40 = 0
Solving for x, you get:
x = 40/19
Using x = 40/19 and the equation x + y = 6, you can solve for y as:
y = 6 - x = 6 - 40/19 = 94/19
Therefore, the minimum value of 3x + 2y subject to the given constraints is:
3(40/19) + 2(94/19) = 222/19
And the values of x and y that minimize this expression are:
x = 40/19 and y = 94/19.
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This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:
5x + y = 10
x + y = 6
x + 4y = 12
The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.
To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.
For example, using the first and second equations, you can solve for x in terms of y as follows:
x = 6 - y (from the second equation)
y = 10 - 5x (from the first equation)
Substituting y = 10 - 5x into the third equation, you get:
x + 4(10 - 5x) = 12
Simplifying this equation, you get:
-19x + 40 = 0
Solving for x, you get:
x = 40/19
Using x = 40/19 and the equation x + y = 6, you can solve for y as:
y = 6 - x = 6 - 40/19 = 94/19
Therefore, the minimum value of 3x + 2y subject to the given constraints is:
3(40/19) + 2(94/19) = 222/19
And the values of x and y that minimize this expression are:
x = 40/19 and y = 94/19.
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Using log evaluate 3^x=10
Answer:
x ≈ 2.09590327429
Step-by-step explanation:
You want the solution to 3^x = 10 using logarithms.
LogsTaking logarithms of both sides of the given equation, we have ...
x·log(3) = log(10)
Dividing by the coefficient of x gives ...
x = log(10)/log(3)
x ≈ 2.09590327429
__
Additional comment
If the logarithm to the base 10 is used, then this becomes ...
x = 1/log₁₀(3)
The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.
For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.
<95141404393>
The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).
Taking the log of both sides, we get:
log(3^x) = log(10)
Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:
x * log(3) = log(10)
Next, we can divide both sides of the equation by log(3) to isolate the variable x:
x = log(10) / log(3)
Using a calculator, we can evaluate the right side of the equation:
x ≈ 1.46497
Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
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Find the angle measure show work too or I won’t get credit
9514 1404 393
Answer:
96°
Step-by-step explanation:
The relevant relations are ...
the sum of arcs of a circle is 360°the measure of an inscribed angle is half the measure of the arc it intercepts__
The measure of arc HPQ is ...
arc HPQ = 360° -108° -60° = 192°
Then the measure of inscribed angle QRH is ...
∠QRH = (arc QPH)/2 = 192°/2
∠QRH = 96°
Help its due today and I'm stuck on this question
Convert 75 gram per cm 3 to pounds per cubic inch (round to nearest tenth) [ 1 pound = 0.4536 kg] [ 1 cm = 0.3937 in] [ 1 kg = 1000g] (Show your work)
2.07 pounds/in 3
1.7 pounds/in 3
2.7 pounds/in 3
3.2 pounds/in 3
Answer:
It’s 2.07 pounds/in 3
Step-by-step explanation:
1 kilogram = 2.2 × pounds, so,2.07 × 1 kilogram = 2.07 × 2.2 pounds (rounded), or2.07 kilograms = 4.554 pounds.Step 2: Convert the decimal part in pounds to ouncesAn answer like "4.554 pounds" might not mean much to you because you may want to express the decimal part, which is in pounds, in ounces which is a smaller unit.So, take everything after the decimal point (0.55), then multiply that by 16 to turn it into ounces. This works because one pound equals 16 ounces. Thus,4.55 pounds = 4 + 0.55 pounds = 4 pounds + 0.55 × 16 ounces = 4 pounds + 8.8 ounces. So, 4.55 pounds = 4 pounds and 8 ounces (when rounded). Obviously, this is equivalent to 2.07 kilograms. Step 3: Convert from decimal ounces to a usable fraction of ounceThe previous step gave you the answer in decimal ounces (8.8), but how to express it as a fraction? See below a procedure, which can also be made using a calculator, to convert the decimal ounces to the nearest usable fraction: a) Subtract 8, the number of whole ounces, from 8.8:8.8 - 8 = 0.8. This is the fractional part of the value in ounces.b) Multiply 0.8 times 16 (it could be 2, 4, 8, 16, 32, 64, ... depending on the exactness you want) to get the number of 16th's ounces:0.8 × 16 = 12.8.c) Take the integer part int(12.8) = 13. This is the number of 16th's of a pound and also the numerator of the fraction.Finalmente, 2.07 quilogramas = 4 pounds 8 3/4 ounces.A fração 12/16 não está simplificada, e ainda pode ser reduzida para 3/4 para que possamos expressar como a fração mais simples possível.In short:2.07 kg = 4 pounds 8 3/4 ounces
Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through (-7,9) and parallel to the line whose equation is 7x - 4y - 9 = 0
The equation of the line in point-slone form is
Answer:
(y - 9) = 7/4(x + 7)
Step-by-step explanation:
If two lines are parallel to each other, they have the same slope slopes.
The first line is 7x - 4y - 9 = 0.
First let's convert this to y = mx + b form.
7x - 4y - 9 = 0Add 4y to both sides.
7x - 9 = 4yDivide each term by 4.
y = 7/4x - 9/4The slope is 7/4. A line parallel to this one will also have a slope of 7/4.
The standard point-slope form is:
(y - y₁) = m(x - x₁)For the point-slope form, you need two things: a point and a slope.
point: (-7, 9)slope: 7/4.Plug in our given information.
(y - 9) = 7/4(x - (-7))Simplify.
(y - 9) = 7/4(x + 7)Learn with another example.
https://brainly.com/question/26681302
Hope this helps!
Let's consider the information given:
line passes through (-7,9)line is parallel to 7x - 4y - 9 = 0What do we want to solve: put the equation of the line in point-slope form
⇒ point-slope form ⇒ \(y-y_{0}=m(x-x_{0} )\)
\((x_{0} ,y_{0} )\) : any point on the linem: slope Find the slope of 7x - 4y = 9⇒ first put it into slope-intercept form \(y = mx +b\)
-where m is the slope and b is the y-intercept
\(7x-4y-9=0\\7x-4y=9\\-4y=-7x+9\\y=\frac{7}{4}x-\frac{9}{4}\)
⇒ Slope is 7/4
2. When two lines are parallel, their two slopes are equal, and since
the line passes through (-7,9), use point-slope form
\(y-9=\frac{7}{4}(x+7)\) <== point-slope form
What do we also want: find the general form ⇒ Ax + By = C
A: coefficient of xB: coefficient of yC: constant To find the general form, move all the variables to one side and the constant to the other, using the point-slope form\(y-9=\frac{7}{4}(x+7)\\ y-9=\frac{7}{4}x+\frac{49}{4} \\-\frac{7}{4}x+y=9+\frac{49}{4} =\frac{36}{4} +\frac{49}{4} =\frac{85}{4} \\-\frac{7}{4}x+y=\frac{85}{4}\)<== general form
Hope that helps!
Calculate the amount you would pay (including tax) for an item normally priced $1199 that is currently 30% off, for which you have an additional 10% off coupon, in an area where sales tax is 7%. (the discounts can be stacked or figured sequentially, tax must be applied after the discounted price is determined)
Answer: The amount you would pay (including tax) for the item is:
$755.37 + $52.88 = $808.25
Step-by-step explanation: irst, we calculate the amount of discount that is applied to the original price:
30% of $1199 = 0.3 x 1199 = $359.70
So, the discounted price is:
$1199 - $359.70 = $839.30
Next, we apply the additional 10% off coupon to this discounted price:
10% of $839.30 = 0.1 x $839.30 = $83.93
The final price after the coupon is applied is:
$839.30 - $83.93 = $755.37
Finally, we calculate the sales tax on this final price:
7% of $755.37 = 0.07 x $755.37 = $52.88
The amount you would pay (including tax) for the item is:
$755.37 + $52.88 = $808.25