Answer:
During the 16th and early 17th Century, the equals, multiplication, division, radical (root), decimal and inequality symbols were gradually introduced and standardized. ... In the Renaissance Italy of the early 16th Century, Bologna University in particular was famed for its intense public mathematics
Prior to the invention of the Mathematical Symbols, mathematical equations were written in words.
For example, Y + 10 = 4.5 would be written as
The thing plus ten equal to eight.
It is true that MOST, that is, the majority of the mathematical symbols we have today were invented in the 16th century. Examples of such symbols are:
Multiplication Sign × (1618)Plus/Minus Sign ± (1628)Inequality Signs > and < (1631)Percentage Sign % (1650)Infinity Sign ∞ (1655)Division Sign ÷ (1659) to mention a few.Prior to the 16th century, some mathematical signs were already in use. They are:
Plus Sign + (1360)Minus Sign - (1489)Square Root Sign (1525)Equals Sign = (1557) to mention a few.See the link below for more about Mathematical Signs:
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solve the system using substitution 5x+3y=-4 y-2x=6
Solving steps:-
5x+3y=−4
y−2x=6
-->To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
5x+3y=−4,−2x+y=6
-->Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
5x+3y=−4
-->Subtract 3y from both sides of the equation.
5x=−3y−4
--> Divide both sides by 5.
x = 1/5(-3y - 4)
--> Multiply 1/5 −3y−4.
x = -3/5y - 4/5
--> Substitute -3y - 4/ 5 for x n the other equation, −2x+y=6.
-2 (-3/5y - 4/5) + y = 6
--> Multiply −2 times -3y - 4/ 5
6/5y + 8/5 + y = 6
--> Add 6y/5 to y
11/5y + 8/5 = 6
--> Subtract 8/5 from both sides of the equation.
11/5y = 22/5
--> Divide both sides of the equation by 11/5, which is the same as multiplying both sides by the reciprocal of the fraction.
y = 2
--> Substitute 2 for y in x= -3/5y - 4/5. Because the resulting equation contains only one variable, you can solve for x directly.
x = -3/5 x 2 - 4/5
--> Multiply -3/5 times 2.
x = -6 - 4/ 5
--> Add -4/5 to -6/5 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
x = -2
--> The equation is now solved.
Answer : x = -2, y = 2
Explanation : If you think this answer is good, please give "Brainliest" or rate/heart my answer. Hope this helps you.
-2(4x-6)=6-6x help me
Answer:
x=3
Step-by-step explanation:
you have to move the terms collect like terms and divide both sides and down load photo math that helps alot with giving answersSelect all that apply.
Zack is taking a test in which he answers questions at a rate of question per minute. If Q represents questions and
M represents minutes, which of the following equations describe this rate relationship?
M= 20 x Q
Q = 2 x M
M=1/2 x Q
Q=1/2 x M
The equation Q = 2 x M represents the relationship between question and time.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
Zack takes a test, in which he answers at rate of 2 question per minute.
Also, Q represents questions
And M represents minutes.
According to given condition,
In 1 minute, Zack answers 2 question,
In M minutes, Zack answers 2 x M question,
Total questions presented by Q,
Q = 2 x M.
The required relationship for M and Q is Q = 2 x M.
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2+2 (I have been having a lot of trouble on this
Answer:
it's 4
Step-by-step explanation:
I hope it helps .....
Answer:
4
Step-by-step explanation:
2+2=4
I'll give a real world problem to help you understand. So pretend that you have 2 cookies on your plate and your sibling has 2 cookies on their plate too. If your siblings gives you their 2 cookies and you add them to your plate, how many cookies are on your plate now? There should now be 4 of them!
Does this help?
Evaluate the given expression for x = 4.
x? + 5x - 8
Answer:
16
Step-by-step explanation:
[tex]x = 4 \\ 4 + 5(4) - 8 = 16[/tex]
There is 60% chance that it will rain today. If it rains, the probability of watching a movie is 0.5. But, if it does not rain then the probability of watching a movie is 0.3. What is the probability of watching a movie today?
Applying the given probabilities, it is found that there is a 0.42 = 42% probability of watching a movie today.
These following probabilities involve a movie being watched today:
0.5 of 0.6(if it rains today).0.3 of 1 - 0.6 = 0.4(if it does not rain today).Hence, adding them:
[tex]p = 0.5(0.6) + 0.3(0.4) = 0.3 + 0.12 = 0.42[/tex]
0.42 = 42% probability of watching a movie today.
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Mike Jones bought a new split-level home for $150,000 with 20% down. He decided to use Victory Bank for his mortgage. They were offering for 25-year mortgages. Provide Mike with an amortization schedule for two periods. (Use Table 15.1(b)). (Do not round intermediate calculations. Round your answers to the nearest cent.) Payment number Portion to— Balance of loan Interest Principal outstanding 1 2
Enter the number that belongs in the green box
Answer:
128 degrees
Step-by-step explanation:
Opposite interior angles
Mary works at a local Burger King restaurant. Her regular hourly wage is $14.70. If she works overtime, she
receives an hourly rate of 14 times her regular hourly rate. If she regularly works 40 hours per week with no
overtime, what is her regular weekly pay?
$882
$2.94
$588
$294
Answer:
I’m pretty sure it’s 588
Step-by-step explanation:
14.70 * 40 = 588
I need help with pre calculus.
Question 1
Answer: Choice A) -7-----------------
Explanation:
To compute f(g(2)), we'll first need to find g(2).
Locate 2 in the x row. Then read straight down until you get to the g(x) row. You should find that g(2) = 4
This means f(g(2)) becomes f(4). We then repeat the same process as before. Locate 4 in the x row, read straight down til you get to the f(x) row to find that f(4) = -9
Overall, we can say f(g(2)) = -9
We do the same set of steps to compute g(f(-1)). You should find that f(-1) = -1 and g(f(-1)) = g(-1) = -2
Lastly, we subtract the results we got:
f(g(2)) - g(f(-1)) = -9 - (-2) = -9+2 = -7
==============================================
Question 2
Answer: Choice B) 0-----------------
Explanation:
If you were to graph each equation, you should get what you see below.
The red and blue curves do not intersect in any way. We need an intersection point to have a solution. Because there are no intersections, we don't have any solutions. The system is considered inconsistent.
==============================================
Question 3
Answer: Choice B[tex]-2x^2+250x-2000[/tex]-----------------
Explanation:
x = number of scooters made and sold
Each scooter costs $150 to make. If you made x of them, then it costs 150x dollars. Then tack on the fixed cost of $2000 to get the expression [tex]150x+2000[/tex]
The cost function is [tex]C(x) = 150x+2000[/tex]. We'll subtract this from the revenue function R(x) to get the profit P(x)
[tex]\text{Profit} = \text{Revenue} - \text{Cost}\\\\P(x) = R(x) - C(x)\\\\P(x) = (400x-2x^2) - (150x+2000)\\\\P(x) = 400x-2x^2-150x-2000\\\\P(x) = -2x^2+250x-2000\\\\[/tex]
==============================================
Question 4
Answer: Choice B[tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]
-----------------
Explanation:
[tex]g(x) = \frac{1}{x+1}\\\\g(f(x)) = \frac{1}{f(x)+1}\\\\g(f(x)) = \frac{1}{x^2+x-3+1}\\\\g(f(x)) = \frac{1}{x^2+x-2}\\\\g(f(x)) = \frac{1}{(x+2)(x-1)}\\\\(g\circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\[/tex]
I started with the outer function g(x) and replaced each x with f(x) in the second step. Then I plugged in f(x) = x^2+x-3 and simplified. Factoring the denominator is helpful to determine where the denominator becomes zero. Specifically, it happens when x = -2 and x = 1. These x values must be kicked out of the domain to avoid a division by zero error.
So we start off with the real number line, and poke holes at x = -2 and x = 1.
The notation [tex]x \in \mathbb{R}[/tex] means x is a real number. Then we tack on [tex]x \ne -2, x \ne 1[/tex]
Overall, the domain is [tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]
Let's see what happens if we tried plugging x = -1 into this composite function:
[tex](g \circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\(g \circ f)(-1) = \frac{1}{(-1+2)(-1-1)}\\\\(g \circ f)(-1) = \frac{1}{(1)(-2)}\\\\(g \circ f)(-1) = \frac{1}{-2}\\\\(g \circ f)(-1) = -0.5\\\\[/tex]
We don't get a division by zero error, so x = -1 is allowed. The same can be said about any other x value as long as it's not -2 and not 1 either.
What is the value -3/5 + (-0.75) +4 7/10
Enter your answer in the box.
Answer:
67/20 as an improper fraction, 3 7/20 as a mixed number and, 3.35 as a decimal
Hope this helped :)
Step-by-step explanation:
How do you use observed data to predict unobserved
Prime number after
167, 118, 82, 57, 41, ?
Prime numbers after 167, 118, 82, 57, 41, are:
37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2
Prime numbers are numbers that only have two factors, 1, and themselves.
Apart from these factors, no number can divide them without a remainder.
By observation, the numbers 167, 118, 83, 57, 41, are written in descending order.
This means that the prime number to be chosen will be lesser than 41
Prime numbers lesser than 41 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
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The sum of two numbers is 30. Their difference is 12. Use substitution to solve a system of equations to solve for the two numbers.
Answer:
9 and 21
Step-by-step explanation:
setting up the equation
let x and y represent the two numbers
this means that x + y = 30
x - y = 12
using substitution to solve
if x - y = 12, that can be rearranged to x = y + 12.
substitute x = y + 12 into x + y = 30
you get (y + 12) + y = 30
simplify
2y + 12 = 30
2y = 18
y = 9
plug this into the original equation x + y = 30. this would be
x + 9 = 30
x = 21
the numbers are 21 and 9.
I need help with this please
Answer:
I’m not sure what that means but I think it’s the one with the blue
Step-by-step explanation:
Which ordered pair is in the solution set of 3x − 2y ≥ -1?
F.(-2, -2.5)
G.(-1, 1)
H.(2, 4)
J.(1, 2.5)
Answer:
G
Step-by-step explanation:
Therefore, the option [tex]G(-1,1)[/tex] is correct.
What is the inequality?
An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Here given inequality equation
[tex]3x- 2y \geq -1[/tex]
When the points [tex](-1,1)[/tex] so it would be
[tex]3(-1)-2(1)\geq -1\\\\-3-2\geq -1\\\\-5\geq -1[/tex]
Hence, the option [tex]G(-1,1)[/tex] is correct.
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A principle at a certain high school claims that the students in her school are above average in SAT. She collects a random sample of 50 students and given an SAT test that provided with a mean score of 541. Is there sufficient evidence statistically to support the principal’s claim? The mean population SAT score is 500 with a standard deviation of 100. SAT scores are normally distributed. Please show all the steps involved in a hypothesis testing including proper statistical symbols, formula used, and report/interpret results in complete sentences.
Using the z-distribution, it is found that since the value of the test statistic is greater than the critical value for the right-tailed test, there is sufficient evidence to support the principal’s claim.
At the null hypothesis, it is tested if they are not above average, that is, their mean is of 500 or below, hence:
[tex]H_0: \mu \leq 500[/tex]
At the alternative hypothesis, it is tested if they are above average, that is, their mean is of more than 500, hence:
[tex]H_1: \mu > 500[/tex]
We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 541, \mu = 500, \sigma = 100, n = 50[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{541 - 500}{\frac{100}{\sqrt{50}}}[/tex]
[tex]z = 2.9[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with the standard 0.05 significance level, is of [tex]z^{\ast} = 1.645[/tex].
Since the value of the test statistic is greater than the critical value for the right-tailed test, there is sufficient evidence to support the principal’s claim.
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What is the value of X
The answer would be 6 I belive make sure to double check it
(Brainliest question) Which type of study best describes the following research most likely to be done? A researcher is trying to determine the effects of animal habitats and animal populations after forest fires. So she visits places that have had a naturally occurring Forest fire to study the area.
Experimental study
Observational study
Simulation study
Double blind study
Answer:
Observational study
Step-by-step explanation:
See the researcher visits the forest.She want to experience or observe the forest fire.She want to observe how it affects the animals.Hence it's observational studyWhat is the constant of proportionality in xy-11=5?
Answer:
xy-11=5
ANSWER:
=16
Step-by-step explanation:
hope it helps to you
mark me as a brainlest please
Write a number using the following clues:
a multiple of 6
greater than 40, but less than 90
Answer:
48
Step-by-step explanation:
There are various multiples of 6 that are greater than 40, but less than 90. Including 42, 48, 54, 60, 66, 72, 78, and 84. :)
Estimate the product of 54 X 68.
Answer:
54 X 68=3672
Step-by-step explanation:
Find the perimeter and area of this polygon.
Answer:
perimeter=114
AREA= 308
Step-by-step explanation:
A^2 + B^2=C^2
then A+B=+C= P for triangle
52= triangle perimeter
rectangle:
(l+w)*2=p for rectangle=62
then add 52+62= 114
AREA- Triangle
b*h/2
22*10=220
220/2
= 110
AREA- Rectangle
l*w=A
22*9=198
ADD BOTH AREAS
198+110=308
HOPE IT HELPS
Which expression is equivalent to w • 35?
Answer:W= B-3 or 3=B-W
Step-by-step explanation:
What is the equation for the line in slope-intercept form?
Enter your answer in the box.
Answer:1+1
Step-by-step explanation:
1+1=2
Francis owns a cake shop. She is currently preparing cupcakes (x) and cookies (y) for two birthday
parties. The first birthday party ordered 20 cupcakes and 40 cookies and their total cost was $61. The second birthday party ordered 30 cupcakes and 30 cookies. Their total cost was $64.50.
Answer:
Step-by-step explanation:
20x + 40y = 61 this is the equation for the first party
30x + 30y = 64.50 this is the equation for the second party.
Maxden wanted to measure the length of the objects below.
For each one circle which unit of measurement he should use.
A. His puppy
Inches or Yards
B. A toy car
Yards or Centimeters
C. Width of his desk
Yards or Feet
D. His foot
Inches or Yards
ANSWER FOR BRAINIEST!!!
How do you answer this and what did I do incorrectly?
Answer:
x=5[tex]\frac{16}{3}[/tex]/(4-[tex]\frac{16}{3}[/tex])
Step-by-step explanation:
Hi, these are not my strong point, Sorry if its incorrect.
6-[tex]\frac{2}{3}[/tex](x+5)=4x
I first did 6-[tex]\frac{2}{3}[/tex]
6/1 -2/3, 18/3-2/3 =16/3
[tex]\frac{16}{3}[/tex](x+5)=4x
I then expanded the bracket to get [tex]\frac{16}{3}[/tex]x+5[tex]\frac{16}{3}[/tex]
[tex]\frac{16}{3}[/tex]x+5[tex]\frac{16}{3}[/tex]=4x
Then I took away [tex]\frac{16}{3}[/tex]x from both sides to get.
5[tex]\frac{16}{3}[/tex]=4x-[tex]\frac{16}{3}[/tex]x
I then factorised x out
5[tex]\frac{16}{3}[/tex]=x(4-[tex]\frac{16}{3}[/tex])
I then divided by the bracket to get:
x=5[tex]\frac{16}{3}[/tex]/(4-[tex]\frac{16}{3}[/tex])
Answer:
4/7
Step-by-step explanation:
[tex]6 - \frac{2}{3} (x + 5) = 4x[/tex]
U take -2/3 into the brackets
[tex]6 - \frac{2}{3} x - \frac{10}{3} = 4x[/tex]
Put all values with x on one side
[tex]6 - \frac{10}{3} = 4x + \frac{2}{3} x[/tex]
Ensure that they all have the same denominator so that u can add and subtract
[tex] \frac{18}{3} - \frac{10}{3} = \frac{12}{3} x + \frac{2}{3} x[/tex]
[tex] \frac{8}{3} = \frac{14}{3} x[/tex]
Drop the denominator since they both have the same denominator
[tex]8 = 14x[/tex]
divide both sides by 14
[tex] \frac{8}{14} = \frac{14}{14} x[/tex]
[tex]x = \frac{4}{7} [/tex]
Write the ratio 4 1/5 to 5 2/5 as a simplified fraction
Answer:
[tex]\huge\boxed{4\dfrac{1}{2}:5\dfrac{2}{5}=5:6}[/tex]
Step-by-step explanation:
[tex]4\dfrac{1}{2}:5\dfrac{2}{5}[/tex]
we convert a mixed number to an improper fraction
[tex]4\dfrac{1}{2}=\dfrac{4\cdot2+1}{2}=\dfrac{9}{2}\\\\5\dfrac{2}{5}=\dfrac{5\cdot5+2}{5}=\dfrac{27}{5}[/tex]
Therefore
[tex]4\dfrac{1}{2}:5\dfrac{2}{5}=\dfrac{9}{2}:\dfrac{27}{5}=\dfrac{9\!\!\!\!\diagup^1}{2}\cdot\dfrac{5}{27\!\!\!\!\!\diagup_3}=\dfrac{1}{2}\cdot\dfrac{5}{3}=\dfrac{1\cdot5}{2\cdot3}=\dfrac{5}{6}=5:6[/tex]
The ratio 4 1/5 to 5 2/5 is equivalent to the simplified fraction 7/9.
How to write the simplified factionTo write the ratio 4 1/5 to 5 2/5 as a simplified fraction, we need to convert both mixed numbers to improper fractions and then find their ratio.
Step 1: Convert the mixed numbers to improper fractions:
4 1/5 = (4 * 5 + 1) / 5 = 21 / 5
5 2/5 = (5 * 5 + 2) / 5 = 27 / 5
Step 2: Find the ratio by dividing the first fraction by the second fraction:
Ratio = (21 / 5) / (27 / 5)
Step 3: To divide by a fraction, multiply by its reciprocal:
Ratio = (21 / 5) * (5 / 27)
Step 4: Simplify the fraction:
Ratio = (21 * 5) / (5 * 27)
Ratio = 105 / 135
Step 5: Simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 15:
Ratio = (105 / 15) / (135 / 15)
Ratio = 7 / 9
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The weights of a certain brand of candies are normally distributed with a mean weight of 0.8593 g and a standard deviation of 0.0511 g. A sample of these candies came from a package containing 464 candies, and the package label stated that the net weight is 396.1 g. (If every package has 464 candies, the mean weight of the candies must exceed 396.1 464=0.8537 g for the net contents to weigh at least 396.1 g.)
Answer:
The package label stated that the net weight is 381.8g If every package has ... brand of candies have a mean weight of 0.8616g and a standard deviation of ...
