The quadratic formula x = [-b (b2 - 4ac)] / 2a] provides the solutions to the quadratic equation ax2 + bx + c = 0. (2a).
Given,
Equation with two answers are quadratic equations.
Quadratic equation;
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).
The solution for quadratic equation;
The quadratic formula x = [-b (b2 - 4ac)] / 2a]gives the solutions to the quadratic equation ax2 + bx + c = 0. (2a). Get the problem into standard form, ax2 + bx + c = 0, and then use the quadratic formula to solve the quadratic equation.
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(c) To reduce the percentage of defective chips, the company contracts with a new supplier for some
important components. In the next month, the sample of 200 chips has only 8 defective ones. Can the
company conclude that the new components have reduced the rate of defective chips produced?
Explain.
Mean: 12
Standard Deviation: 3.3586
This is binomial distribution.
There is enough evidence to conclude that the new components have reduced the rate of defective chips produced.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the amount has decreased, that it still is of 12, hence:
[tex]H_0: \mu = 12[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the amount has decreased, that is, it is less than 12, hence:
[tex]H_1: \mu < 12[/tex]
We have a left-tailed test, with a significance level of 0.05, hence the test statistic needed for there to be enough evidence is less than -1.645, which is the critical value.
What is the test statistic?The equation that determines the test statistic is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[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 population.n is the sample size.The parameters in this problem are of:
[tex]\overline{x} = 8, \mu = 12, \sigma = 3.3586, n = 12[/tex]
Hence the test statistic is of:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{8 - 12}{\frac{3.3586}{\sqrt{12}}}[/tex]
z = -4.13.
Less than the critical value, hence there is enough evidence that the amount has decreased.
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Ashley buys 6 bottles of orange juice at the corner store for a total cost of $2.40. If each bottle costs the same amount, how much is each bottle of juice?
mr. smith has two children. at least one of them is a boy. what is the probability that both children are boys?
The probability that both children are boys is 1/2.
What is probability?
The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty).
Given in the question,
Mr. Smith has two children, one of them is boy.
So, the possible combinations are,
(Boy, Boy) and (Boy, Girl)
It means number of total outcomes is 2,
we have to find probability of (Boy, Boy)
It means number of favorable outcomes is 1,
The formula for the calculation of probability is:
Probability = number of favorable outcomes/ number of total outcomes,
So,
Probability = 1/2
Therefore, The probability that both children are boys is 1/2.
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What’s the value of x?
Answer:
a value that is not yet known
Find the demand function for the marginal revenue function. recall that if no items are sold, the revenue is 0.
R′(x)=0.06x2−0.05x+138
The required demand function for the marginal revenue function is P = 0.02x² - 0.025x.
What is demand function for the marginal revenue function?Marginal Revenue is the revenue that is gained from the sale of an additional unit. It is the revenue that a company can generate for each additional unit sold; there is a marginal cost attached to it, which must be accounted for.
According to question:The marginal revenue function, find the demand capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .
Considering that,
We need to find for the peripheral income capability, find the interest capability.
Recollect that the pay is zero assuming no things are sold:
R'(x) = 0.06x² - 0.05x + 138
p(x) is what.
That's what we know,
MR = dTR/dx = 0.06x² - 0.05x + 138
Incorporating the marginal revenue function , we get complete income capability,
MR = TR
= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 138x
= (0.06x³)/3 - (0.05x²)/2 + 138 x
TR = 0.02 x³ - 0.025 x² + 138 x
TR = (P)(Q) = (P)(x) = 0.02 x³ - 0.025 x² + 138 x
P = ( 0.02 x³ - 0.025 x² + 138 x)/x
P = 0.02x² - 0.025x + 138
In this manner, The marginal revenue function, find the interest capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .
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type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. while making oatmeal cookies, angela needs to add 12 cup of milk to her dough. however, she has only a 14-cup measuring cup. how many times does she need to fill the measuring cup to pour 12 cup of milk? the number of times angela needs to fill the 14-cup measuring cup to pour 12 cup of milk is
Therefore , Angela needs to fill this cup 6/7 times.
What is fraction ?A fraction represents a component of a whole or, more generally, any number of equal parts. As in one-half, eight-fifths, and three-quarters, a fraction in conversational English denotes the number of components of a specific size.
Here,
To her dough, Angela needs to add 12 cups of milk. She only has a measuring cup that holds 14 cups.
Thus, the number of times angela needs to fill cup are = 12/14 times
thus ,
=> 12/14 =6/7
Therefore , Angela needs to fill this cup 6/7 times.
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Which statement is TRUE for f(x)= x³+4x²+x-6?
( x - 1 ) is the factor of f(x) as remainder is 0
What is Polynomial ?A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
According to the given information
The given polynomial is
f(x) = [tex]x^{3} + 4x^{2} +x -6[/tex]
According to the remainder theorem
( x - 1 ) will be the factor of f(x) , if f(1) is zero
So
= [tex]1^{3} + 4(1)^{2} + 1 -6[/tex]
= 1+4+1-6
= 6-6
= 0
So
( x - 1 ) is the factor of f(x) as remainder is 0
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I need help understanding number 3, please help!
Answer:
Step-by-step explanation:
It's asking you to find the measures for all the angles.
For example, angle 1 would be 59° because it is equal to the angle across from it.
Angle 2 would equal 31° because it's a supplement angle to 59° and so on
Maya uses 14 blue tiles and 10 white tiles to design section of an outdoor patio. Which ratio compares the number of blue tiles to the total number of tiles in the section
Answer:9 : 20
Step-by-step explanation:
a family of four went out to dinner. the cost of their meal was $75.99. Tax on the meal is 6.75% and they left a 19% tip on the cost of the meal. what is the total amount they will pay
The total amount they will pay would be $95.557
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Given that the cost of their meal was $75.99. Tax on the meal is 6.75% and they left a 19% tip on the cost of the meal.
Cost of meal = $75.99
The tax amount = 6.75% of 75.99
= ( 6.75/100 ) x 75.99
= $5.129
Tip amount = 19% of 75.99
= (19/100) x 75.99
= $14.438
Thus, the Total amount they will pay
= $75.99 + $5.129 + $14.438 = $95.557
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Solve the system by substitution.
y = -2x + 16
y = 2x
Answer: y = 8 , x = 4
Step-by-step explanation:
gosh darn i haven done this since algebra 1 !!
since both equations equal y, we can make them equal to each other since y = y
-2x +16 = 2x (im just gonna simplify without all the extra steps sorry)
x = 4 (this is the first answer)
now we can plug in x to find y
y = 2(4)
y = 8 (second answer)
im sorry if the grammar is horrid its 3 am
rachel needs to identify the domain for the function {(-1,5) , (2, 3), (33, 6), (32, 7)}. what answer should she get?
The domain for the given function is {-1, 2, 33, 32}.
A function's or relation's domain is the set of all possible independent values that the relation can take. It is the sum of all possible inputs.
A function's or relation's range is the set of all possible dependent values that the relation can produce from the domain values. It is the sum of all possible outputs.
When dealing with sets of ordered pairs, we simply divide the pairs into x- and y-coordinates. The domain is formed by the x-coordinates, which are independent values. The y-coordinates are the dependent values, i.e. they define the range.The domain in the set of ordered pairs {(a,b); (c,d); (e,f); (g,h)} is the set of the first number in each pair (those are the x-coordinates): {a,c,e,g}. The range is the set of all the pairs with the second number (the y-coordinates): {b,d,f,h}.
Given,
The set of ordered pair = {(-1,5) , (2,3), (33,6), (32,7)}
then,
the Domain = {-1, 2, 33, 32}
Range = {5, 3, 6, 7}
Thus, the domain for the given function is {-1, 2, 33, 32}
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assume there are 5 red balls, 6 blue balls, and 4 green balls. if the balls are removed from the box one at a time, in how many different orders can the balls be removed assuming two balls of the same type are indistinguishable?
The number of ways that we can remove the balls one at a time from the box is 1307674368000
Given,
The number of balls in a box;
5 red balls
6 blue balls
4 green balls
We have to find the number of ways the balls can removed from the box one at a time;
Here,
Order is indistinguishable, so combination can be followed;
Combination formula;
ⁿCr = n! / r1(n - r)!
Here,
Total number of balls in the box = 5 + 4 + 6 = 15 balls
Then.
¹⁵C₁₅ = 15! / 15! (15 - 15)! = 15! = 1307674368000
That is,
We can remove the balls one at a time from the box in 1307674368000 ways.
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What is the slope of the line whose equation is 2y=3x +4
solve for y
y = 1.5x + 2
notice this is in form y = mx + b
m is slope, b is y intercept
m = 1.5
slope is 1.5
hope this helps :)
jeron
sarah used 2.5 cups of cheese in a dish that serves 10 people. what constant of proportionality relates the number of servings to cups of cheese?
The constant of proportionality that relates the number of servings to cups of cheese is 0.25.
According to the question,
Sarah used 2.5 cups of cheese in a dish that serves 10 people, this can be written as :
let the c be the cups of cheese : c = 2.5 cups of cheese
let n be the number of the people that is been served
Then the equation can be written as :
c ∝ n
then we can bring in the proportionality constant sign as ;
then c = kn
then we can introduce the given figures into the equation as ;
=> 2.5=k (10)
the we can determine the value of the constant as :
=> k=2.5/10 = 0.25
Hence, constant of proportionality relates the number of servings to cups of cheese is 0.25
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the coefficient of determination resulting from a particular regression analysis was 0.85. what was the correlation coefficient, assuming a positive linear relationship? group of answer choices -0.5 0.922 0.5 there is insufficient information to answer the question.
The coefficient of determination resulting from a particular regression analysis was 0.85. Then, the correlation coefficient, assuming a positive linear relationship is 0.922.
The coefficient of determination, denoted R2 or r2 and pronounced "R-squared," is the proportion of predictable variation in the dependent variable from the independent variables.
R2 has several definitions, sometimes the same. One class of such cases involves simple linear regression where r2 is used instead of R2. If only one bin is included, r2 is simply the square of the sample correlation coefficient (that is, r) between the observed outcome and the observed prediction. If additional regressors are included, R2 is the square of the multiple correlation coefficient. In both cases, the coefficient of determination is usually between 0 and 1.
Regression analysis consists of a dependent variable (often called the "outcome" or "response" variable, or "label" in machine learning parlance) and one or more independent variables (often called "predictors"). ). ', 'covariate', 'explanatory variable' or 'feature'). The most common form of regression analysis is linear regression, which finds the best fit line (or more complex linear combination) to the data according to mathematical criteria. For example, the ordinary least-squares method computes a unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). For certain mathematical reasons (see linear regression), researchers can estimate the conditional expected value (or population mean) of the dependent variable given that the independent variable takes on a particular set of values . Less common forms of regression use slightly different techniques to estimate alternative site parameters (such as quantile regression and requirement analysis, or conditional expectations on a broader collection of nonlinear models. estimating values (such as nonparametric regression). Regression analysis is primarily used for two conceptually distinct purposes.
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i need help asap please! 100 points
f(-2) = 254 , meaning if the company sells shirts -2 , they would make a profit of 254 dollars. This interpretation is true in the context of the problem.
f(12) = 266 , meaning if the company sells shirts 12 , they would make a profit of 266 dollars. This interpretation is true in the context of the problem.
f(17.5) = 270.25, meaning if the company sells shirts 17.5 , they would make a profit of 270.25 dollars. This interpretation is true in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is x ≥ - 2.
How to calculate Functions and values?Functions and values given the function that represents elevation, in feet, of Jayden hikes expressed as:
f(x)=(x+2)²+250.
If the domain value of the function is -4, then;
f(-4)=(-4+2)²+250
f(-4) = 4 + 250
f(-4) = 254
f(-4) = 254 means If Jayden hikes 4 miles to the south, his elevation would be 254 feet. This interpretation is true in the context of the problem
If the domain value of the function is -4, then;
f(2)=(2+2)²+250
f(2) = 16 + 250
f(2) = 266
f(2) = 266 means If Jayden hikes 2 miles to the north, his elevation would be 266 feet. This interpretation is true in the context of the problem
If the domain value of the function is 2.5, then;
f(2.5)=(2.5+2)²+250
f(2.5) = 20.25 + 250
f(2.5) = 270.25
f(2.5) = 270.25 means If Jayden hikes 2.5 miles to the north, his elevation would be 270.25 feet. This interpretation is true in the context of the problem
Determining the domain
The domain exist for the value of (x+2)² ≥ 0
x + 2 ≥ 0
x ≥ - 2
Based on the observation above, it is clear that an appropriate domain of the function is x ≥ - 2
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does this graph represent a function?why or why not x 2 2 3 4 5 y 1 4 4 2 5
The correct statement regarding whether the graph represents a function is given as follows:
B. No, because it fails the vertical line test.
When does a graph represent a function?A graph is a relation, and it represents a function if each value of the input is mapped to only one output, that is, if the graph does not contain vertically aligned points.
From the graph given by the image at the end of the answer, the inputs for x > 2 are mapped to multiple outputs, meaning that a vertical line at any of these points would cross the function twice, meaning that the graph has vertically aligned points.
Since the graph has vertically aligned points, it fails the vertical line test, and hence the graph does not represent a function, and option B is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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If 75% of a number is 24, what is 50% of the number? A. 64 B. 16 C. 12 D. 9
Answer:
16
Step-by-step explanation:
What is slope simple answer?
The slope is the measure of the steepness and direction of a line. You can predict whether lines in a coordinate plane are parallel, perpendicular, or none by finding the slope of the lines.
There are two distinct points on any line that can be used to calculate its slope. Between two distinct points on a line, the slope formula calculates the ratio of vertical and horizontal changes. In mathematics, the slope is calculated as the ratio of the rise to the run, or as the rise divided by the run. The slope is a measure of how steep a line is in a coordinate plane.
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What is a split sentence in grammar?
Answer:
A split infinitive is a common grammatical mistake that can be hard for writers to spot. Many people think they are not a big deal, but they can often have a major impact on your writing and make it hard for a reader to understand what you have to say.
Step-by-step explanation:
Take, for example, this sentence:
I like to on a hot day eat a lot of ice cream.
Did you have to read it twice to be clear what it was saying? I know I did. But let's make just a little adjustment:
On a hot day, I like to eat a lot of ice cream.
2.8+1.36 divided by 4-2.7
Answer:
0.44
Step-by-step explanation:
find the difference. (7x-6 2/3) - (-3x + 4 3/4)
10x-61/12 is the difference of (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex]).
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex])
7x-[tex]6\frac{2}{3}[/tex]+3x- [tex]4\frac{3}{4}[/tex]
7x-20/3+3x-19/4
Add the variable terms and constant terms.
10x-20/3-19/4
The LCM of 3 and 4 is 12/
10x-4-57/12
10x-61/12
Hence, 10x-61/12 is the difference of (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex]).
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What is the radius of a circle whose equation is x2 y2 â 10x 6y 18 0 2 units 4 units 8 units 16 units?
The radius of the circle having the equation x² + y² - 10x + 6y + 18 = 0 is 4 units , the correct option is (b) .
In the question ,
it is given that ,
the circle is having equation ⇒ x² + y² - 10x + 6y + 18 = 0 ,
we know that ,
general equation of circle is ⇒ x² + y² + 2fx + 2gy + c = 0 ;
So , radius of circle is calculated using the below formula ,
radius [tex]=[/tex] √(f² + g² - c)
On comparing, given equation of circle with general equation of circle ,
we get , the values of f = -5 and g = 3 .
So after substituting values of f , g and c in radius formula ,
we get ,
radius = √(25 + 9 - 18)
= √(34 - 18)
= √16 = 4 .
Therefore , the given circle has radius = 4 units .
The given question is incomplete , the complete question is
What is the radius of a circle whose equation is x² + y² - 10x + 6y + 18 = 0 ?
(a) 2 units
(b) 4 units
(c) 8 units
(d) 16 units
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a teach selects 77 students from her class of 2727 students. how many ways are there for her to select the students if the chosen students
888030 ways are there for teachers to select the students.
What is the combination?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Here, we have
A teacher selects 7 students from her class of 27 students.
We have to find how many ways are there for her to select the students of the chosen students.
The order of selecting the students does not matter here so the number of ways to select 7 students from the class of 27 to work together on a project is:
C(27,7) = 27!/(7!*(27-2)! = 888030
Hence, 888030 ways are there for teachers to select the students.
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An altitude is drawn from the vertex of an isosceles triangle, forming a right angle
and two congruent triangles. As a result, the altitude cuts the base into two equal
segments. The length of the altitude is 15 inches, and the length of the base is 11
inches. Find the triangle's perimeter. Round to the nearest tenth of an inch.
The perimeter of the triangle is 50.96 inches.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
An isosceles triangle.
This means,
Two sides are equal.
Now,
The length of the altitude = 15 inches.
The length of the base = 11 inches.
Now,
The right triangle:
Base = 11/2 = 5.5 inches.
Height = 15 inches.
The other side = x
Applying the Pythagorean theorem.
x² = 5.5² + 15²
x² = 30.25 + 225
x² = 255.25
x = √255.25
x = 19.98 inches.
Now,
The perimeter of the triangle.
= 2x + 11
= 2 x 19.98 + 11
= 50.96 inches.
Thus,
The triangle's perimeter is 50.96 inches.
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What is 5-kilometers / 400 meters
Answer: 12.5 meters!
Step-by-step explanation:
1km = 1000 meters
So 5km = 5000 meters
So take 5000 divided by 400 = 12.5 meters
Answer:
12.5 is the answer for this question
What is the equation of the line that passes through the points − 1/3 and 1 11?
the equation of the line that passes through the points − 1/3 and 1 11 is
y = 3x + 8 with slope 12 1/3.
1. Find the slope of the line.
m = (11 - -1/3) / (1 - -1/3)
m = 12 1/3
2. Using the point-slope equation, substitute the slope and one point from the line
y - y1 = m(x - x1)
y - -1/3 = 12 1/3 (x - (-1/3))
3. Solve for y
y = 12 1/3x + 8
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Consider an ideal gas at 27.0 degrees Celsius and 1.00atmosphere pressure. Imagine the molecules to be uniformly spaced,with each molecule at the center of a small cube. What is thelength Lof an edge of each small cube if adjacent cubes touch but don'toverlap?
The length L of an edge of each small cube if adjacent cubes touch but don't overlap is 3.45 nm.
The formula to be used for calculation is -
PV = Nkt, where P is pressure, V is volume, N is number of molecules, k is Boltzmann constant and T is temperature in Kelvin.
T = 273 + 27
Performing addition on Right Hand Side of the equation
T = 300 K
P = 101325 Pa
k = 1.38 × [tex] {10}^{-23} [/tex] J/K
Now finding the volume
V = (1 × 1.38 × [tex] {10}^{-23} [/tex] × 300)/101325
Performing multiplication and division on Right Hand Side of the equation
V = 4.09 × [tex] {10}^{-3} [/tex] m³
As we know, V = L³
So, L = [tex] {V}^{1/3} [/tex]
Keep the value of volume
L = [tex] { (4.09/1000) }^{1/3} [/tex]
Performing calculations
L = 3.45 × [tex] {10}^{-9} [/tex] m
Hence, length is 3.45 nm.
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50 points please help me
think sometimes prob 4x5 i don't know