I prefer solving quadratic equations with the quadratic formula. The formula is great for solving any equations like ones that factoring can’t. It is also easy to memorize and type in and check with a calculator.
I always prefer quadratic formula as compared to factoring or completing the square to solve a quadratic equation.
What is a quadratic equation?"A quadratic equation is an algebraic equation of the second degree in 'x'. The quadratic equation in its standard form is ax² + bx + c = 0, where 'a' and 'b' are the coefficients, 'x' is the variable, and 'c' is the constant term."
In order to solve a quadratic equation, I always prefer quadratic formula as compared to the other methods.
In many cases, a quadratic equation can not be converted into a square or into factors.
Therefore, quadratic formula is the only method to solve all type of quadratic equation.
Learn more about quadratic equation here: https://brainly.com/question/2263981
#SPJ3
61 sample problems. The new algorithm completes the sample problems with a mean time of 14.06 hours. The current algorithm completes the sample problems with a mean time of 16.43 hours. Assume the population standard deviation for the new algorithm is 3.004 hours, while the current algorithm has a population standard deviation of 4.568 hours. Conduct a hypothesis test at the 0.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Le
Answer:
There is sufficient evidence to conclude that the new algorithm has a lower mean completion time than the current algorithm
Step-by-step explanation:
From the question we are told that
The sample size for each algorithm is [tex]n_1 = n_2 = n = 61[/tex]
The sample mean for new algorithm is [tex]\= x_1 = 14.06 \ hr[/tex]
The standard deviation for new algorithm is [tex]\sigma _1 = 3.004 \ hr[/tex]
The sample mean for the current algorithm is [tex]\= x_2 = 16.43 \ hr[/tex]
The standard deviation for current algorithm is [tex]\sigma _2 = 4.568[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu _2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 < \mu_2[/tex]
Here [tex]\mu _1 \ and \ \mu_2[/tex] are population mean for new and current algorithm
Generally the test statistics is mathematically represented as
[tex]Z = \frac{ \= x _1 - \= x_2 }{ \sqrt{\frac{ \sigma_1 ^2 }{n_1} + \frac{\sigma^2_2 }{ n_2}} }[/tex]
=> [tex]Z = \frac{ 14.06 - 16.43 }{ \sqrt{\frac{ 3.004^2 }{61} + \frac{4.568^2 }{ 61}} }[/tex]
=> [tex]Z = -3.39[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P(Z < -3.39 )[/tex]
From the z-table
[tex]P(Z < -3.39 ) = 0.0003[/tex]
=> [tex]p-value = P(Z < -3.39 ) = 0.0003[/tex]
From the calculated value we see that [tex]p-value < \alpha[/tex] hence the null hypothesis is rejected
Hence we can conclude that there is sufficient evidence to conclude that the new algorithm has a lower mean completion time than the current algorithm
If RT=36, find the value of x
Answer:
4
Step-by-step explanation:
So we know that RT is 36.
Note that RT is the combined length of RS and ST. Therefore:
[tex]RT=RS+ST[/tex]
Substitute. RT is 36, RS is 6x+1 and ST is x+7:
[tex]36=(6x+1)+(x+7)[/tex]
Combine like terms and add:
[tex]36=7x+8[/tex]
Subtract 8 from both sides:
[tex]28=7x[/tex]
Divide by 7:
[tex]x=4[/tex]
So, our answer is 4 :)
Kate is making a pasta salad for her family party. She has 3 pounds of pasta salad to serve 12 people. She wants to give an equal amount of pasta salad to each person in her family. How much pasta salad should Kate put in each person’s bowl?
Answer:
0.25 of a pound, 1/4
Step-by-step explanation:
3 divided by 12 = 0.25
What is the volume of a sphere with a diameter of 12 cm.
Answer:
288π cm³, 904.32 cm³, and 904.778683 cm³
Step-by-step explanation:
The volume of a sphere can be found using the following formula.
[tex]V=\frac{4}{3} \pi r^3[/tex]
We are given the diameter, so we must find the radius.
The radius is half of the diameter.
r= d/2
The diameter is 12 cm.
r= 12 cm/2
r= 6 cm
The radius is 6 centimeters. Let's return to the formula and substitute 6 cm in for r.
[tex]V=\frac{4}{3} \pi (6cm)^3[/tex]
Evaluate the exponent.
[tex](6 cm)^3= 6 cm * 6 cm * 6cm = 36 cm^2 * 6cm= 216 cm^3[/tex]
[tex]V=\frac{4}{3} \pi * 216 cm^3[/tex]
Multiply 4/3 and 216 cm^3
[tex]V= (\frac{4}{3} * 216 cm^3)\pi[/tex]
In terms of pi:
[tex]V= 288\pi cm^3[/tex]
Using 3.14 as pi:
[tex]V= 288 \pi cm^3[/tex]
[tex]V= (288 * 3.14) cm^3[/tex]
[tex]V= 904.32 cm^3[/tex]
Using 3.14159265 as pi:
[tex]V= 288 \pi cm^3[/tex]
[tex]V= (288 * 3.14159265) cm^3[/tex]
[tex]V=904.778683 cm^3[/tex]
The volume of the sphere is 288π cm³, 904.32 cm³, and 904.778683 cm³
Answer:
Volume of sphere by formula is V= 4/3πr^3
Since d= 12
Then r = d/2
Radius = diameter / 2
r = 12/2
r = 6
V = 4/3 x 22/7 x 6^3
V = 1.33 x 3.14 x 216
V = 902.1cm^3....
Thanks
f(t)= (t-5)^2 - 9 what are the zeros of the function? Smaller T: Larger t: What is the vertex of the parabola?: (__,__)
Smaller t = 2
Larger t = 5
Step-by-step explanation:
Given:
The given function is.
Find the zeros of the function.
Solution:
Simplify the equation above equation.
Now, we first find the root of the above equation.
Use quadratic formula with .
Put a, b and c value in above equation.
For positive sign
t = 2
For negative sign
t = 5
Put t = 2 in given function.
Put t = 5 in given function.
So, the zeros of the function is t = 2 or 5
Therefore, the smaller value of t = 2 and larger value of t = 5.
Find the distance represented by 4.9 inches is 1 inch =50
Answer:
distance = 245 in
Step-by-step explanation:
1 in = 50
distance = 4.9 in x 50
distance = 245 in
Answer: 245 miles
Step-by-step explanation:
fg
State the domain and range of the following function using set notation. G(x)= -5x2 write the domain of the function set
The domain of the function is [tex]\mathbb{R}[/tex] or in set notation [tex](-\infty, \infty)[/tex].
The range of the function is [tex][0, -\infty)[/tex].
Hope this helps.
Hurry Please!!! Which two numbers on the number line have an absolute value of 4 Select the location of both numbers on the number line.
Answer:
-4 and 4
Step-by-step explanation:
Hello!
An absolute value is a number regardless if it is negative or positive
For example, the absolute value of -6 is 6, -3 is 3 and 5 is 5
So numbers that have an absolute value of 4 are 4 and -4
Hope this Helps!
the product of a number and 9
Answer:
9x
Step-by-step explanation:
let's say that x is the number we don't know
the product means multiplication
9*x=9x
so the answer is 9x
Answer:
[tex]\Huge \boxed{9x}[/tex]
Step-by-step explanation:
Let the unknown number be x.
The product of x and 9.
The product refers to multiplication.
[tex]x \times 9[/tex]
Convert the angle θ=29π/15 radians to degrees
Answer:
The answer is
[tex] 348\degree[/tex]Step-by-step explanation:
To convert any angle from radians to degrees multiply that angle by
[tex] \frac{180 \degree}{\pi} [/tex]So for the above angle in the question we have
[tex] \frac{29\pi}{15 } \times \frac{180}{\pi} [/tex]Reduce the fraction with π
That's
[tex] \frac{29}{15} \times 180 \\ = \frac{5220}{15} [/tex]We have the final answer as
[tex]\theta \: = 348\degree[/tex]Hope this helps you
What is the explicit rule for the geometric sequence? 4.05,1.35,0.45,0.15,...
Step-by-step explanation:
Since the above sequence is a geometric sequence
For an nth term in a geometric sequence
That's
[tex]A(n) = a( {r})^{n - 1} [/tex]
where
r is the common ratio
a is the first term
n is the number of terms
From the question
a = 4.05
r = 1.35 / 4.05 = 0.33
Substitute the values into the above formula
We have
[tex]A(n) = 4.05( {0.33})^{n - 1} [/tex]
Hope this helps you
10 x 4 thousands in unit form
Answer:
Step-by-step explanation:
Simplify.
10 x 4000
40000
Unit form.
forty-thousand = four thousands
I'm sorry if I misunderstood.
Please add Brainliest if you'd like, not that it matters.
Multiplication is the process of multiplying. The value of the expression 10 × 4,000 is 40,000.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
In the given expression 10×4000, the symbol of '×' represents that the two digits should be multiplied. Therefore, the value of the multiplication of 10 and 4,000 is,
10 × 4,000 = 40,000
Hence, the value of the expression 10 × 4,000 is 40,000.
Learn more about Multiplication here:
https://brainly.com/question/14059007
#SPJ2
A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function of Size (measured in thousands of square feet) and whether or not there is a fireplace (FP is 0 if there is no fireplace, 1 if there is a fireplace). The regression output is provided below. Some of the information has been omitted.
Source of variation SS df MS F
Regression 3177.17 2 1588.584
Residual 17 17.7 17 13
Total 3478.36 19
Which of the following conclusions can be made based on the F-test?
A) The estimates were based on a sample of 19 houses.
B) At least one of the predictors is useful in explaining Y.
C) The model is of no use in predicting selling prices of houses.
D) The p-value on the F-test will be very high.
Answer:
The correct option is B.
Step-by-step explanation:
The ANOVA table is as follows:
Source of variation SS df MS F
Regression 3177.17 2 1588.584 ___
Residual ___ 17 17.71713
Total 3478.36 19
The complete table is as follows:
Source of variation SS df MS F
Regression 3177.17 2 1588.584 89.663
Residual 301.1941 17 17.7173
Total 3478.36 19
The critical value of F is:
[tex]F_{\alpha, (\eta_{1}, \eta_{2})}=F_{0.05, (2,17)}=3.5915[/tex]
Decision rule:
If the calculated value of the F test statistic is more than or equal to the critical value.
[tex]F=89.663\geq F_{2,17}=3.5915[/tex]
The null hypothesis will be rejected.
Conclusion:
At least one of the predictors is useful in explaining Y.
Thus, the correct option is B.
circumference or area how many times must a horse go around a horse walker to walk 1 mile
Answer:
circumference
Step-by-step explanation:
Going around is the circumference
What is the value of (45−13)×52+56 expressed in simplest form?
Solve the problem.When exposed to ethylene gas, green bananas will ripen at an accelerated rate. The number of days for ripening becomes shorter for longer exposure times. Assume that the table below gives average ripening times of bananas for several different ethylene exposure times. Plot the data and then find a line approximating the data. With the aid of this line, determine the rate of change of ripening time with respect to the exposure time. Round your answer to two significant digits.
The table and the plotted data are in the attachment.
Answer and Step-by-step explanation: A line of best fit is the best approximation of the given data. It is used to show the relation of two variables and it can be determined, more accurately, by the Least Square Method.
To use the method, follow the steps:
1) Calculate the mean of the two variables:
[tex]X = \frac{\Sigma x_{i}}{n}[/tex]
[tex]Y=\frac{\Sigma y_{i}}{n}[/tex]
2) The Slope of the line is given by:
[tex]m=\frac{\Sigma (x_{i}-X)(y_{i}-Y)}{\Sigma (x_{i}-X)^{2}}[/tex]
3) The y-intercept is found by the formula:
[tex]b=Y-mX[/tex]
For the ripening of bananas, the least square method gives the line:
y = -0.142x + 5.56
The rate of change of a line equation is its slope, so
Rate of change = -0.14
The rate of change of ripening time with respect to exposure time is -0.14, which means the more expose the fruit is, the less time it needs to ripe.
Select the appropriate technique with the problem you are looking for.
a. Checking the equal variance assumption
b. Checking the normal assumption
c. Check for model misspecification
d. Check for dependent errors
1. Create a scatterplot of hat versus your QN X's
2. Create a stem-and-leaf display of the zresiduals
3. Create a scatterplot of the residuals versus time period collected
4. Create a scatterplot of the residuals versus yhat
5. Create a scatterplot of the residuals versus your QN X's
Answer:
A, B, C, D
Step-by-step explanation:
(A) Checking the Equal Variance Assumption, the appropriate technique to use is:
- The ANOVA (Analysis of Variance) F test
- Plot residuals against fitted values
(B) Checking the Normal Assumption, the appropriate techniques to use are:
- Test for Kurtosis & Skewness
- Kolmogorov-Smirnov Test
- Q-Q Plots (the graphical method) also known as Quantile Plot
- Do not use a histogram; it is not advisable
(C) Checking for Model Misspecification, the appropriate techniques to use are:
- The Ramsey Regression Specification Error Test; also called RESET
- The Davidson & MacKinnon J. Test
(D) Checking for dependent errors, the appropriate technique to use is:
- Plot residuals against time variables
What is 3.173 rounded to the nearest tenth
THE answer is 3.173≅3.2(nearest tenth)
While playing a video game a player collected 18 of the 45 available coins right and simplify a fraction to represent the situation
Answer:
2 / 5
Step-by-step explanation:
Fractions are written in the form part/whole, in this case, the part is 18 and the whole is 45 so the fraction would be 18 / 45 which simplifies to 2 / 5.
4,336 is 10 times as much as?
Answer:
433.6
Step-by-step explanation:
Below is the graph of a polynomial. Which of the following statements about
this graph is true?
Which of the following is a step in simplifying the expression x multiplied by y to the power of 4 over x to the power of negative 5 multiplied by y to the power of 5, the whole to the power of negative 3.? x to the power of negative 3 multiplied by y, the whole over x to the power of negative 8 multiplied by y to the power of 2. x to the power of negative 3 multiplied by y to the power of negative 12, the whole over x to the power of negative 5 multiplied by y to the power of 5. x to the power of negative 3 multiplied by y, the whole over x to the power of negative 5 multiplied by y to the power of 5. x to the power of negative 3 multiplied by y to the power of negative 12, the whole over x to the power of 15 multiplied by y to the power of negative 15.
Answer:
x to the power of negative 3 multiplied by y to the power of negative 12, the whole over x to the power of 15 multiplied by y to the power of negative 15.
Step-by-step explanation:
Given is expression below to be simplified:
(xy⁴/x⁻⁵y⁵)⁻³The step in simplifying is the power of the power, which is equal to product of powers: (xᵃ)ᵇ = xᵃᵇ. So, power of -3 of the whole equals to:
(x⁻³y⁻¹²)/(x¹⁵y⁻¹⁵)This expression is same as the last option:
x to the power of negative 3 multiplied by y to the power of negative 12, the whole over x to the power of 15 multiplied by y to the power of negative 15.So, this is the correct one.
Answer:
other answer was correct
Step-by-step explanation:
find the unknown angles. please help
Answer:
60°, 60°, 60°
Step-by-step explanation:
Since, two side of the given triangle are congruent l. Therefore, measures of both the interior angle will be equal.
By remote interior angle theorem:
120° = x + x
120° = 2x
120°/2 = x
60° = x
Third angle = 180° - 120° = 60°
Hence measure of all the three angles of the triangle are 60°, 60° and 60°
Trigonometry question! NEED HELP ASAP
Answer:
12.3 = y
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hyp
cos 35 = y/15
15 cos 35 = y
12.28728066 = y
To the nearest tenth
12.3 = y
Find the greatest common factor of 16 and 36
Answer:
GCF= 4
Step-by-step explanation:
A factor is a number that evenly divides into another number.
First, list the factors of 16.
1 , 2, 4, 8, 16
Next, list the factors of 36
1 , 2 , 3, 4, 6, 9, 12, 18, 36
Now, find the GCF, or greatest common factor. The GCF is the largest factor that both numbers share.
16 : 1 , 2, 4, 8, 16
36 : 1 , 2 , 3, 4, 6, 9, 12, 18, 36
When we compare the lists, we see the biggest number that appears in both lists is 4.
The Greatest Common Factor of 16 and 36 is 4.
Answer: 4
Step-by-step explanation: The Greatest Common Factor of two
numbers is the largest factor shared by both numbers.
As a review in case you didn't know, a factor of a
number divides into that number without a remainder.
To find the greatest common factor of 16 and 36,
we begin by finding all of the factors of each number.
Let's start by finding the factors of 16.
16 ÷ 1 = 16
16 ÷ 2 = 8
16 ÷ 4 = 4
We can stop here because if we continue
dividing, we won't find any new factors.
So the factors of 16 are 1, 2, 4, 8, and 16.
Now let's find the factors of 36.
36 ÷ 1 = 36
36 ÷ 2 = 18
36 ÷ 3 = 12
36 ÷ 4 = 9
36 ÷ 6 = 6
So the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Now find the largest number shared by the two lists.
In this case, the largest number is 4.
So the greatest common factor of 16 and 36 is 4.
Find the exact trigonometric ratios for the angle x whose radian measure is given. $$\frac{3 \pi}{4} $$
Answer:
Step-by-step explanation:
Before we can determine the exact trigonometric ratios for the angle x whose radian measure is given as [tex]\dfrac{3\pi}{4}[/tex], we need to first determine the quadrant the angle falls into.
The angle [tex]\dfrac{3\pi}{4}[/tex] = [tex]\dfrac{3*180}{4} = 135^0[/tex] and it falls in the second quadrant. since the angle is positive, we will use the trigonometry ratio that is positive in the second quadrant. The trigonometry ratio that is positive in the second quadrant is sin(x) while others are negative.
[tex]sin \frac{3\pi}{4} = sin (\pi - \frac{\pi}{4} ) = sin\frac{\pi}{4} = \frac{1}{\sqrt{2} } \\cos \frac{3\pi}{4} =cos (\pi - \frac{\pi}{4} ) = -cos\frac{\pi}{4} = -\frac{1}{\sqrt{2} } \\tan \frac{3\pi}{4} = tan (\pi - \frac{\pi}{4} ) = -tan\frac{\pi}{4} = -1[/tex]
How do you simplify x-2/2-x?
Answer:
-1
Step-by-step explanation:
Simplify the following:
x - 2/2 - x
Hint: | Reduce (-2)/2 to lowest terms. Start by finding the GCD of -2 and 2.
The gcd of -2 and 2 is 2, so (-2)/2 = (2 (-1))/(2×1) = 2/2×-1 = -1:
x + -1 - x
Hint: | Group like terms in x - 1 - x.
Grouping like terms, x - 1 - x = (x - x) - 1:
(x - x) - 1
Hint: | Look for the difference of two identical terms.
x - x = 0:
Answer: -1
Which of the following fractions would convert into a repeating decimal
Answer: [tex]\frac{2}{9}[/tex]
Step-by-step explanation: It is 2/9 because 2/9 converts to 0.222222222...
Hope it helps!
A student wrote three papers in mathematics examination marks for two papers we're 77and 72 respectively.to obtain grade A, an average of not less than 75marks is required for the three papers
Answer:
The student must score at least 76 in the third subject
Step-by-step explanation:
Given
Scores in 2 subjects = 77 and 72
Number of subjects = 3
Required
Determine the scores in the third subject to get an average of 75
Represent the score in the third subject with y
Average in 3 scores is calculated as thus;
[tex]Average = \frac{Sum\ of\ 3\ scores}{3}[/tex]
Substitute 75 for Average
[tex]75 = \frac{Sum\ of\ 3\ scores}{3}[/tex]
Multiply both sides by 3
[tex]3 * 75 = \frac{Sum\ of\ 3\ scores}{3} * 3[/tex]
[tex]3 * 75 = Sum\ of\ 3\ scores[/tex]
[tex]225 = Sum\ of\ 3\ scores[/tex]
Substitute (77 + 72 + y) for Sum of 3 scores
[tex]225 = 77 + 72 + y[/tex]
[tex]225 = 149 + y[/tex]
Subtract 149 from both sides
[tex]225 - 149 = 149 - 149 + y[/tex]
[tex]225 - 149 = y[/tex]
[tex]76= y[/tex]
[tex]y = 76[/tex]
Hence, the student must score at least 76 in the third subject
Two co- interior angles are in the ratio 5:7 find the angles
Answer:
75°
105°
Step-by-step explanation:
Two co-interor= 180°
5+7= 12
ratio12= 180°
{find the other ratios, 5 and 7)
12=180°
5×180÷12 = 75°
To find 7, just subtract 180-75= 105°