The discriminant is:
D = 5^2 - 4*3*(-8) = 121
Then we have two real solutions.
How to determine the discriminant?
For a quadratic equation:
a*x^2 + b*x + c = 0
The discriminant is:
D = b^2 - 4ac
If D > 0, we have two real solutions.
If D = 0 we have one real solution (it is thought as two equal solutions)
if D < 0, we have two complex solutions.
In this case, the quadratic equation is:
3x^2 + 5x - 8 = 0
Then:
a = 3
b = 5
c = -8
The discriminant is:
D = 5^2 - 4*3*(-8) = 121
Then we have two real solutions.
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The test statistic value calculated by the statistical procedure selected is known as the?
The test statistic value calculated by the statistical procedure selected is known as the T-test.
What is a T-test?
The mean difference between two sets of observations is zero using the T-test, also known as the dependent sample t-test. When the population standard deviation is unknown, the student's t-test is a statistical tool for assessing assumptions about the mean of a small sample taken from a normally distributed population.
Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.
Therefore, the test statistic value calculated by the statistical procedure selected is known as the T-test.
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The cost of bananas varies directly with the number of pounds bought. If 6 pounds
cost $5.22, find the cost of 3 pounds.
Answer:
$2.61
Step-by-step explanation:
So, We have $5.22 for 6 pounds of Bananas.
If we need to find the cost for 3 pounds, we would divide $5.22 by 2 because 6/2=3
In order to do this, we need to turn 5.22 into a whole number, so we multiply by 100
5.22*100=522
Now we divide
522/2 = 261
Now we divide 261 by 100, since we multiplied by 100 earlier.
261/100 =2.61
So our answer is $2.61 for 3 pounds of bananas .
Hope this helps! ^^
Answer:$2.61 for 3 pounds
Thank for the brainliest
Step-by-step explanation:first you divided $5.22/6 because the money always goes on the top and you get 0.87, you multiply 0.87 by 3 which is $2.61
If 0.25 cm represents 5 feet on a blueprint, what is the actual length of a room that is 8.5 inches long?
In proportion , 13 ft is the actual length of a room.
What in mathematics is a proportion?
A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
0.25 inches 8.5 inches
---------------- = --------------
5 ft x ft
Using cross products
0.25x = 8.5 * 5
Divide each side by 0.25
0.25x/0.25 = 8.5 * 5/0.25
x = 13
x = 13 ft
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give the type of triangle that has these angles
27 degrees
63 degrees
91 degrees
A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x - xo), where x and f(x) are measured in miles. find the rate of change of elevation when x = 2.
The rate of change of elevation is 0.32.
What is the rate of change of elevation?An easy-to-remember equation for finding change in elevation as a decimal is “rise over run,” meaning the rise (the change in vertical distance) divided by the run (the change in horizontal distance).
So the problem wants to ask to calculate the rate of change of the elevation if x=2 in the function f(x) = 0.32x. So base on that, the rate of change of elevations can be get through the formula of slope intercept form and the answer would would 0.32 is the rate of change in disregard of the value of x.
Hence, The rate of change of elevation is 0.32.
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which statements are true regarding the sequence below? check all that apply. 10/3,4,24/5,144/25,...
Answer:
A) It can be represented using the formula f(x + 1) = 6/5(f(x)) when f(1) = 10/3.
C) It can be represented using the formula f (x) = 10/3(6/5)/\x-1
What is sequence?
A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given:
10/3, 4, 24/5, 144/25, ...
From the above sequence we can generate the formula,
f (x) = 10/3
Also, for f(x+1) we can have
x=1,
f(1)= 10/3
f(2)= 4
So, f(x + 1) = 6/5(f(x))
Step-by-step explanation:
3.5 lb of cheese for $8.94
$_
per lb
Answer:
your answer is $2.55
The following are the weights (in pounds) of seven people:
100, 115, 135, 140, 180, 197, 230.
find the 80th percentile.
The 80th percentile is 125.37.
It is required to find the solution.
What is percentage?A part of a whole expressed in hundredths a high percentage of students attended. Also the result obtained by multiplying a number by a percent the percentage equals the rate times the base.
Given:
The weights (in pounds) of seven people:
100, 115, 135, 140, 180, 197, 230.
We have to find the 80th percentile first we have to find the mean of seven people.
Mean=100+ 115+135+140+ 180+197+ 230/7
Mean=156.71
100 percent=156.71
80 percent=156.71*80/100
80 percent=125.37.
Therefore, the 80th percentile is 125.37.
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Carnegie Learning, Inc.
Victor drew a square with vertices at (1, 2), (3, 2), (3, 4), and (1, 4). He slides the square 5 units
up to create an image. What are the vertices of the image and the algebraic rule?
A (6,2), (8, 2), (8, 4), and (6, 4); (x + 5, y)
B (1,7), (3, 7), (3, 9), and (1, 9); (x, y + 5)
C (1, -3), (3, -3), (3, -1), and (1, -1); (x, y - 5)
D (1,-2), (3,-2), (3, -4), and (1,-4); (x, -y)
Why a is wrong?
And why b is correct
Answer:
B
Step-by-step explanation:
The y coordinate tells us when we are going up for down. So the rule would be (x, y + 5) So, the x coordinate stays the same and the y goes up 5.
(1,2) The 2 is the y coordinate. It will increase by 5 and become (1,7)
(3,2) The 2 is the y coordinate. It will increase by 5 and become (3,7)
(3,4) The 4 is the y coordinate. It will increase by 5 and become (3,9)
(1,4) The 4 is the y coordinate. It will increase by 5 and become (1,9)
Find the lowest common denominator for the following set of fractions: 4/21, 3/7, 4/9
The lowest common denominator for 4/21, 3/7, 4/9 is 63.
Lowest common denominator is the lowest number that is divisible by the denominators of the set of fractions.
Step 1: we will write down the prime factors of all the denominators.
[tex]21=7^{1} *3^{1}[/tex]
[tex]7=7^{1}[/tex]
[tex]9=3*3=3^{2}[/tex]
Step 2 : write down highest power of each prime number.
[tex]7^{1} ,3^{2}[/tex]
Step 3 : Multiply the values
7x9=63
Therefore , The lowest common denominator for 4/21, 3/7, 4/9 is 63.
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A middle school took all of its 6th grade students on a field trip to see a ballet at a theater that has 1700 seats. The students filled 442 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answer:
26%
Step-by-step explanation:
Number of seats by 6th graders / Number of seats in total × 100% = Percentage of seats by 6th graders
442/1700 × 100% = 26%
Hope this helps! ^^
Go to school kid and pay attention
Find the value of y is x = -3
y = 4x² + 2x - 9
Find a and b so that f(x) is continuous for all values of x f(x)={x^2-4/x-2 if x<2 ax^2-bx+3 if 2<=x<3 2x-a+b if x>=3
The values a = 1/3 and b = 1/6.
Given function is, f(x) =
[tex]\frac{x^2-4}{x-2}\ \ \ if\ x < 2 \\ax^2-bx+3 \ \ \ if\ 2\leq x < 3\\2x-a+b\ \ \ if\ x\geq 3[/tex]
The interval in which the function is defined is broke down into three. They are: x<2, 2≤x<3 and x≥3.
Now the function [tex]\frac{x^2-4}{x-2}[/tex] is continuous except at x = 2. But this function is defined in the interval x>2. The other two function are defined as polynomial, so are continuous any way.
So for the whole function f(x) to be continuous, we need to check the continuity at x = 2, x = 3.
When x = 2, [tex]\frac{x^2-4}{x-2}[/tex] =[tex]\frac{(x+2)(x-2)}{x-2}=x+2 = 4[/tex] and [tex]ax^2-bx+3[/tex] = 4a-2b+3
⇒ 4a-2b+3 = 4
⇒4a- 2b-1 = 0, for the function to be continuous at x = 2.
When x = 3, [tex]ax^2-bx+3[/tex] = 9a-3b+3 and 2x-a+b = 6-a+b
⇒ 9a-3b+3 = 6-a+b
⇒ 10a -2b-3 = 0, for the function to be continuous at x = 3.
On solving 4a-2b-1 = 0 and 10a -2b-3 = 0 by subtracting the two,
we get, -6a+2 = 0
⇒ a = 1/3 and therefore, b = 1/6
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Need these pleaseeeeee
2, 4, 8, 16, 32, 64, ... The number 4,096 belongs to this sequence. What is the number that immediately precedes it?
A basic slime recipe calls for 1 part borax, 24 parts white glue, and 48 parts water. The relationship between borax, white glue and water is proportional. If Catalina has 3 tablespoons of borax and will use it all, how many cups of white glue will she need
Answer:
I am more on the sure side it's 8
Step-by-step explanation:
And if it isn't im so so sorry
Two boats are traveling in a canal in opposite directions, where x represents the distance, in feet, between the boats. the equation 2(x 1) = 2x 2 models the paths of the boats. solve for x.
Answer: Hi The Answer is 3 (the third one)
Step-by-step explanation: Am not sure if this is correct am taking the test right now
Answer:
all real numbers
Step-by-step explanation:
Florida
Use the roster method to write the given set the set of integers x that satisfy 2x-1= -13
The only set of elements that satisfied the equation 2x-1= -13 is {-6}.
What is a set?A set is a combination of specific quantities in which the meaning of each variable must be the same.
For example {1,2,3,4,5,6...} is a set of natural numbers in which each variable is representing a natural number so the overall meaning is the same among all.
Another example could be a set of whole numbers like that.
Given the equation,
2x-1= -13
By taking -1 right-hand side
2x = -13 + 1 = -12
By dividing 2
x = -6
Hence "The only set of elements that satisfied the equation 2x-1= -13 is {-6}".
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The recommended mass m of a baseball is 145 grams. The actual mass is allowed to vary by up to 2 grams. What are the minimum and maximum allowed baseball masses?
The minimum and maximum allowed baseball masses are 143 grams and 147 grams
What are the minimum and maximum allowed baseball masses?The given parameters are
Mass = 145 grams
Vary = 2 grams
This means that the allowed baseball masses are
Allowed baseball masses = Mass ± Vary
This gives
Allowed baseball masses = (145 - 2, 145 + 2) grams
Evaluate
Allowed baseball masses = 143 grams, 147 grams
Hence, the minimum and maximum allowed baseball masses are 143 grams and 147 grams
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Work out the area of the rectangle
Answer:
11.2 or 11 1/5
Step-by-step explanation:
multiply it ez
Answer: Use a=wl, 13.3
Step-by-step explanation:
a=wl
4.75*2.8=13.
Order 3/8, 3/7, and 3/9 from least to greatest withour writing equivalent fractions with a common denomanator. explain your strategy.
Answer:
3/9 3/8 3/7
Step-by-step explanation:
The higher the denominator, the higher number of times a number will be divided which means, the number will become smaller.
Find the greatest common factor for each list of numbers 12,18,26,32
Using heron's formula the sides of the tringleare 70cm,80cm and 90cm.find its area(use root 5=2.23)
The area of the triangle is 1200√5 cm².
Given that, the sides of the triangle are 70cm,80cm and 90cm.
We need to find the area of a triangle using Heron's formula.
What is Heron's formula?As per Heron's formula, the value of the area of any triangle having lengths, a, b, c, perimeter of the triangle, P, and semi-perimeter of the triangle as 's' is determined using the below-given formula:
Area of triangle = √s(s-a)(s-b)(s-c), where s = Perimeter/2 = (a + b + c)/2
Now, semi perimeter = (70+80+90)/2=120
Area of triangle=√120(120-70)(120-80)(120-90)
=√120×50×40×30
=√40×3×2×25×40×30
=40×5√3×2×3×2×5
=40×5×3×2√5
=1200√5 cm²
Therefore, the area of the triangle is 1200√5 cm².
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Your bank offers you a 36-month, 3 pr car loan for a $50000 new mercedes slk300 roadster. what will your monthly payment be?
The monthly payment will be $1454.06048
You can calculate the Car Loan EMI Amount with the help of the mathematical formula: EMI Amount = [P x R x (1+R)^N]/[(1+R)^N-1] , where P, R, and N are the variables. This also means that the EMI value will change, each time you change any of the three variables. Let’s discuss these three variables in detail.
‘P’ stands for the Principal Amount. It is the original loan amount given to you by the bank on which the interest will be calculated.
‘R’ stands for the Rate of Interest set by the bank.
N is the number of years given for the repayment of the loan. As you must pay the EMIs each month, the duration is calculated in the number of months.
Here , P=$50000,R=3/12/100=0.0025,N=36 Months.
EMI=[50000 x 0.0025 x (1+0.0025)^36]/[(1+0.0025)^36-1]
= $1454.06048
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N (-5,2) Q (1,-5)
What is the length of QN
The length between the two points is 9.2 units.
Given points are:
Q(1,₋5)
P(₋5,2)
Let the two points be denoted as
Q(1,₋5) as (x₁,y₁)
P(₋5,2) as (x₂,y₂)
Distance between two points is calculated as:
d = √(x₂ ₋ x₁)² ₊ (y₂ ₋ y₁)²
d = √(₋5 ₋ 1)² ₊ (2 ₋ (₋5))²
d = √(₋6)² ₊ (7)²
d = √36 ₊ 49
d = √85
d = 9.2
Hence the length of QN is 9.2 units.
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What multiplies to 26 and adds to 27
Answer: 1 and 26
Step-by-step explanation:
One bridge design has supports that form an X in the center. Find the measure of each numbered angle.
The measure of angle is 52, 128 and 132
What are angles?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
Given:
one angle = 52
So,
<2 = 52 (vertically opposite angle)
<1 + <2 = 180 ( linear pair)
<1 + 52 = 180
<1 = 128
and, <1 = < 3 ( vertically opposite angle)
<3 = 132
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Value of x
Pls show steps
Answer:
x = 18
Step-by-step explanation:
Vertical angles are congruent.
4x + 3 = 75 Subtract 3 from both sides of the equation
4x = 72 Divide both sides by 4
x = 18
Land's bend sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 8 sales receipts for mail-order sales results in a mean sale amount of $61.80 with a standard deviation of $17.75. A random sample of 13 sales receipts for internet sales results in a mean sale amount of $77.40 with a standard deviation of $29.75. Using this data, find the 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed.
A. Find the critical value that should be used in constructing the confidence interval. B. Find the standard error of the sampling distribution to be used in constructing the confidence interval.
C. Construct the 80% confidence interval.
The assumption that the population variances are not equal and that the two populations are normally distributed is −35.713332; 0.313332.
What is a random sample?A simple random sample (or SRS) in statistics is a subset of individuals (a sample) chosen at random from a larger set (a population) with the same probability. It is the process of selecting a sample at random.To assume that the population variances are not equal and that the two populations are normally distributed:
Given:
n1 = 11 sample sizex1 = 79 for the sample means1 = 18.25 standard deviationn2 = 18 sample sizex2 = 96.70 for the sample means2 = 20.25 standard deviationSo, df = n1 + n2 - 2; 11 + 18 - 2 = 27.
T critical = T0.01, 27 = 2.473
Let,
S = sqrt[(s1²/n1) + (s2²/n2)]S = sqrt[(18.25^2 / 11) + (20.25^2 / 18)]S = 7.284Then,
(μ1 - μ2) = (x1 - x2) ± T critical × S(μ1 - μ2) = (79 - 96.70) ± 2.473*7.284(μ1 - μ2) = - 17.7 ± 18.013332Now,
-17.7 - 18.013332 ; - 17.7 + 18.013332−35.713332 ; 0.313332Therefore, the assumption that the population variances are not equal and that the two populations are normally distributed is −35.713332; 0.313332.
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