Answer:
Solving the equation using quadratic formula we get [tex]\mathbf{x=0.119\:or\:x=-2.785}[/tex]
Step-by-step explanation:
We need to use the quadratic formula to find the solutions for
[tex]y = 3x^2 + 8x - 1[/tex]
(Note: quadratic formula is used when x^2 is in the equation. So considering 3x^2 instead of 3x^3)
The quadratic formula is: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
From the given equation [tex]y = 3x^3 + 8x - 1[/tex] we have a =3, b=8 and c =-1
Putting values in the formula and finding solutions:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-8\pm\sqrt{(8)^2-4(3)(-1)}}{2(3)}\\x=\frac{-8\pm\sqrt{64+12}}{6}\\x=\frac{-8\pm\sqrt{76}}{6}\\x=\frac{-8\pm8.71}{6}\\x=\frac{-8+8.71}{6}\:or\:x=\frac{-8-8.71}{6}\\x=0.119\:or\:x=-2.785[/tex]
So, Solving the equation using quadratic formula we get [tex]\mathbf{x=0.119\:or\:x=-2.785}[/tex]
Your test in math class has problems worth 2 points and problems worth 4 points. Altogether the test has 100 points. Write an equation that represents the total points on the test formed by the number of 2-point problems and the number of 4-point problems.
Answer:
100 = 2x + 4y
Step-by-step explanation:
The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5. (a) What is the point estimate of the population mean? 8.75 Incorrect: Your answer is incorrect. (b) What is the point estimate of the population standard deviation? (Round your answer to three decimal places.) (c) With 95% confidence, what is the margin of error for the estimation of the population mean? (Round your answer to one decimal place.) (d) What is the 95% confidence interval for the population mean? (Round your answer to one decimal place.) to
Answer:
10 ; 3.464 ; 2.4 ; (7.6, 12.4)
Step-by-step explanation:
Given the data :
10, 8, 12, 15, 13, 11, 6, 5
Point estimate of population mean :
m = ΣX / n
n = sample size = 8
(10+8+12+15+13+11+6+5) / 8
= 10
Point estimate of population standard deviation :
Sqrt(Σ(X - m)^2 / n-1)
((10-10)^2 + (8-10)^2 + (12-10)^2 + (15-10)^2 + (13 - 10)^2 + (11-10)^2 + (6-10)^2 + (5-10)^2) / 7
= sqrt(84/7)
= 3.464
Margin of error at 95%:
Zcritical * sqrt(sd²/n)
Zcritical at 95% = 1.96
1.96 * sqrt(3.464^2 / 8)
Margin of Error = 2.4
Confidence interval :
m ± Z(s/sqrt(n))
10 - 1.96(3.4634/sqrt(8)) = 7.6
10 - 1.96(3.4634/sqrt(8)) = 12.4
Which equation represents the function shown on the graph? y = x y = x y = 2x y = 4x
Answer:
The correct answer is y=4x
Step-by-step explanation:
Please answer quickly Thank You
Answer:
A. $ 46
B. 12 people.
Step-by-step explanation:
From the question given above, we obtained the following:
C(x) = 6.5x + 20
Where:
C => total cost of bowling
x => number of people
A. Determination of the of bowling for 4 people.
Number of people (x) = 4
Total cost (C) of bowling =?
C(x) = 6.5x + 20
C(4) = 6.5(4) + 20
C(4) = 26 + 20
C(4) = $ 46
Thus, it will cost $ 46 for 4 people to bowl
B. Determination of the number of people that can bowl for $ 98.
Total cost (C) of bowling = $ 98
Number of people (x) =?
C(x) = 6.5x + 20
98 = 6.5x + 20
Collect like terms
98 – 20 = 6.5x
78 = 6.5x
Divide both side by 6.5
x = 78 / 6.5
x = 12
Thus, 12 people can bowl for $ 98.
Chase is making a cake for his daughter's birthday. The normal recipe calls for 8 ounces of butter and 16 ounces of sugar. Chase then decides to make a slightly smaller cake and only use 6 ounces of butter. How many ounces of sugar will he need in his smaller cake?
Answer:
A lot
Step-by-step explanation:
Why am I baking cakes. I SUCK.
There are 12 ounces of sugar will he need in his smaller cake.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The normal recipe calls for 8 ounces of butter and 16 ounces of sugar.
Let the amount of sugar will he need in his smaller cake = x
So, By definition of proportion, we get;
⇒ Amount of Butter / Amount of Sugar
⇒ 8 / 16 = 6 / x
⇒ x = 6 × 16 / 8
⇒ x = 12 ounces
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Find the vertex of the parabola defined by the following equation. 3x^2-12x+11
Answer:
y= 3(x-2)^2-1
Step-by-step explanation:
Scottie is testing to see if people who go to a lot of movies do better than average on the Verbal SAT (which has a mean of 500 and a standard deviation of 100 and is normally distributed). She has a sample of six people. What kind of hypothesis testing do we use
Answer:
The kind of hypothesis testing we can use is z-test for means
Step-by-step explanation:
Given that;
sample mean x" = 500
standard deviation σ = 100
sample size n = 6
What kind of hypothesis testing do we use?
There are two cases where z-test can be use;
first, when we know the population standard deviation or variance
and secondly, when the population size is more than 30.
So from the question, the population standard deviation was given, which is 100.
Since we know the S.D, it meets the first condition.
Therefore, The kind of hypothesis testing we can use is z-test for means
Find the product of (1)(3)(x).
Your
answer
Answer:
2/5.
Step-by-step explanation:Start with fractions for which you need to find the product. In this example, we will multiply the fractions 4/6 and 3/5.
Simplify the fractions to the lowest terms. A fraction needs to be simplified if the same number can divide both the numerator and denominator of a fraction. So 4/6 would become 2/3 and you would multiply by 3/5.
Multiply the numerators. Multiply the top number in one fraction by the top number in the other fraction. In this case 2 x 3 = 6.
Multiply the denominators. Multiply the bottom number of one fraction by the bottom number in the other fraction. In this case 3 x 5 = 15
Simplify the product again if necessary. Your product of 6/15 can be converted into 2/5 by dividing both the numerator and denominator by 3. So the product of 4/6 and 3/5
Determine which choice best shows the distributive property of multiplication.
Question 2 options:
1 × 6 = 6
6 × 9 = 9 × 6
6 × (9 + 8) = (6 × 9) + (6 × 8)
6 × (9 × 8) = (6 × 9) × 8
Answer:
c) 6× (9+8) = (6 × 9) + (6× 8)
Step-by-step explanation:
Distributive property of multiplication
The distributive property of multiplication
a(b+c) = a b + a c
(a+b)c = ac + bc
6× (9+8) = (6× 9) + (6×8)
Max walks 10 meters in 4 seconds what is his walking rate in meters per second
Answer:
2.5 m/s
Step-by-step explanation:
10/4 gets the answer. it is just distance over time
Answer: 2.5 m/s
Step-by-step explanation:
Select all the correct answers.
Janine needs to calculate the value of log , 81
Which expressions could she input into her calculator to find this value?
In 81
12
✓
in 81
In 12
log 81
log 12
log 81
In 12
log 12
log 81
Answer:
In 81 / In 12 ;
log 81 / log 12
Step-by-step explanation:
Log 12 81
Log 81 base 12
According to rule of logarithm :
Log 81 base 12 = (log 81 base 10) / log 12 base 10)
Obtaining the value :
(log 81 base 10) / log 12 base 10) = 1.7684564
Using trial and error method :
log 81 / In 12 = 0.7680308
In 81 / In 12 = 1.7684564
In 81 / 12 = 0.3662040
Hence, the correct answers are :
In 81 / In 12
log 81 / log 12
11. A man is buying a lot which measures 7,860 square meters. How many
hectares of land is he buying?
A. 78,600 hectares
B. 0.7860 hectare
C. 786,000 hectare
D. 0.07860 hectare
Answer:
C. 786,000 hectare
Step-by-step explanation:
This question can be solved by proportions, using conversion of units.
Each hectare has 10 000 square meters.
So 7,860 square meters is equal to:
7,860*10000 = 786,000 hectares
The answer is given by option C.
find the value of x
Recall the Spice Girls Emporium example. A list of useful information is given below. n = 36 The sample mean income is $41,100 The population standard deviation is estimated to be $4,500 What if we wanted to change our level of confidence to be 99%? What would our new margin of error be? Your answer should be given as an integer.
Answer: Margin of error = 1932
Step-by-step explanation: Margin of Error is the amount of variation a survey's results have. In other words, it is understood as the measure of variation one can see if the same survey was taken multiple times.
Margin of error is calculated as [tex]z\frac{\sigma}{\sqrt{n}}[/tex]
z is z-score related to the percentage of confidence, in this z = 2.576
σ is population standard deviation
n is how many individuals are there in the sample or population
With a new level of confidence of 99%:
ME = [tex]2.576.\frac{4500}{\sqrt{36}}[/tex]
ME = 2.576(750)
ME = 1932
The new margin of error would be 1932.
Corey need a 24 boards that are 47 1/2 inches long
A. How many feet a boards should he buy? Explains.
B. if you can only buy 8-fot boards, how many should he buy? explain
Answer:
Step-by-step explanation:
1 foot = 12 inches
47.5 inches × (1 foot)/(12 inches) = (47.5/12) feet
24 boards × ((47.5/12) feet)/board = 95 feet
:::::
(8 feet)/board × (12 inches)/foot = (96 inches)/board
96/47.5 = 2 remainder 1
An 8-foot board provides two 47.5" boards, with an inch wasted.
He needs to buy 12 of the 8-foot boards.
calculate the pay for the following day of a weekly time card given a wage of $16/hr
Answer:
24x16x7
Step-by-step explanation:
Answer:
$2,688 a week
Step-by-step explanation:
16 x 7 x 24 would be 2,688
What is the result when 6x3 + 11x2 + 9x + 2 is divided by 3x + 1?
Answer:
(6x^(3)+11x^(2)-19x+5)-:-(3x-2)
Step-by-step explanation:[tex]63+112+32+1[/tex]
for some reason it showed that but yeah hope this helps!
A superball rebounds half the height it drops. A student drops the superball from the top of a building, 176 feet above the ground. How far
above the ground is the ball when it has traveled a distance of 500 feet?
Answer:
62.48 ft.
Step-by-step explanation:
Initial height: 50 ft.
First rebound: 10 ft.
Second rebound: 2 ft.
Third rebound: 0.4 ft.
Fourth rebound: 0.08 ft.
If we approximate the fourth rebound to zero, we'll have:
50 + 10 + 2 + 0.4 + 0.08 = 62.48 ft.
Write an algebraic expression. The product of two numbers is 94, and one of the numbers is n. What is the other number?
Answer:
Let say the another number y
N×Y=94
Y=94/N
So the algebric expression is 94/N
10. Find the rate of change in the table below.
Show all work.
х
18
20
22
24
y
4.5
5
5.5
6
Answer:
it's times 4 every time
Step-by-step explanation:
4.5 times 4 is 18 etc
Solve the Equation
P + 75 = 100.
Answer:
P= 25 so
25+75= 100
Step-by-step explanation:
100-75
Answer:
P=25
Step-by-step explanation:
P+75=100
-75 -75
_________
P=25
A ccompany offers free shipping on orders that weigh less than 3,000 grams. How much is this in kilograms. Be sure to include the correct unit in your answer.
Answer:
The answer is 5 Kilos.
Step-by-step explanation:
There are 1000 grams in 1 Kilo, thus 1000g= 1k, so 5000g=5k.
Answer:
its 3kg
Step-by-step explanation:
If the data below were represented by a comparative bar chart, the bar
representing which of these would be the tallest?
A. Left-handed girls
B. Right-handed boys
C. Right-handed girls
D. Left-handed boys
Answer:
b right handed boys
Step-by-step explanation:
HELP PLEASE IM BEGGING PLEASE PLEASE PLEASE
Answer:
h - 18 = 67
Step-by-step explanation:
If h is her height, then her height minus 18 is 67, or h - 18 = 67
Answer:
67 = h - 18
Step-by-step explanation:
Sry I meant h-18 = 67
Evaluate y=3x for x=2.
y=
Answer:
y=6
Step-by-step explanation:
y=3x x=2
y=3(2)
y=6
For the given expression, the value of y is 6.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ y = 3x
Now, For value of x = 2;
The value of y is,
⇒ y = 3x
Substitute x = 2;
⇒ y = 3 × 2
⇒ y = 6
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PLEASE HELP I NEED HELP WITH AN ALGEBRA 2 QUESTION ILL GIVE BRAINLEST
Answer:
the zeros of the function are those that result, when plugged into the equation, in zero; the zeros are -3, 1, and 1/2
Step-by-step explanation:
all possible factors:
±3/2, ±1/2, ±3, ±1
2x³ + 3x² - 8x + 3
let '2' = p and let '3' = q
factors of 'p' are 1 and 2
let '3' = q
factors of 'q' are 1 and 3
possible factors are q/p
Two pencils and one pen cost $0.80, and one pencil and two pens cost $1.15. How many cents would three pencils cost
Answer:
.33 cents
Step-by-step explanation:
121/2% in to a fraction
9514 1404 393
Answer:
1/8
Step-by-step explanation:
You can replace % with /100 to make it a fraction.
12 1/2% = (12 1/2)/100 = (25/2)/100 = 25/200 = 1/8
__
Or, you can reduce the decimal fraction.
12.5% = 12.5/100 = 0.125 = 125/1000 = 1/8
Can someone help me Write an equation for this graph?
Answer:
y = (2/3)x - 1
Step-by-step explanation:
y = mx + b
m = (y₂ - y₁) ÷ (x₂ - x₁)
m = (1 - (-1)) ÷ (3 - 0)
m = 2 ÷ 3
m = 2/3
Insert slope and one of the points. I'm using (0, -1).
Solve for b.
-1 = (2/3)0 + b
-1 = 0 + b
-1 = b
∴ y = (2/3)x - 1
What is 83% as a decimal SHOW WORK IF U CAN HELP ASAP!!
0.83Answer:
Step-by-step explanation:
83% means 83 per 100 or 83/100 if you divide 83 by 100 you get 0.83
Answer:
.83
Step-by-step explanation:
to turn a percentage into a number you have to divide by 100, meaning you need to move the decimal point to the left 2 times so you get:
.83
hope this helps!!
