The value of x in the equation x² = 16 is ± 4
What is the value of x?This is a quadratic equation in one variable.Here, x² = 16
Taking square root on both sides,
[tex]\sqrt{x^{2} } =\sqrt{16}\\[/tex]
Simplifying the radicals,
x = ± 4
Any equation that can be stated as a[tex]x^{2}[/tex] + bx + c = 0, where a, b, and c are coefficients and a 0, is a quadratic equation in x.A quadratic equation in one variable, x, is an equation that can be stated as ax squared plus bx plus c = 0, where the values of a, b, and c are merely constants and the value of a does not equal 0.The degree power of one variable is twice that of another variable, giving quadratic equations their characteristic second degree curve appearance.To learn more about radicals, refer:
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You are interested in finding a 90% confidence interval for the average number of names that people can correctly recall after being introduced to 40 people at a party. Based on past research, you know that the standard deviation for this number is 6.34 names. Suppose you surveyed 55 randomly selected people and found that they correctly remembered an average of 18.16 names. The standard deviation for this group was 4.28 names. Round your answers to two decimal places.
A. The sampling distribution follows a __________ distribution.
B. With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between ______ and _______
C. If many groups of 55 randomly selected people were surveyed, then a different confidence interval would be produced for each group. About _____ percent of these confidence intervals will contain the true population mean number of names remembered and about ______ percent will not contain the true population mean number of names remembered.
Answer:
A. The sampling distribution follows a normal distribution
B. With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between 17.04 and 19.28
C. If many groups of 55 randomly selected people were surveyed, then a different confidence interval would be produced for each group. About 90 percent of these confidence intervals will contain the true population mean number of names remembered and about 10 percent will not contain the true population mean number of names remembered
Step-by-step explanation:
The given parameters are;
The known population standard deviation of the number of names that people can recall after being introduced to 40 people in a party, σ = 6.34 names
The number of people randomly selected in the survey, n = 55 people
The average number of names correctly remembered, [tex]\overline x_1[/tex] = 18.16
The standard deviation of the group surveyed, s = 4.28
A. Based on the Central Limit Theorem CLT, the sampling distribution follows a normal distribution
B. The 90% confidence interval is given as follows;
[tex]C.I.=\bar{x}\pm z_{\alpha /2}\cdot \dfrac{\sigma}{\sqrt{n}}[/tex]
Where [tex]z_{\alpha /2}[/tex] at 90% = 1.65, we have;
[tex]C.I.=18.16\pm 1.65 \times \dfrac{4.28}{\sqrt{55}}[/tex]
C.I. ≈ 17.20 < μ < 19.11
With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between 17.04 and 19.28
C. The 90% confidence interval gives the certainty that if different groups of 55 randomly selected people were surveyed, then about 90 percent of the confidence intervals will contain the true population mean number of names remembered and about 10 percent will not contain the true population mean number of names remembered.
Help Plz
Will mark brainliest
Answer:
b. [tex] (x - 2) ^{2} - 36[/tex]
d. [tex] (x - 2) ^{2} - 36[/tex]
Step-by-step explanation:
[tex](x + 4)(x - 8) \\ \\ = {x}^{2} - 8x + 4x + 4( - 8) \\ \\ = {x}^{2} - 4x - 32 \\ \\ = {x}^{2} - 4x + 4 - 4 - 32 \\ \\ = {x}^{2} - 4x + {2}^{2} - 36 \\ \\ = (x - 2) ^{2} - 36[/tex]
Can someone help me please I will give you Brainly if you get it right
Answer:
Hi! The answer to your question is A. 4 hours
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
Answer:
4
Step-by-step explanation:
I got it wrong at first but someone corrected me ;n;
4y^2+20y+25
Factor the polynomial completely
Answer:
(2y+5)^5
Step-by-step explanation:
Use the "PERFECT SQUARE RULE"
the second part is thiss
Step-by-step explanation:
Question b has already been answered in part one. This is an exponential function.
C) 7 is the initial number of people who received the email;
7*2^n is the number of people who receive the email on day n;
2 is the factor of which the number of people increases each day.
D) On day 5,
[tex] {2}^{5} \times 7 = 32 \times 7 =224[/tex]
people will have received the email.
E) 2; 0 (no people has received the email on day 0). The equation is
[tex]y = {2}^{x} \times 7[/tex]
With x in the natural numbers
f(x)=3(x+1)^2-4 then evaluate when x=3
Step-by-step explanation:
given
[tex]f(x) = 3{(x + 1)}^{2} - 4 \\ f(3) = 3 {(3 + 1)}^{2} - 4 \\ = 3 {(4)}^{2} - 4 \\ = 3(16) - 4 \\ = 48 - 4 \\ = 44[/tex]
Answer:
3(3+1)²-4
3(16)-4
48-4 = 44
HELP PLEASE ,DUE TONIGHT
Answer:
Might be C if im wrong sorry
Step-by-step explanation:
Mathew builds a model of a house that is 2 in tall, 6 in wide, and 3 in long. The real house is 20 ft tall, 60 ft wide and 30ft tall. What is the scale used to build the house?
Answer: 1inch : 10 feet
Step-by-step explanation:
Since we are informed that Mathew builds a model of a house that is 2 in tall, 6 in wide, and 3 in long while the real house is 20 ft tall, 60 ft wide and 30ft tall.
For the length, we can see that the relay house is (30/3) = 10 times the model. The same thing is applicable to others as well as the width and height is 10× the scale used. Therefore, the scale used to build the house is 1inch:10 feet
The data set shows the numbers of miles Ms.Franklin drove on five days. answer choices are in the picture ( please no files or links just the answer)
Choose the equation below that matches the word sentence: "3 increased
by x is 9."
A.3x = 9
B.3/x = 9
C.3 + x = 9
D.3 - x= 9
Step-by-step explanation:
32 9655 9655 + 965 + 965 + 965 + 982
(3.15x10^4) (5.15x10^-7 express the result as a decimal
Answer: 1.62225 x 10^-2 or 0..0162225
Step-by-step explanation:
Can someone help me real quick?
Answer:
2:3
Step-by-step explanation:
You do 8+10 for red and yellow so 12:18 but we need to simplify so 6:9 2:3
2:3 is the correct answer
I really need help with this. Can you help me please?
Answer:
Solve the equation using the method of completing the square.
Step-by-step explanation:
Hello, I gotta turn it turn in this question today, help!!!!!!
Answer:
2 or -2
Step-by-step explanation:
If x² - 8x = -12
Step 1
We find x by solving
x² - 8x = -12
We equate to zero
x² - 8x + 12 = 0
We factorise
x² - 6x - 2x + 12 = 0
x(x - 6) -2(x - 6) = 0
(x - 6) (x - 2) = 0
x - 6 = 0, x = 6
x - 2 = 0, x = 2
x = 6 or 2
Step 2
What is x - 4?
When x = 6
= 6 - 4 = 2
When x = 2
= 2 - 4 = -2
Therefore, x - 4 = 2 or -2
Someone help me please extra points & brainlest!
Answer:
my best bet is d
Step-by-step explanation:
tell me if im wrong
Answer:
7x-11
Step-by-step explanation:
remove parentheses
4x-7+3x-4
group like terms
4x+3x-7-4
add similar elements
7x-7-4
then solve
7x-11
What is the value of m in the equation 5m = 20.05?
25.05
15.05
4.10
4.01
please help if you know the pythagorean thereom
Answer:
AD= square root of 221
:)
Step-by-step explanation:
Use the information shown in the line plot.
How many fruit baskets weigh more than
4
1
2
412
pounds and less than
6
pounds?
Enter your answer in the box.
_____fruit baskets
Answer:
8.
Step-by-step explanation:
5 and 5 1/2 are the only fractions between 4 and 6. There are 4 dots above each, and 4 x 2 = 8. (I know the amount of dots because I had this question.)
There are two baskets that weigh more than 4 but less than 6.
The weights of fruit baskets are:
4, 1, 2, 5, 5(1/2), 6
What is weight?Weight is the quantity of matter in a physical body.
We can see that fruit baskets that weigh more than 4 pounds but less than 6 pounds are ones with weights of 5 pounds and 5(1/2) pounds.
So, there are two baskets that weigh more than 4 but less than 6.
Thus, there are two baskets that weigh more than 4 but less than 6.
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Freddy pays $840 per year in
insurance.
How much should he budget
monthly for it?
A) $70
B) $92
C) $140
D) $142
(y+7) what does that equal
James bought 3 books for $8 each and 4 DVDs for $15 each he paid with a $100 how much change did he receive?
Answer:
He received $16 change
Step-by-step explanation:
3 books for $18 is $24
4 DVDs for $15 is $60
His total is $84
$100 - $84 = $16
Answer:
6 dollars
Step-by-step explanation:
you multiply 3 by 8 which is 24. Then you multiply 4 by 15 and that's 70. So then you add 24 and 70 together which is 94. Lastly you subtract 94 from 100 and you get 6.
Ahmad invested in a savings bond for 5 years and was paid simple interest at an annual rate of 2%. The total interest that he earned was $800. How much did he invest?
please dont give me a file
The upper quartile is the right edge of the green box.
This is at 300 minutes.
The answer is 300 minutes.
Please help me❗️❗️
A ball thrown into the air is modeled by the
equation
h(t) = -t2 + 4t + 5. Where h represents
the height of the ball and t represents
time.
What is the starting height of the ball?
What is the time the ball reaches its
maximum height?
What is the maximum height?
When does the ball hit the ground?
How high is the ball 1 second into
flight?
Answer:
Below in bold.
Step-by-step explanation:
Starting height is when t = 0
It is 5 units.
To find the maximum height we convert the equation to vertex form:
h = -t^2 + 4t + 5
h = -(t^2 - 4t - 5)
= - [(t - 2)^2 - 9]
= -(t - 2)^2 + 9
From this we see that the ball reaches max height after 2.
Maximum height = -2^2 + 4(2) + 5
= 9 units.
Ball reaches the ground after 2*2 = 4 .
Distribute and combine like terms: 8(1 + 6 p)
Answer:
8 + 48p
Step-by-step explanation:
Which equation matches this statement?
Finn buys a toy boat for $45.50 including tax. He was charged 7% sales tax on the original price.
HELPPPP PLEASE!!!
Sandy plays tennis once every 6 six days. Jim plays once every 8 eight days. If they both played tennis today, in how many days will play on the same day.
24...
8x3=24
6x4=24
Thats the soonest theyll play together.
Isaiah started with 421 letters. At each stop he makes, he delivers 29 letters. How many letters are leftover?
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[tex]I \: \: Think \: \: The \: \: Answer \: \: Is \: \: \red{ \boxed{ \boxed{ \huge{ \tt{{ \: 392 \: }}}}}}[/tex]
Answer:
2.) Isaiah started with 421 letters. At each stop he makes, he delivers 29 letters. How many letters are leftover? *
Step-by-step explanation:
A tent is in the shape of a triangular prism shown below.
What is the lateral surface area of the prism?
Question 2
Use pythagroean theorem to find the value of the missing side. Leave answers in simplest radical form.
Answer:
C
Step-by-step explanation:
a^2 + 49 = 169
-49 - 49
a^2 = 120
√120 = 2√30