What number must you add to x² + 16x = 3 to complete the square 64: Option C
What is a perfect square?You should be aware that a perfect square is a term that has two common factors
The given equation is x² + 16x = 3
To make the equation a perfect square, Add the square of half of the coefficient of s to both sides
This is to say that (16/2)² = 8² = 64
The equation becomes x²+16x+64 = 3+64
Then you can factorize the equation and simplify the right hand side
Learn more about perfect squares on https://brainly.com/question/385286
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A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a standard deviation of 4.2 years. The distribution of life spans for electric ranges has a mean of 13.4 years and a standard deviation of 3.7 years. Both distributions are moderately skewed to the right. Suppose we take a simple random sample of 35 gas ranges and a second SRS of 40 electric ranges. Which of the following best describes the sampling distribution of the difference in mean life span of gas ranges and electric ranges?
a. Mean = 1.6 years, standard deviation = 7.9 years, shape: moderately right-skewed.
b. Mean = 1.6 years, standard deviation - 0.92 years, shape: approximately Normal.
c. Mean= 1.6 years, standard deviation = 0.92 years, shape: moderately right skewed.
d. Mean =1.6 years, standard deviation =0.40 years, shape: approximately Normal.
e. Mean =1.6 years, standard deviation =0.40 years, shape: moderately right skewed.
Answer:
b. Mean = 1.6 years, standard deviation - 0.92 years, shape: approximately Normal.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal Variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a standard deviation of 4.2 years. Sample of 35:
This means that:
[tex]\mu_G = 15[/tex]
[tex]s_G = \frac{4.2}{\sqrt{35}} = 0.71[/tex]
The distribution of life spans for electric ranges has a mean of 13.4 years and a standard deviation of 3.7 years. Sample of 40:
This means that:
[tex]\mu_E = 13.4[/tex]
[tex]s_E = \frac{3.7}{\sqrt{40}} = 0.585[/tex]
Which of the following best describes the sampling distribution of the difference in mean life span of gas ranges and electric ranges?
Shape is approximately normal.
Mean:
[tex]\mu = \mu_G - \mu_E = 15 - 13.4 = 1.6[/tex]
Standard deviation:
[tex]s = \sqrt{s_G^2+s_E^2} = \sqrt{0.71^2+0.585^2} = 0.92[/tex]
So the correct answer is given by option b.
Panchito discovered the summer’s most refreshing beverage by mixing a 80% cranberry juice with a 4% of orange juice. How much of each should he mix together to make 190 ml of a 60% cranberry-orange juice blend
Answer:
Quantity of cranberry juice = 95 ml
Quantity of orange juice = 95 ml
Step-by-step explanation:
Step 1
Given ,
We have 80% cranberry juice and 4% of orange juice.
We have to find how much each should be mixed to make 190 ml of a 60% cranberry-orange juice blend.
Step 2
Let's assume
Quantity of cranberry juice =x ml
Quantity of orange juice =y ml
Then,
x + y = 190
and
x×80100 +y×4100 = 190×60100
⇒ 0.8x+0.4y = 114
⇒ 2x+y = 285
⇒ y = 285−2x
Step 3
Substituting y = 285−2x in x + y = 190
⇒ x+285−2x = 190
⇒ −x = 190−285
⇒ −x = −95
⇒ x = 95 ml
Substituting x = 95 in x + y = 190
⇒ 95 + y = 190
⇒ y = 190−95
⇒ y = 95 ml
So,
Quantity of cranberry juice =95 ml
Quantity of orange juice = 95 ml
Myles bought 4 rose bushes and 4 tulip plants. Let r represent the number of roses in bloom on each rose bush and t represent the number of tulips in bloom on the each tulip plant. Myles and Jenna each wrote an expression that represents the total number of flowers in bloom. Are the expressions equivalent? Justify your answer.
Answer:
what are the choices of answers
Step-by-step explanation:
whoever gets this correct gets brainliest
does 5+4=8 and does 1+1=2
Answer:
5+4=9
and the second one is right
Step-by-step explanation:
;)
Answer:
the first one is incorrect but the second one is correct!
Step-by-step explanation:
5 + 4 = 9
if you have 5 apples and you want to add 4 more
5 + 1 + 1 + 1 + 1 = 9
The Booster Club sells meals at basketball games . Each meal comes with a choice of a main: hamburgers , pizza , hot dogs, cheeseburgers , or tacos, and a choice of a drink: root beer, lemonade, milk, coffee, tea, or cola. How many possible sandwich/drink combinations are there? (Show work) (2 pts)
30 combinations is the answer.
Step-by-step explanation:
Each meal comes with a choice of hamburgers, pizza, hot dogs , cheeseburgers or tacos means 5 options.
And a choice of root beer lemonade, milk , coffee, tea or cola means 6 options.
So, possible combination can be = combinations.
Ahmed buys a house for £179500
A year later he sells the house for £190 270
Calculate the percentage profit Ahmed makes.
I
Total mar
Answer: 6% of profit
Step-by-step explanation:
Find the % of profit
179 500 / 190 270 ≈ 0,94 = 94 %
100% - 94% = 6%
Sam drove for 2 hours at 45 mph. He has the same distance remaining. How fast should he drive to make his average speed 60 mph?
Answer:
Step-by-step explanation:
2 hours at the speed of 45 mph = 90 miles in 2 hours
He should drive 60 miles per hour to make his speed 60 mph.
An organization published an article stating that in any one-year period, approximately 10.2% of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, nine of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country.
1. Calculate the following.
a. x =
b. p' =
c. n =
2. Calculate σx.
3. Find the p-value.
Answer:
W21221
Step-by-step explanation:
a rectangle prism has a volume of x^3 + 6x^2 - 7x - 60. If the height of the prism is x + 4, the dimensions of the base are
A theater owner wants to provide enough seating for 928 people. The main floor has 25 rows of 22 seats in each row. If the balcony has 21 rows, how many seats must be in each row to satisfy the owner’s seating requirements?
Answer:
18 seats in each row
Step-by-step explanation:
25 x 22 = 550
928 - 550 = 378
378 / 21 = 18
sqrt x^7 ...........
Answer:
[tex]x^{3}[/tex][tex]\sqrt{x}[/tex]
Step-by-step explanation:
An easier way to approach this is to separate the inside first.
[tex]\sqrt[]{x*x*x*x*x*x*x}[/tex]
Now you can group together pairs of 2, and they come out as one.
[tex]x*x*x\sqrt{x}[/tex]
Multiply all the xs on the outside, and you get
[tex]x^{3}[/tex][tex]\sqrt{x}[/tex]
please help get this right please I'm nut sire if it right
what is a salesperson Commission on a $600 sale if the commission rate is 30%
Answer:
180
Step-by-step explanation:
The difference of a number and 8 is -15
Answer:
-7
Step-by-step explanation:
x-8=-15
x=-7
very got on the bus at 4:20 P.M. The trip took 80 minutes. Then she walked for 49 minutes to get home. At what time did Avery arrive at home?
Answer:
6:29pm
Step-by-step explanation:
there 60min in a hour and that's what I got
-6y+11x=-34
-4y+7x=-24
Answer:
no idea but mabye someone whose NOT in 3rd grade will know?
I need help with these pls
Factorise 3x⁴-4y⁴ completely
Answer:
Step-by-step explanation:
[tex]3x^4-4y^4\\=(\sqrt{3}x^2)^2-(2y^2)^2)\\=(\sqrt{3}x^2+2y^2)(\sqrt{3}x^2-2y^2)\\=(\sqrt{3} x^{2} +2y^{2} )((3^{\frac{1}{4} } x)^2-(\sqrt{2} y)^{2} )\\=(\sqrt{3} x^{2} +2y^{2} )(3^{\frac{1}{4} } x+\sqrt{2} y)(3^{\frac{1}{4} } x-\sqrt{2} y)[/tex]
The Davis family is going to reseed the grass in the backyard. Their yard is irregularly shaped with a cement patio and rectangular garden as shown below. Given that the family will not need grass seed for the patio or the garden areas, what is the total area of the land will they be reseeding?
Answer:
1,482 square feet
Step-by-step explanation:
Find total area - 37 x 46 = 1,702
Find area of patio and garden - 16 x 10 = 160 for the patio, 12 x 5 = 60 for the garden
Subtract from total area - 1702 - 160 = 1542, 1542 - 60 = 1,482 sq ft
What is the area of the triangle?
16
8
10
Answer:
64
Step-by-step explanation:
Find the area of both triangles inside the bigger triangle and add them together.
Use the Pythagorean theorem to find the missing length of the leg in the smallest triangle:
a² + b² = c²
8² + b² = 10²
64 + b² = 100
36 = b²
6 = b
Calculate the area of the smaller triangle:
1/2(bxh)
1/2(6 x 8)
1/2(48)
24
Calculate the area of the bigger triangle:
We know that the longer leg is 10 units because we were able to subtract the length of the smaller triangle's leg from 16.
1/2(bxh)
1/2(10 x 8)
1/2(80)
40
Add both areas to find the area of the largest triangle:
40 + 24 = 64
A square pyramid has a base with a side length of 6 inches and lateral faces with heights of 11 inches. What is the surface area of the pyramid?
Answer:
[tex]\huge\boxed{\sf 168\ in.\²}[/tex]
Step-by-step explanation:
Surface area of the base:
= Length * Length
= 6 * 6
= 36 in.²
Surface Area of 1 Lateral Face:
= [tex]\sf \frac{1}{2} (Base * Height)[/tex]
Base = 6 inches
Height = 11 inches
= 1/2 (6*11)
= 3 * 11
= 33 in.²
Surface Area of 4 lateral faces:
= 33 * 4
= 132 in.²
Surface Area of the whole pyramid:
= 132 + 36
= 168 in.²
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer:
SA = 168 in.²
Step-by-step explanation:
The surface area is the sum of the area of the base and the areas of the 4 congruent triangular sides.
s = side of the base
h = height of each side
SA = s² + 4(sh/2)
SA = (6 in.)² + 4(6 in.)(11 in.)/2
SA = 36 in.² + 132 in.²
SA = 168 in.²
Which triangle makes this statement true?
Answer:
Step-by-step explanation:
A restaurant is offering 15 percent off beverages. The check is $90.00 with the beverage total being $15.00. What is the check total after the discount ?
A 77.75
B 76.50
C.75.00
D.87.75
b because 90
15
15
-_____
76.50
Could someone help?
What is the common ratio of the sequence?
-2, 6, -18, 54,...
A. −3
B. −2
C. 3
D. 8
Answer:
A
Step-by-step explanation:
because just multiply each number by -3 and it should be the next nember
Answer:
A
Step-by-step explanation:
-2×(-3)=6 then 6×(-3)=-18 and so on
Jessica is playing a game where there are 4 blue markers and 6 red markers in a box. She is going to pick 3
markers without replacement.
If she picks all 3 red markers, she will win a total of $500. If the first marker she picks is red but not all 3 markers
are red, she will win a total of $100. Under any other outcome, she will win $0.
What is the expected value of Jessica's winnings?
Round your answer to the nearest cent.
Answer:
The probability of Jessica picking 3 consecutive red markers is: (1/6)
The probability of Jessica's first marker being red, but not picking 3 consecutive red markers is:
(3/5)−(1/6)=(13/30)
So i am bit stuck here
what i think is it shouldn't be that complex it should be as simple as chance of Jessica's first marker being red=chance of getting red 1 time i.e P(First marker being red)=(6/10) can any explain me the probability of Jessica's first marker being red=(13/30)?
Step-by-step explanation:
Answer:
$126.67
Step-by-step explanation:
Charles wanted to graph the amount of sugar (in teaspoons) used in cups of coffee at a schoolevent. He used the coffee and sugar usage table to make the graph below
( will give brainliest if you help)
Answer:
Its a
Step-by-step explanation:
Solve for n
56 = -4n
a. 60
b. -4
c. -14
d. 224
Which set of numbers may represent the sides of a triangle
A: {2,5,9}
B: {6,6,7}
C {6,4,2}
D {7,8,1}
Answer:
C.(6, 4,2)
since every element of B is also an even number,so is an element of C
what is the domain of the function y=2 square root x-6
Answer:
6 ≤ x < ∞
Step-by-step explanation:
interval notation: [6, ∞)
set builder notation: {x|x ≥ 6}