Answer:
2/3 = Two-thirds
Step-by-step explanation:
We want to find:
[tex]x = \log_{27}{9}[/tex]
Logarithm concepts:
[tex]log_{b}{a} = c[/tex] means that:
[tex]a = b^{c}[/tex]
So
[tex]x = \log_{27}{9}[/tex]
[tex]27^{x} = 9[/tex]
[tex]3^{3x} = 3^{2}[/tex]
Then
[tex]3x = 2[/tex]
[tex]x = \frac{2}{3}[/tex]
So the correct answer is:
2/3 = Two-thirds
Answer:
C 2/3
Step-by-step explanation:
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A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario? f(x) = 1500(1.15)x f(x) = 1500(115)x f(x) = 1500(2.15)x f(x) = 1500(215)x
Answer:
the first one f(x) = 1500(1.15)x
Step-by-step explanation:
100% is written as 1 -> 100% of 36 is 36 so 36 * 1 = 36
hope this helps
The Formula for the area of a trapezoid is A=1/2(b1+b2)h when this equation is solve for B1, One equation is b1=2A/h -b2 which of the following is an equivalent equation to find b1
Answer:
see below
Step-by-step explanation:
Multiply by 2 and expand the right side:
2A = b1h +b2h
Subtract the b2 term:
2A -b2h = b1h
Divide by h:
b1 = (2A -b2h)/h
Answer:
A
Step-by-step explanation
Step-by-step explanation:
Multiply by 2 and expand the right side:
2A = b1h +b2h
Subtract the b2 term:
2A -b2h = b1h
Divide by h:
b1 = (2A -b2h)/h
Find the equation for the plane through the points Upper P0 (-2 ,2 ,-5),Q0 (1,2,-1), and Upper R0 (-1,-5,4 ).
The equation of plane is:________
Answer:
28x - 23y - 21z = 3
Step-by-step explanation:
First, we need to find two vectors in the plane as:
vector PQ = Q - P = (1, 2, -1) - (-2, 2, -5) = (3, 0, 4)
vector PR = R - P = (-1, -5, 4) - (-2 ,2 ,-5) = (1, -7, 9)
Then, we need to find a normal vector to the plane as:
PQ x RQ = ((0*9)-(4*-7), -(3*(9)-(4*1), (3*-7)-(0*1))
PQ x RQ = (28, -23, -21)
Finally, the equation of a plane is:
A(x-x0) + B(y-y0) + C(z-z0) = 0
Where (A,B,C) is a normal vector to the plane and (x0, y0, z0) is a point in the plane. So, replacing (A,B,C) by (28, -23, -21) and (x0, y0, z0) by P0(-2,2,-5), we can write the equation of the plane as:
28(x+2) - 23(y-2) - 21(z+5) = 0
Solving, we get:
28x + 56 - 23y + 46 - 21z - 105 = 0
28x - 23y - 21z - 3 = 0
28x - 23y - 21z = 3
The height of a stream of water from the nozzle of a fire hose is modeled by h(x) =-0.03x2+ 2x + 38 where h(x) is the height in feet, of the stream of water x feet from the fire truck. 1. What is the maximum height the water from this nozzle can reach? What is the maximum distance from the firetruck a firefighter can stand and still reach the fire?
Answer:
height: 71.33 feetreach: 82.10 feetStep-by-step explanation:
The equation can be rewritten to vertex form:
h(x) = -0.03(x² - 200/3x) +38
h(x) = -0.03(x² -200/3x +(100/3)²) +38 +.03(100/3)²
h(x) = -0.03(x -33 1/3)² +71 1/3
The vertex is (33 1/3, 71 1/3), so the maximum height the water will reach is 71 1/3 feet.
__
When h(x) = 0, the water reaches as far as it possibly can.
0 = -0.03(x -33 1/3)² +71 1/3
(-71 1/3)/(-0.03) = (x -33 1/3)² . . . subtract 71 1/3; divide by -0.03
√(2377.78) = x -33.33 . . . . . . . . positive square root
82.10 ≈ x
The maximum distance the water will reach is 82.10 feet.
After 2 hours, there are 1,400 mL of fluids remaining in a patient’s IV. The fluids drip at a rate of 300 mL per hour. Let x be the time passed, in hours, and y be the amount of fluid left in the IV, in mL. Write a linear function that models this scenario.
Answer:
[tex] y(2) = 1400[/tex]
Using this condition we got:
[tex]1400= -300*2 +b[/tex]
And solving for b we got:
[tex] b= 1400+ 600= 2000[/tex]
So then our linear function is given by:
[tex] y = -300x +2000[/tex]
Where y is the amount of fluid left and x the number of hours ellapsing
Step-by-step explanation:
We want to set up a linear function like this one:
[tex]y = mx+b[/tex]
Where y is the amount of fluid left, m the slope and b the initial amount. From the info given we know thatm = -300. And we also have the following condition:
[tex] y(2) = 1400[/tex]
Using this condition we got:
[tex]1400= -300*2 +b[/tex]
And solving for b we got:
[tex] b= 1400+ 600= 2000[/tex]
So then our linear function is given by:
[tex] y = -300x +2000[/tex]
Where y is the amount of fluid left and x the number of hours ellapsing
A tube of tennis balls has the following measures: a 4 diameter of 4 inches and a height of 8 inches. What is the surface area of the tube of tennis balls?
Answer:
40[tex]\pi[/tex] or 125.66
Step-by-step explanation:
Use the formula 2[tex]\pi[/tex]r² + 2[tex]\pi[/tex]rh
2[tex]\pi[/tex](2)² + 2[tex]\pi[/tex](2)(8)
8[tex]\pi[/tex] + 32[tex]\pi[/tex]
= 40[tex]\pi[/tex] or 125.66
The Fan Cost Index (FCI) represents the cost of four average-price tickets, refreshments, and souvenirs to a sporting event. The FCIs for an independent golf league and an independent arena football league totaled $124.41. The arena football FCI was $7.79 more than that of golf. What were the FCIs for these sports?
Answer:
Golf league FCI = $58.31
Arena football league FCI = $66.10
Step-by-step explanation:
Let G be the fan cost index for the golf league and F be the fan cost index for the football league. The following system of equations can be modeled from the given information:
[tex]F+G = 124.41\\F=G+7.79[/tex]
Solving this linear system (substituting the second equation into the first one):
[tex]7.79+G+G = 124.41\\G= \$58.31\\F = 58.31+7.79\\F=\$66.10[/tex]
Golf league FCI = $58.31
Arena football league FCI = $66.10
which table has the largest area, square tables with a side length of 36 inches, rectangular table 20 inches wide and 73 inches long, round tables with a diameter of 42 inches
Answer:
rectangular table
Step-by-step explanation:
You want to know the largest area of tables that are ...
36 inches square20 inches by 73 inches42 inches in diameterArea FormulasThe formulas for the areas of the various shapes are ...
square: A = s²rectangle: A = LWcircle: A = πr² . . . . . . where r is half the diameterSquareThe area of the square table is ...
A = (36 in)² = 1296 in²
RectangleThe area of the rectangular table is ...
A = (20 in)(73 in) = 1460 in²
CircleThe area of the round table is ...
A = π(21 in)² ≈ 1385 in²
The rectangular table has the largest area.
__
Additional comment
You can eliminate the square table right away by realizing the rectangular table is more than twice as long, and more than half as wide. If the rectangle were 18 in by 72 in, it would have the same area as the square.
True or False - the following scenario depicts an independent relationship between variables (tree growth and air quality): 20% of trees growing in a particular region are not growing to their expected height. In a particular neighborhood in that region, the Air Quality Index is labeled as "Unhealthy for Sensitive Groups" or worse 30% of the time. 10% of the trees in the region grow in this neighborhood. If you randomly measured the growth of a tree in that neighborhood, then the probability that that tree is not growing to its expected height is 33.33%.
The angles of a triangle are such that one angle is 100 degrees more than the smallest angle, while the third angle is 2 times as large as the smallest angle. Find the measure of all three angles.
Answer:
20, 40, 120
Step-by-step explanation:
Smallest angle = x
Second angle = x + 100
Third angle = 2x
4x + 100 = 180
4x = 80
x = 20
20, 120, 40
Write systems of equations from context Lincoln is preparing many gifts for a family holiday party each gift must either be wrapped with wrapping paper or prepared in a gift bag. Lincoln can wrap a single gift in 6.5 minutes and he can do a gift bag in 2 minutes Lincoln prepared a total 13 gifts in 57.5 minutes. Write a system of equations that could be used to determine the number of gifts Lincoln wrapped and the number of gift bags he prepared define the variables that you use to write the system.
Answer:
w + b = 136.5w + 2b = 57.5Step-by-step explanation:
Let w represent the number of gifts wrapped. Let b represent the number of bags prepared.
w + b = 13 . . . . gift bags and gifts wrapped
6.5w +2b = 57.5 . . . . total time spent preparing gifts
_____
Lincoln wrapped 7 gifts and bagged 6.
I need help please! Can someone please I beg you help me
Answer:
Insert x's for every x in your equaton.
Step-by-step explanation:
h(×)=4(-5)+5=-15
h(×)=4(-1)+5= 1
To examine the effect of high-dose green tea extract on weight loss, researchers conducted a randomized, double-blind trial on a random sample of 115 women with obesity from Taiwan. Some of these women were randomly assigned to the main treatment group taking a high-dose green tea extract ("EGCG") daily for 12 weeks. The published abstract of this 2015 study reports that, "Significant weight loss, from 76.8 ± 11.3 kg to 75.7 ± 11.5 kg (p = 0.025), was observed in the treatment group after 12 weeks of high-dose EGCG treatment."
Which of the following inference procedures would be used to reach the quoted conclusion?
a. Z procedure for a proportion
b. Chi-square for two-way tables
c. Chi-square for goodness of fit
d. Two sample t procedure for two means
e. One sample or matched-pairs t procedure for a mean
f. ANOVA for several means
Answer:
d. Two sample t procedure for two means.
Step-by-step explanation:
The study have a treatment group, which is the group of women that are taking the high dose of green tea extract, and a control group, in order to compare. They are assigned randomly to each group.
Then, the difference fo the two sample means is calculated and a t-test is performed in order to conclude if the two populations means are significantly different.
Apparently they are significantly different, as this is the conclusion with a P-value of 0.025.
(3х^2y^3)^3 =
3x^5y^6
9х^6y^9
27x^5y^6
27x^6y^9
Answer:
27x^6y^9
Step-by-step explanation:
The outside exponent multiplies all of the inside exponents. The applicable rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
__
(3x^2y^3) = (3^3)(x^(2·3))(y^(3·3)) = 27x^6y^9
What is a perfect cube and how can you check if a given number is a perfect cube? Explain why.
Answer:
Read below.
Step-by-step explanation:
A perfect cube is a number cubed (If that makes sense). Such as 3³ will equal a perfect cube because it's being multiplied by itself 3 times. 3×3×3=9. It will work for any whole number. You can check if a given number is a perfect cube by using the cube root ([tex]\sqrt[3]{x}[/tex]).
Hope it makes sense!
Step-by-step explanation:
A perfect cube is a cube whose cube root can be easily gotten by using methods such as factor method eg 125 is a perfect cube whose cube root is 5. You can know if a number is a perfect cube 1.) if it gives you a perfect cube root
If x^2-y^2=55 and x-y=5 then what is the value of x
Answer: See below
Step-by-step explanation:
1. x²-y²=55 or (x+y)(x-y)=55
2. x-y=5
Solution (1) (x+y)5=55
______ (2) x+y=55/5
______ (3) x+y=11
______ (4) x+y+x-y=11+5 The equation we got before we can use now
______ (5) 2x+y-y=16 see this y-y=0
______ (6) 2x=16 2x+0=16 that's mean 2x=16
______ (7) x=8 Got the answer
Hope that help
URGENT!!!! WILL GIVE BRANLIEST !!! Find the height, x, of the tree. A) 124.74 ft B) 70.83 ft C) 111.8 ft D) 79.03 ft
Answer:
71.95
Step-by-step explanation:
Use SOH , CAH, TOA
Hypotenuse = N/A
Opposite = 94ft
Adjacent = x
Angle = 37 degrees
Theta = Angle
We are using TOA
T = Tan
O = Opposite
A = Adjacent
Tan(theta) = O/A
Tan(37) = 94/A
Tan(37) x 94 = 71.9489
Rounded to = 71.95
Answer:
70.83 ft
Step-by-step explanation:
I took the quiz got it right
The Coffee Spot recently served 12 pastries, including 3 bran muffins. Considering this data, how many of the next 16 pastries served should you expect to be bran muffins?
Answer:
Number of bran m muffins in 16 pastries = 4 bran muffins
Step-by-step explanation:
Given:
Total number of pastries = 12
Bran muffins (Include) = 3
Find:
Number of bran m muffins in 16 pastries.
Computation:
⇒ Ratio of bran muffins to total pastries = 3 / 12
⇒ Ratio of bran muffins to total pastries = 1 / 4
⇒ Ratio of bran muffins to total pastries = 0.25
Number of bran m muffins in 16 pastries = Number of total pastries × Ratio of bran muffins to total pastries
⇒ Number of bran m muffins in 16 pastries = 16 × 0.25
⇒ Number of bran m muffins in 16 pastries = 4 bran muffins
A 2-column table with 5 rows. Column 1 is labeled Item with entries Italian Salad, Fettucine Alfredo, Subtotal, Sales Tax (5 percent), Total. Column 2 is labeled Price with entries 3 dollars and 99 cents, 7 dollars and 17 cents, 11 dollars and 16 cents, 56 cents, 11 dollars and 72 cents. Abelita and Franco had great service during the meal. They would like to tip the server 20 percent. Which of these expressions would find the total bill, including tax and gratuity? Check all that apply. (0.2)(11.72) 11.72 – [(0.2)(11.72)] 11.72 + [(0.2)(11.72)] (1.2)(11.72)
ASAP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZ!!!!!!!!!!!!!!!!!!!!!!!
Answer:
(C)11.72+[(0.2)(11.72)]
(D)(1.2)(11.72)
Step-by-step explanation:
From the table:
The Total =$11.72
They would like to tip the server 20 percent. Therefore, their total bill will be :
[tex]11.72+(20\%$ of 11.72)\\=11.72+[(0.2)(11.72)][/tex]
We can also re-write this by factorizing as shown below:
[tex]11.72+[(0.2)(11.72)]\\=11.72[1+0.2]\\=(1.2)(11.72)[/tex]
The correct options are C and D,
Answer: c and d
Step-by-step explanation: 2020 edg
The product of 5 and the sum of 12 and a certain number is 10. What is the number 4
Answer:
-10
Step-by-step explanation:
5(12 + x) = 10
60 + 5x = 10
5x = -50
x = -10
The graph shows the estimated value of a piece of land, where x is the number of years since the purchase and y is the estimated value in thousands of dollars. The graph shows the estimated value of a piece of land, where x is the number of years since the purchase and y is the estimated value in thousands of dollars. What was the purchase price of the land? $10,200 $100,000 $102,000 $1,000,000
The correct answer is B. $100,000
Explanation:
The graphic shows how the value of the piece of land changed from the moment it was bought to five years later by relating the value in the y-axis to the years passed in the x-axis. The initial value or purchase price of the land is the value shown in the y-axis at 0 years (x-axis )or the first orange dot because this is the initial value of the land before any time had passed. According to this, the value is $100,000 considering the number in this intersection is 100 but this is the value in thousands of dollars.
Answer:
It's B or $100,000
Step-by-step explanation:
The composite figure is made up of a___a0___a1 on top of a___a2___.a3
Answer:
The composite figure is made up of a rectangular prism on top of a rectangular prism.
Step-by-step explanation:
The figure on top is a rectangular prism. It is a 6 sided figure with each side a rectangle. The figure on bottom is also a rectangular prism. It is a 6 sided figure with each side a rectangle.
Flip the coin below. Suppose that you win a prize if it comes up heads. What is p, the probability of success? What is 1 – p, the probability of failure?
Answer:
"p," the probability of success, is the chance of winning a prize. This is equal to 50% (1/2).
1 - p, the probability of failure, is the chance of not winning or losing a prize. This is equal to 50$ (1 - 0.5).
Step-by-step explanation:
When an outcome is obtained from two events, the probability of the outcome happening is 50% (1/2).
On the other hand, the probability of the intended outcome not happening is the difference between 1 and the probability of obtaining the outcome from the two events. This is statistically expressed as 1 - p.
The probability of getting heads is 1/2 or 0.5 and the probability of failure is 0.5 or 50%.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
Win a prize if it comes up heads.
p(getting heads) = win prize
Number of outcomes = {H, T}
Total number of outcomes = 2
Favourable outcomes = {H}
Number of favourable outcomes = 1
p(getting heads) = 1/2 = 0.5
The complement probability of the above event:
= 1 - p
= 1 - 0.5
= 0.5 or 50%
The above probability represents the chances not getting head or probability of failure.
Thus, the probability of getting heads is 1/2 or 0.5 and the probability of failure is 0.5 or 50%.
Learn more about the probability here:
brainly.com/question/11234923
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I will give brainlisest!!!
Lines x and y are parallel.
Parallel lines x and y are intersected by lines s and t. At the intersection of lines x, t, and s, clockwise from top left, the angles are blank, blank, (6 x + 8) degrees, blank, (7x minus 2) degrees, blank. At the intersection of lines x and y, the angles are 106 degrees, 1, blank, blank. At the intersection of lines y and t, the angles are 2, blank, blank, blank.
Given the diagram, which statement is not true?
m∠1 = (6x + 8)° because they are corresponding angles.
m∠1 = 74° because ∠1 is supplementary to the angle marked 106°.
m∠1 + (6x + 8)° + (7x – 2)° = 180° because they can form a straight line which measures 180°.
(7x – 2)° + m∠2 = 106° because the sum of the remote interior angles equals the exterior angle.
Answer:
the third one since the other ones are correct
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
There are 360 animals on a form 1/5 are cows and 3/8 are sheep then the numbers of cows is
135
72
180
Answer: 72 cows
Step-by-step explanation:
Since the question is asking for cows, we will use the given information to do so. Since 1/5 of the animals are cows, we multiply 1/5 and 360 to find the total amount of cows.
[tex]360*\frac{1}{5} =72[/tex]
Stephanie spent $110 on 1.7 pounds of coffee. she wants to know how much each pound costs. how would she find out how much each pound costs? write equation and explain how you got that answer.
$64.71 rounded, explanation attached
Explain why the terms of the polynomial y2 + 7 are said to be realitvley prime
Answer:
The terms of the polynomial are relatively prime because the highest integer that divides them both is 1.
Step-by-step explanation:
Two numbers are said to be relatively prime if their greatest common factor ( GCF ) is 1 .
Now, the expression we are given in the question is a polynomial;
y² + 7.
The terms of the polynomial y² + 7 are y² and 7 and have no common factor and in fact cannot be factorized further. Thus, these terms are said to be relatively prime because the highest integer that divides them both is 1.
-3
n is an integer.
Write down the possible values of n.
I
Answer:
since n is an integer you substitute n with all the integers. But since that is too much you should use infinity.
n=[-∞,+∞] where -∞ is a negative infinity which stands for negative numbers and +∞ is a positive infinity where it stands for positive numbers.
an integer contains negative and positive numbers so above is the answer.
Step-by-step explanation:
(3x^7)^2 i need help look at the pictures
Answer:
9x^14
Step-by-step explanation:
(3x^7)^2= 3^2x^(7*2)= 9x^14
no picture?
Answer:
[tex]9x^{14}[/tex]
Step-by-step explanation:
[tex](3x^7)^2[/tex]
[tex]3^2 \times x^{7 \times 2}[/tex]
[tex]9 \times x^{14}[/tex]