Answers
[tex]Domain:x\in\mathbb{R^+}[/tex]
[tex]0.5\log_3x=2\ \ \ |\cdot2\\\\\log_3x=4[/tex]
[tex]Use\ the\ de finition\ of\ the\ logarithm:\\\\\log_ab=c\iff a^c=b[/tex]
[tex]Therefore\ we\ have:\\\\\log_3x=4\iff3^4=x\to x=81[/tex]
Answer: C. 81.
[tex]0.5 log_3 (x) = 2[/tex]
Multiply both sides by 10 to get rid of the decimal:
[tex]10 * 0.5 log_3 (x) = 10 * 2[/tex]
[tex]5 log_3 (x) = 20[/tex]
Divide 5 out
[tex]\frac{5 log_3 x}{5} = \frac{20}{5}[/tex]
[tex]log_3 x = 4[/tex]
Now use the log rule [tex]a = log_b b^a[/tex]
[tex]4 = log_3 (3^4) = log_3 (81)[/tex]
Since we have the same base
[tex]log_3 (x) = log_3 (81)[/tex]
x = 81
Related Questions
Line m has a slope of -1 over 5. What is the slope of a line that is perpendicular to line m?
Answers
The line perpendicular to a line with slope = -1/5 has a slope of 5.
eliminate the parameter,t, in the parametric equation, x=6cos t, and y =3 sin t
Answers
To eliminate the parameter t in the parametric equations x = 6 cos t and y = 3 sin t, we can use the trigonometric identity
cos²t + sin²t = 1cos²t + sin²t = 1.
Starting with x=6 cos t, we can rewrite it as cos t=x6 and from y=3 sin t, we can rewrite it as sin t = (y/3).
Now, we square both equations:
(cos t)² = (x/6)²
(sin t)² = (y/3)²
As soon as we multiply both sides by 36, we arrive at:
x² + 4y² = 36
Therefore, the equation x² + 4y² = 36 is the Cartesian equation that eliminates the parameter t from the given parametric equations.
To eliminate the parameter t in the parametric equations x=6 cos t and y=3 sin t, we use trigonometric identities.
From x=6 cost, we get cos t = x//6, and from y = 3 sin t, we get sin t = (y/3).
Squaring both equations and using the identity cos2t+sin2t=1 we obtain (x/6)² + (y/3)² = 1. Simplifying, we get (x²/36) + (y²/9) = 1 which, after multiplying by 36, becomes x² + 4y² = 36. Thus x² + 4y² = 36 is the Cartesian equation eliminating the parameter t.
Complete Question:
Eliminate the parameter, t, in the parametric equation, x=6 cos t, and y =3 sin t.
What is the value of x? sin49°=cosx Enter your answer in the box.
Answers
if sin A=cos B
then
angle A and angle B are complementary angles
A+B=90°
in this problem
sin49°=cosx
so
49°+x=90-------> x=90-49--------> x=41°
the answer is
x=41°
Answer:
[tex]x=41^o[/tex]
Step-by-step explanation:
We have been given an equation [tex]sin(49^o)=cos(x)[/tex] and we are asked to find the value of x.
Since we know that trigonometric ratios are applied to right triangles and we also know that [tex]sin(a)=cos(b)[/tex], where a and b are the angles other than 90 degree angle.
As one angle of our triangle is given 49 degrees, so to find the value of angle x we need to subtract 49 degrees from 90 degree angle as 49 degree angle and x will be equal to 90 degrees.
[tex]x=90^o-49^o[/tex]
[tex]x=41^o[/tex]
Therefore, the value of x is 41 degrees.
Tony is making small bags of bird seed from a larger bag of bird seed that wieghs 11.6 pounds if he puts the same amount in each of 6 bags how much will each bag wiegh?
Answers
Weight each bag = Total weight / number of bags
Substituting values we have:
Weight each bag = (11.6) / (6)
Weight each bag = 1.933333333 pounds
Answer:
each bag will wiegh about:
1.933333333 pounds
one of the largest animal rehab places facilities in Montana. If there success rate, depending on the year is between 35 and 40 percent. According to the website is 2015, 234 raptors were taken in. Based on this data about how many rapotors were successful that year?
Answers
Final answer:
To estimate the number of successful raptors in 2015, we can use the success rate provided by the website. If we assume a success rate of 35 percent, approximately 82 raptors were successful that year.
Explanation:
To estimate the number of successful raptors in 2015, we can use the success rate provided by the website. The success rate is between 35 and 40 percent. So, if we assume a success rate of 35 percent, we can calculate the number of successful raptors as follows:
Number of successful raptors = 35% of 234 raptors
Number of successful raptors = 0.35 * 234
Number of successful raptors = 81.9
Rounding to the nearest whole number, approximately 82 raptors were successful in 2015.
the height of triangle is 8 meters less than its base. if the area of the triangle is 212.5 square meters, find the length of its bas and heiight.
Answers
b = length of base in meters, then
h = (b-8) m
Area of a triangle, A = (1/2)bh
Therefore,
212.5 = (1/2)(b)(b-8) = (1/2)(b^2-8b)
425 = b^2-8b
b^2 - 8b -425 =0
Solving the resulting quadratic equation;
b = [8+/- Sqrt [8^2 - 4(1)(-425)]]/2(1) = 4+/- 21 = 4+21 = 25 m (ignore negative value as it is not applicable)
Then,
h = b-8 = 25 - 8 = 17 m
Therefore,
Base = 25 m
Height = 17 m
Final answer:
The base of the triangle is 25 meters, and the height is 17 meters. This was calculated using the area formula for a triangle and by solving the resulting quadratic equation by using the quadratic formula.
Explanation:
The area of a triangle is given by the formula 1/2 × base × height. Given that the area is 212.5 square meters and the height is 8 meters less than the base, let's call the base 'b' and the height will then be 'b - 8'. Using the area formula:
Area = 1/2 × base × height
212.5 = 1/2 × b × (b - 8)
Multiplying both sides by 2 to get rid of the 1/2 gives:
425 = b × (b - 8)
Now we have a quadratic equation in the form of:
b² - 8b - 425 = 0
We can solve this equation by factoring or using the quadratic formula. In this case, the equation doesn't factor neatly, so we use the quadratic formula:
b = (-(-8) ± √((-8)² - 4 × 1 × (-425)))/(2 × 1)
b = (8 ± √(64 + 1700))/2
b = (8 ± √(1764))/2
b = (8 ± 42)/2
Since the base cannot be negative, we take the positive root:
b = (8 + 42)/2
b = 25 meters
Therefore, the base of the triangle is 25 meters and the height is b - 8 = 25 - 8 = 17 meters.
What is the volume of the cylinder below? Radius of 8 height of 3
Answers
So 3.14x8^2x3
8^2 (8 squared=64)
So the answer is 3.14x64x3 which equals 602.88
The volume of the cylinder is
[tex]V= 602.88 \: square \: units[/tex]
EXPLANATION
The formula for calculating the volume of a cylinder is,
[tex]V = \pi \: {r}^{2} h[/tex]
Where
[tex]r = 8[/tex]
is the radius of the cylinder and
[tex]h = 3[/tex]
is the height of the cylinder.
Also we use the approximate value for π which is
[tex]3.14[/tex]
We substitute the above values into the formula to get
[tex]V = 3.14\times {8}^{2} \times 3[/tex]
[tex]V =3.14\times 64 \times 3[/tex]
[tex]V = 602.88 \: square \: units[/tex]
Hence the volume of the cylinder is 602.88 square units.
hey can you please help me posted picture of question
Answers
144
Explanation:
In the closet, we have:
6 pairs of pants
8 shirts
3 pairs of shoes
To know the number of possible combinations that could be made from the available objects, all we have to do is multiply all three numbers together.
Therefore:
possible outcomes = number of pants * number of shirts * number of shoes
possible outcomes = 6 * 8 * 3
possible outcomes = 144
This means that the tree diagram would have 144 leaves to represent all possible combinations.
Hope this helps :)
5 Stars and Brainliest to correct answer
Answers
r = 2 - 2sin(θ)
The measure of forecast error when the average absolute error of each forecast is shown as a percentage of demand is
Answers
_________________________________________________________
You invest $230 to start a sandwich stand and decide to charge $4.25 per sandwich. How much money will you make if you sell 75 sandwiches?
Answers
So you'll make $318.75
We have been given that the cost to start the sandwich stand is $230.
Now, the cost of one sandwich is given by $4.25
Also, it has been given that total 75 sandwiches sold.
Thus, the cost of 75 sandwiches is given by
[tex]75 \times 4.25\\ \$ 318.75[/tex]
Now, the sandwich stand cost $230 and the earning in selling of 75 sandwiches is $ 318.75.
Therefore, the profit is given by
[tex]318.75-230 =\$88.75[/tex]
Hence, I can make $88.75 on selling of 75 sandwiches.
HELP ASAP! Which figure shows how a shape can be rotated about an axis to form the given object?
Answers
Answer:
Option D.
Step-by-step explanation:
To find the answer we will analyse each options.
Option A.
If we rotate a semicircle by a vertical axis then an sphere will be formed. Therefore this option is not correct.
Option B.
In this rotation we will get a hollow sphere, so this option is also not correct.
Option C.
By rotation of a strip we will find the shape similar to the given object but there will not be a hole at the center. Therefore, the option is not correct.
Option D.
When we rotate this strip with a distance from vertical axis, we will find the same shape as given in the picture.
Option D is the correct option.
The probability that it will snow on Friday is 70%, and the probability that it will snow on Saturday is 50%.
What is the probability that it will snow on both days? Express your answer as a decimal rounded to the nearest hundredth.
What is the probability that it will not snow on either day? Express your answer as a decimal rounded to the nearest hundredth.
Answers
P(Snow Saturday) = 0.3, P(No snow Saturday) = 1-0.3 = 0.7
Then,
P(Snow Friday) and P(Snow Saturday) = 0.7*0.3 = 0.21
P(No snow Friday) and P(No snow Saturday) = 0.3*0.7 = 0.21
write an inequality to represent the situation. the temperature stayed above -15 degrees
Answers
t > -15°
t will represent temperature
t > -15°
(a^3 / 4)^2
Simplify
Answers
I hope this helps!
-Raiden
Jim is climbing a mountain that has a base 150 feet above sea level. If he climbs 233 feet then descends into a cave 64 feet, how far above sea level is Jim? A. 86feet, B. 169 feet, C. 214 feet, D. 319 feet.
Answers
1) Jim is climbing a mountain that has a base -----> 150 ft above sea level
2) He climbs 233 ft------------> 150 ft+233 ft----> 383 ft above sea level
3) He descends into a cave 64 ft------> 383 ft-64 ft----> 319 ft above sea level
the answer is
the option
D. 319 feet.
Which of the choices below represents the definition of information secrecy?
Answers
Secrecy (also called clandestinity or furtiveness) is the practice of hiding information from certain individuals or groups who do not have the "need to know", perhaps while sharing it with other individuals. That which is kept hidden is known as the secret.
Which distance measurement is the most precise?
A). 20.1 yards
B). 7 yards
C). 15.98 yards
D). 19 yards
Answers
Answer:
Step-by-step explanation:
Alright, lets get started.
The most precise measurement is, the one which has most numbers after the decimal.
The number round off to hundred decimal place is more precise than the number round off to tenth decimal place.
There are 4 different numbers in which two numbers are complete number 7 and 19.
20.1 is rounded off to nearest tenth.
15.98 is rounded off to nearest hundred.
So, 15.98 yards is the most precise. : Option C
Hope it will help :)
Answer:
15.98 yards
Step-by-step explanation:
Concerned about graffiti, mayors of nine suburban communities instituted a citizen community watch program. community monthly incidents after monthly incidents before burr oak 2 7 elgin corners 3 2 elm grove 6 2 greenburg 4 3 huntley 5 11 north lyman 3 9 south lyman 3 5 pin oak 5 7 victorville 2 3 click here for the excel data file (a) choose the appropriate hypotheses to see whether the number of graffiti incidents declined. assume μd is the mean difference in graffiti incidents before and after.
Answers
After it, the mean and standard deviation of the differences should also be calculated. Then, we state the null and alternative hypotheses.
The null hypothesis is [tex]H_{0}: \mu_d=0[/tex]
The alternative hypothesis is [tex]H_a: \mu_d\ \textgreater \ 0[/tex]
These are the required hypotheses to see whether the number of graffiti incidents declined.
The null hypothesis H₀ represents what is believed true if the data don't prove the opposite.
The alternative hypothesis H₁ is the conclusion we want to deduce from the test.
If we call d the difference in graffiti before (B) and after (A) (pay attention to the order) d = B - A.
We want to prove that the incidents are declined, therefore B should be greater than A and d would be positive.
Therefore:
H₀ : μd ≤ 0
H₁ : μd > 0
simplify: -7/3 - (-61/6)
Answers
Final Answer: 47/6
Answer is=47/6[/tex]
Hope it helped you.
-Charlie
please help!!! trying to finish early
Answers
The linear functions have the form y=mx+b
where m is the slope and b is the y- intercept
Therefore, you have:
1) The slope -6/5 and b=(0,8) is:
y=(6/5)x+8
2) You have 3x-2y=1. Then, you only have to clear y:
y=(3/2)x-1/2
Y=-6x-5 x and y intercept form
Answers
y intercept = -5
Now solve for x.
y = -6x - 5
-6x = y + 5
x = -1/6y - 5/6
x intercept = -5/6
Ginger is filing her federal income tax return with the 1040EZ form, and she received two W-2 forms, with the federal income tax withheld on one being $4530, and the federal income tax withheld on the other being $540. If Ginger received a Making Work Pay credit of $400, and if lines 9a and 9b in the Payments, Credits, and Tax section below are $0, what should she enter on line 10?
A. $4670
B. $4930
C. $5470
D. $5070
Answers
Answer - C
Add 4530 + 540 + 400 = 5470
You spend $77 shopping. You buy some shirts at $12 each, and spend $5 on food. How many shirts did you buy?
A.
5x + 12 = 77
B.
x(12 + 5) = 77
C.
12x + 5 = 77
D.
12*5+x=77
Answers
12x + 5 = 77
This means that the correct answer to your question is going to be option C.
Let me know if you have any further questions.
:)
Scientists discovered a large star 400,000 light years from Earth.A light-year is about 5,880,000,000,000 miles.What is the distance of the large star from Earth in scientific notation?
Answers
2.35200000E+18. So your answer would be 2.35200000E+18 in scientific notation it would be 2.35200000x10^18. I hope this helps!
The graph represents f(x), and g(x) = 7x – 42.
Which statement about these functions is true?
A) The y-intercept of g(x) is less than the y-intercept of f(x).
B) The y-intercept of g(x) is greater than the y-intercept of f(x).
C) The x-intercept of g(x) is less than the x-intercept of f(x).
D) The x-intercept of g(x) is greater than the x-intercept of f(x).
Answers
[tex]f(x)=ax+b\\\\y-intercept\ of\ f(x):\ (0;\ -3)\\\\x-intercept\ of\ f(x):\ (6;\ 0)[/tex]
Answer:
A) the y-intercept of g(x) is less than the y-intercept of f(x).
Clem Colfax had $10 to buy groceries. He needed milk costing 70 cents a carton, bread costing 60 cents a loaf, breakfast cereal costing 50 cents a box, and meat costing $1.50 a pound. He bought twice as many cartons of milk as he did loaves of bread, the number of boxes of cereal was one more than the number of loaves of bread, and the number of pounds of meat was the same as the number of boxes of cereal. How many of each did he buy if the total he spent was exactly $10?
Answers
w: pounds of meat
x: carton of milk
y: loaf of bread
z: cereal breakfast box
We write the system of equations:
0.70x + 0.60y + 0.50z + 1.50w = 10
x = 2y
z = y + 1
w = z
Solving the system we have:
w = 3
x = 4
y = 2
z = 3
Answer:
3 pounds of meat
4 cartons of milk
2 loaves of bread
3 boxes of breakfast cereal
Find the work done by the force field f(x,y,z)=3xi+3yj+7kf(x,y,z)=3xi+3yj+7k on a particle that moves along the helix r(t)=3cos(t)i+3sin(t)j+3tk,0≤t≤2π
Answers
Swapping the [tex]\mathbf{ijk}[/tex] notation out for ordered component notation, I'll write
[tex]\mathbf r(t)=(x(t),y(t),z(t))=(3\cos t,3\sin t,3t)[/tex]
so that
[tex]\dfrac{\mathrm d\mathbf r}{\mathrm dt}=(-3\sin t,3\cos t,3)[/tex]
The line integral reduces to[tex]\displaystyle\int_0^1(9\cos t,9\sin t,7)\cdot(-3\sin t,3\cos t,3)\,\mathrm dt[/tex][tex]=\displaystyle\int_0^1(-27\cos t\sin t+27\sin t\cos t+21)\,\mathrm dt[/tex][tex]=\displaystyle21\int_0^1\mathrm dt=21[/tex]
For 10 days in a row Fiona and Gary timed how long they brushed their teeth
Find the mean of each data set
Answers
(x+y)/6
The mean or the average of a number is calculated by adding the frequencies of the given data and then dividing by the total frequency. It is represented by the formula mentioned under -
Mean = [tex] \frac{Sum of all the frequencies}{Number of frequencies} [/tex]
Similarly, here, we need to find the mean of their time spent in brushing.
It will be calculated as -
For Fiona
Mean of time spent in brushing = [tex] \frac{Sum of the total time spent in 10 days}{10 days} [/tex]
Similarly, for Gary
Mean of time spent in brushing = [tex] \frac{Sum of the total time spent in 10 days}{10 days} [/tex]
Suppose sarah is trying to design a metal box (a rectangular prism), which will hold 200 cubic centimeters of liquid. the length of the box must be 4 times as large as the width.
Answers
so 2000 cm^3 = lwh
we know that l = 4w so sub that into the equation
2000 = (4w)*w*h
2000 = 4w^2*h
You didn't include the rest of the question so this is as far as i can go.