Answer:
x = -1/4
Step-by-step explanation:
[tex]81^{x}[/tex] = 1/3
[tex]3^{4}^{x}[/tex] = [tex]3^{-1}[/tex]
4x = -1
x = -1/4
Answer:
x = - [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Using the rules of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
Given
[tex]81^{x}[/tex] = [tex]\frac{1}{3}[/tex] [ note that 81 = [tex]3^{4}[/tex] ] , then
[tex](3^4)^{x}[/tex] = [tex]3^{-1}[/tex] , that is
[tex]3^{4x}[/tex] = [tex]3^{-1}[/tex]
Since the bases on both sides are equal, both 3, then equate exponents
4x = - 1 ( divide both sides by 4 )
x = - [tex]\frac{1}{4}[/tex]
Tile is to be placed in an entryway, as shown below.
At $6.25 per square foot, how much does it cost to tile the entryway?
Calculate the area by using 2 rectangles:
13 x 5 = 65 square feet
5 x 4 = 20 square feet
Total area = 65 + 20 = 80 square feet.
Multiply price per square foot by total area:
6.25 x 80 = 500
Cost = $500
10. In a group of 50 people, there are two types of professionals, engineers and managers. If 36 of them are engineers and 24 of them are managers, how many persons are both managers and engineers?
Step-by-step explanation:
The photo above is the Venn diagram
Now, the number of persons that are both managers and engineers= n
Since, Total number of persons is 50
Therefore, 50= M+n+E
M only = 36-n
E only = 24-n
Therefore, 50= 36 - n + n + 24 - n
50 = 36+24-n
50 = 60 - n
60 - n = 50
-n = 50 - 60
-n = - 10
Therefore, n = 10
Therefore, the number of persons that are both Managers and Engineers is 10persons.
Wesley is making a patio from stones of two sizes, 5 inch wide and 10 inch wide. He wants to begin and end his pattern with a 10 inch stone so there will be one more of the 10 inch stones than of 5inch stones. His patio will be 130 inches wide.
How many 10 inch stones will Wesley need for one row?
9514 1404 393
Answer:
9
Step-by-step explanation:
If x is the number of 10-inch stones, then (x-1) is the number of 5-inch stones, and the total width is ...
10x +5(x-1) = 130
15x -5 = 130 . . . . . . . eliminate parentheses
15x = 135 . . . . . . add 5
x = 9 . . . . . . . divide by 15
Wesley will need 9 10-inch stones for one row.
You have $2,000 on a credit card that charges a 16% interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?
9514 1404 393
Answer:
$48.64
Step-by-step explanation:
The monthly payment amount is given by the amortization formula ...
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where P is the loan amount, r is the annual interest rate compounded n times per year for t years.
Here, you have P=2000, r=0.16, n=12 (months per year), t=5 (years), so the payment is ...
A = $2000(0.16/12)/(1 -(1 +0.16/12)^(-12·5)) = $320/(12(0.54828942))
A ≈ $48.636 ≈ $48.64
You will need to pay $48.64 each month to pay off the charge in 5 years.
3. In A PQR, MZP=(4x-5),
m2Q=(8x-50), and MZR=(3x+10).
Which of the following best describes
APQR?
® Right triangle
® Isosceles triangle
© Equlateral triangle
Scalene triangle
Answer:
B
Step-by-step explanation:
The sum of all of them will result in 180. 15x-45=180. x=15. P=55, Q=70 and R=55. It's an isosceles triangle
Answer:
b
Step-by-step explanation:
its b
write your answer in simplest radical form
Answer:
x = 2 yd
Step-by-step explanation:
Angles of 45 degreees = two congruent legs
for the Pythagorean theorem
2x^2 = 8
x^2 = 4
x = 2
? Question
Use the drawing tools to form the correct answer on the graph.
Graph this step function:
Answer:
start on (0,1) and go up two and left three. keep going until you run out of room. then, draw a line through the points.
Step-by-step explanation:
Find theta to the nearest tenth of a degree, if theta is between 0 degrees and 360 degrees for sin theta = 0.4649 with theta in quadrant 2
9514 1404 393
Answer:
152.3°
Step-by-step explanation:
The arcsine function only gives angles in quadrants I and IV. Since this is a quadrant II angle, its value will be ...
θ = 180° -arcsin(0.4649) = 180° -27.7°
θ = 152.3°
Solve for the unknown variable
4y-2=8-2y+4y
y=?
Step-by-step explanation:
I hope it helped and it is easy to understand i hope it was helpful
1)4y-2=8-2y+4y
=4y-2y+4y=8-2
2y +4y=8-2
6y+6
12
please help
Question: 6b = 18
Answer: ?
Answer:
6b=18
b=18/6
b=3
.
.
.
.
.
.
Answer:
6b=18
b=18/6
b=3
.
Step-by-step explanation:
Translate and solve: fife less than z is 4
Answer:
z=9
Step-by-step explanation:
z-5=4. /+5
z=4+5
z=9
Answer:
z<-1
Step-by-step explanation:
5<z=4
collect like terms
z=<4-5
z<-1
Tìm diện tích của mặt. Phần mặt x2+y2+z2=9 nằm bên trên mặt phẳng z=1.
If you're familiar with surface integrals, start by parameterizing the surface by the vector-valued function,
r(u, v) = 3 cos(u) sin(v) i + 3 sin(u) sin(v) j + 3 cos(v) k
with 0 ≤ u ≤ 2π and 0 ≤ v ≤ arccos(1/√8).
Then the area of the surface (I denote it by S) is
[tex]\displaystyle\iint_S\mathrm dA = \int_0^{2\pi}\int_0^{\arccos\left(1/\sqrt8\right)}\left\|\dfrac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm dv\,\mathrm du \\\\ = \int_0^{2\pi}\int_0^{\arccos\left(1/\sqrt8\right)}9\sin(v)\,\mathrm dv\,\mathrm du \\\\ =18\pi \int_0^{\arccos\left(1/\sqrt8\right)}\sin(v)\,\mathrm dv = \boxed{\frac{9(4-\sqrt2)\pi}2}[/tex]
The mean output of a certain type of amplifier is 102102 watts with a standard deviation of 1212 watts. If 6363 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by greater than 3.43.4 watts
Answer:
0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Mean of 102, standard deviation of 12:
This means that [tex]\mu = 102, \sigma = 12[/tex]
Sample of 63:
This means that [tex]n = 63, s = \frac{12}{\sqrt{63}}[/tex]
What is the probability that the mean of the sample would differ from the population mean by greater than 3.4 watts?
Below 102 - 3.4 = 98.6 or above 102 + 3.4 = 105.4. Since the normal distribution is symmetric, these probabilities are equal, and thus, we find one of them and multiply by two.
Probability the mean is below 98.6.
p-value of Z when X = 98.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{98.6 - 102}{\frac{12}{\sqrt{63}}}[/tex]
[tex]Z = -2.25[/tex]
[tex]Z = -2.25[/tex] has a p-value of 0.0122.
2*0.0122 = 0.0244
0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.
A welding drawing shows that the weld-root reinforcement cannot exceed
" in thickness. Your weld measurement tools are metric, so this value needs to be converted to millimeters. You know that one inch equals 2.54 centimeters. What is the maximum weld-root reinforcement allowed in millimeters? Round your answer to the nearest tenth of a millimeter.
Answer:
3.2 millimeters
Step-by-step explanation:
1/8*2.54 *10 = 3.175
= 3.2 millimeter. (rounded to nearest tenth)
The bar graph shows the z-score results of four students on two different mathematics tests. The students took Test 1 and then, a month later, took Test 2. Which student had the lowest score on Test 2? Euan Felicia Dave Carla
Answer:
euan had lowest score on test 2
The student with lowest score on test 2 is Euan.
What is bar graph ?Bar graph is used for the graphical representation of data or quantities by using bars or strips.
Here,
The z-score results of four students on two different mathematics tests is represented by the given bar graph.
Calculating the scores of each students for the two tests respectively.
1) Carla
Test 1: 0.75
Test 2: -0.5
2) Dave
Test 1: -0.5
Test 2: 1
3) Euan
Test 1: 0.25
Test 2: -1
4) Felicia
Test 1: 1.25
Test 2: 1.5
Hence,
The student with lowest score on test 2 is Euan.
To learn more about bar graph, click:
https://brainly.com/question/17343218
#SPJ3
solve for x please help (show work)
Answer:
x=-2
Step-by-step explanation:
3x+8x - 3 = -25
Combine like terms
11x -3 = -25
Add 3 to each side
11x -3+3 = -25+3
11x = -22
Divide by 11
11x/11 = -22/11
x = -2
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:3x \: + \: 8x \: - \: 3 \: = \: - 25[/tex]
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:11x \: - \: 3 \: = \: - 25[/tex]
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:11x \: = \: - 25 \: + \: 3[/tex]
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:11x \: = \: - 22[/tex]
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \: x \: = \: {\cancel\frac{ {- 22} \:^{ - 2} }{11}} \\ [/tex]
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:x \: = \: - 2[/tex]
find the equation of the line
A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds. Test at an alpha level at α=.05 and report results using APA format.
Answer:
Hence we do not have enough evidence to conclude that a liquid diet caused more weight loss.
Step-by-step explanation:
Here the answer is given as follows,
Part C
Based on feedback from an independent research firm, the flashlight manufacturer has decided to change the design of the flashlight. The reflector now needs to extend 4 centimeters past the center of the bulb, as shown in the diagram. In the new design, how wide will the reflector (CD) be at its widest point? Show your work.
Answer:
The answer is "18".
Step-by-step explanation:
In the given graph by concluding we observe that on the x-axis, one step is 2 units, and when we half each of the steps it will= 1 unit
[tex]\therefore\\\\CD = distance\ from\ -(8+1)\ to\ (8+1)\ = \text{distance between} -9 \ to\ 9\ = 18[/tex]
Help me with this please.
Answer:
the answer should be B
Step-by-step explanation:
take the total of people who got the flu(63) and the amount of them who were vaccinated(35) and write it as a fraction. 35/63 in its simplest form is 5/9
Consider the graph below, and identify the piecewise function that describes it.
Answer:
f(x)=-x when x belongs to (-infinity, 3)
f(x)=-2 when x belongs to [3, 6]
f(x)=2x-7 when x belongs to (6, infinity)
Average person who drives car in United States drives 15, 350 miles which is 50% more than an average driver in Europe. We assume that the number of yearly miles by U.S. drivers is approximately a normal random variable of standard deviation of 4200 miles. Calculate percent of drivers who traveled between 10,000 to 12,000 miles in a year.
Answer:
7,675
that is your answer
I need help this is confusing to me
Answer:i think it is b not really sure
Step-by-step explanation:
find the volume of the following figure round your answer to the nearest tenth if necessary and make sure to use pi
Answer:
524cm^2
Step-by-step explanation:
Formula for Volume of sphere= 4/3 πr^2
We have,
r=5cm
Now,
Volume(v)=4/3 πr^2 = 4/3π 5^3= 4/3π 125 = 166.666666667π = 523.598775599
Rounding to the nearest tenth,
Volume=524cm^2
The answer pl shhaoksngausinxbbs pls
Answer:
D. 3
Step-by-step explanation:
A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
Simply stated, any polygon with three (3) lengths of sides is a triangle.
In Geometry, a triangle is considered to be the most important shape.
Generally, there are three (3) main types of triangle based on the length of their sides and these include;
I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.
II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.
III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.
In Geometry, an acute angle can be defined as any angle that has its size less than ninety (90) degrees.
Hence, we can deduce that the greatest number of acute angles that a triangle can contain is three (3) because the sum of all the interior angles of a triangle is 180 degrees.
round 32.68 to the nearest hundredth
Answer:
32.70
Step-by-step explanation:
round up
if PQR measures 75° , what is the measure of SQR
Answer:
PQR+SQR=180°(angles in a triangle)
75°+SQR=180°
SQR=180°-75°
SQR=105°
This semester, the tuition fee increased to $5,871. If this represents an increase by 14%, what was the original fee?
Rotation 90° counterclockwise around the origin of the point (-8,1)
A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trip times to be normally distributed.
(a) What is the probability that a trip will take at least ½ hour?
(b) If the office opens at 9:00 A.M. and he leaves his house at 8:45 A.M. daily, what percentage of the time is he late for work?
(c) If he leaves the house at 8:35 A.M. and coffee is served at the office from 8:50 A.M. until 9:00 A.M., what is the probability that he misses coffee?
(d) Find the length of time above which we find the slowest 10% of trips.
(e) Find the probability that 2 of the next 3 trips will take at least one half
1/2 hour.
Answer:
Step-by-step explanation:
a) Probability-Above 30 min = 5.72% = .0572
b) Probability-Above 15 min = 99.11% = .9911
c) *Probability-Between 1 - 59.49% = .4051
d) 19.136 minutes z = -1.28
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
What do you mean by normal distribution ?
A probability distribution known as a "normal distribution" shows that data are more likely to occur when they are close to the mean than when they are far from the mean.
Let assume the time taken for a one way trip be x .
x ⇒ N( μ , σ ²)
x ⇒ N( 24 , 3.8 ²)
a)
The probability that trip will take at least 1/2 hour or 30 minutes will be :
P ( x ≥ 30)
= P [ (x - μ) / σ ≥ (30 - μ) / σ ]
We know that , (x - μ) / σ = z.
= P [ z ≥ (30 - 24) / 3.8)]
= P [ z ≥ 1.578 ]
= 1 - P [ z ≤ 1.578 ]
Now , using the standard normal table :
P ( x ≥ 30)
= 1 - 0.9394
= 0.0606
b)
The percentage of the time the lawyer is late for work will be :
P ( x ≥ 15)
= P [ z ≥ -2.368 ]
= P [ z ≤ 2.368]
= 0.9918
or
99.18%
c)
The probability that lawyer misses coffee :
P ( 15 < x < 25 ) = P ( x < 25 ) - P ( x < 15)
= P [ z < 0.263] - P ( z < -2.368)
or
= 0.3659
d)
The length of time above which we find the slowest 10% of trips :
P( x ≥ X ) ≤ 0.10
= 0.5438
e)
Let's assume that y represents the number of trips that takes at least half hour.
y ⇒ B ( n , p)
y ⇒ B ( 3 , 0.0606)
So , the probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is :
P ( Y = 2 )
= 3C2 × (0.0606)² × ( 1 - 0.0606)
= 0.0103
Therefore , the answers are :
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
Learn more about normal distribution here :
https://brainly.com/question/26822684
#SPJ2
