Answer:
Option C.
Step-by-step explanation:
The given logarithmic equation is
[tex]\log_2(x+11)=4[/tex]
It can be written as
[tex](x+11)=2^4[/tex] [tex][\because log_ax=y\Leftrightarrow x=a^y][/tex]
[tex]x+11=16[/tex]
[tex]x=5[/tex]
Now, to check whether [tex]x=5[/tex] is a true solution or not. Substitute [tex]x=5[/tex] in the LHS of given equation.
[tex]LHS=\log_2(5+11)[/tex]
[tex]LHS=\log_2(16)[/tex]
[tex]LHS=\log_22^4[/tex]
[tex]LHS=4[/tex] [tex][\because log_aa^x=x][/tex]
[tex]LHS=RHS[/tex]
Hence, [tex]x=5[/tex] is a true solution because [tex]\log_2(16)=4[/tex].
Therefore, the correct option is C.
Answer:
C on edge2021
Step-by-step explanation:
A plane intersects the prism perpendicular to the base, intersecting opposite sides of the base. Which best describes the cross section?
Answer:
Step-by-step explanation:
For a rectangular prism, a plane intersecting this prism produces a two dimensional figure as its cross section and in this case the cross section is a rectangle.
For a triangular prism, a plane intersecting this prism produces a two dimensional figure as its cross section and in this case the cross section is a triangle.
2/5 of the members of a school band are 6th graders. What percent of
the students in the band are non-sixth graders?
Answer:
60%
Step-by-step explanation:
3/5 is 60%
Answer:
60%
Step-by-step explanation:
5/5 minus 2/5 is 3/5
5 divided by 3 is .6
in order to find out the percent move the decimal over to the right
If \\(z_1=3+2i\\) and \\(z_2=4+3i\\) and are complex numbers, find \\(z_1z_2\\)
[tex]z_1z_2=(3+2i)(4+3i)=3\cdot4+2i\cdot4+3\cdot3i+2i\cdot3i[/tex]
[tex]z_1z_2=12+8i+9i+6i^2[/tex]
[tex]i^2=-1[/tex], so
[tex]z_1z_2=12+8i+9i-6=\boxed{6+17i}[/tex]
If 9x+2y^2−3z^2=132 and 9y−2y^2+3z^2=867, then x+y =
Answer:
[tex]x + y = \frac{1000}{9}[/tex]
Step-by-step explanation:
Step 1: Identify the approach:
With this problem, the general solution is to try manipulate given data and transform data into a new form, in which, the desired value [tex](x + y)[/tex] is on the left side and all of other components which do not contain [tex]x[/tex] or [tex]y[/tex] are on the right side.
Step 2: Analyze:
[tex]9x + 2y^{2} - 3z^{2} = 132\\9y - 2y^{2} + 3z^{2} = 867[/tex]
Realize that in both equations, the [tex]2y^{2}[/tex] and [tex]3z^{2}[/tex] are in form of different signs. Then adding up corresponding sides of both equation can help eliminate these undesired components.
Step 3: Perform manipulation:
[tex]9x + 2y^{2} - 3z^{2} + 9y - 2y^{2} - 3z^{2} = 132 + 867[/tex]
Rearrange:
[tex](9x + 9y) + (2y^{2} - 2y^{2}) +(3z^{2} - 3z^{2}) = 132 + 867[/tex]
Simplify:
[tex]9(x + y) + 0 + 0 = 1000[/tex]
Simplify:
[tex]x + y = \frac{1000}{9}[/tex]
Hope this helps!
:)
At the beginning of year 1, Paolo invests $500 at an annual compound
interest rate of 4%. He makes no deposits to or withdrawals from the
account.
Which explicit formula can be used to find the account's balance at the
beginning of year 5? What is the balance?
Answer:
see below
Step-by-step explanation:
The way the problem is worded, we expect "n" to represent the year number we're at the beginning of. That is the initial balance is that when n=1, and the balance at the beginning of year 5 (after interest accrues for 4 years) is the value of obtained when n=5.
After compounding interest for 4 years, the balance will be ...
500·1.04^4 = 584.93
The matching answer choice is shown below.
Answer:
b
Step-by-step explanation:
Question 1 of 20 :
Select the best answer for the question.
1. Divide7/15 by 3/5
OA%
O B./25
O c. 75/21
O D.21/75
Answer:
7/9
Step-by-step explanation:
7/15 ÷ 3/5
Copy dot flip
7/15 * 5/3
7/3 * 5/15
7/3 * 1/3
7/9
Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone. What probability distribution describes this situation and what are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day
Answer:
We use the binomial distribution to describe this situation.
The mean number of phone sales is 749.7 with a standard deviation of 15.
Step-by-step explanation:
For each shopper, there are only two possible outcomes. Either they plan to purchase the newly released smart phone, or they do not. Each customer is independent of other customers. So we use the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone.
This means that [tex]p = \frac{35}{50} = 0.7[/tex]
What are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day
1071 shoppers, so [tex]n = 1071[/tex]
Mean
[tex]E(X) = 1071*0.7 = 749.7[/tex]
Standard deviation
[tex]\sqrt{V(X)} = \sqrt{1071*0.7*0.3} = 15[/tex]
The mean number of phone sales is 749.7 with a standard deviation of 15.
What is the equation of the line that passes through (5, -2) and (-3, 4)?
Answer:
y = (-3/4)x + 7/4
Step-by-step explanation:
Step 1: Define general form of equation of line
An equation of a straight line on two-dimensional plane could be represented in form of: y = Mx + b, with M is slope and b is y-intercept
Step 2: Set up the system to solve for parameters of equation of line
(solve for M and b)
That equation passes 2 points, which are represented in form of (x, y), (5, -2) and (-3, 4).
Substitute these values of x and y into the original equation in step 1:
-2 = 5M + b
4 = -3M + b
Step 3: Solve the system of equations in step 2 for M and b
Subtract 1st equation from 2nd equation:
6 = -8M
=> M = -6/8 = -3/4
Substitute M back into 1st equation:
=> -2 = 5*(-3/4) + b
=> b = -2 + 15/4
=> b = 7/4
=> The equation of the line that passes through (5, -2) and (-3, 4):
y = (-3/4)x + 7/4
Hope this helps!
:)
Answer:
Y= -4/3(x-7/2)
Step-by-step explanation:
So first calculate the difference between them,
changes by 8 x units, and -6 y units.
Then substitute them into y/x to find gradient
-6/8 = -4/3
so now we have a part of the equation:
Y= -4/3(x-a)
substitute Y= -2 and x=5 (from (5,-2))
-2= -4/3(5-a)
-2= -20/3+4a/3
Multiply by 3 on both sides
-6= -20+4a
add 20 on both sides
14=4a
a=7/2
use this as the value of a
Y= -4/3(x-7/2)
An oval shaped walking path at a local park is 3/4 of a mile long. Four walkers recorded the number of laps they walked and the time it took them in them.
laps Minutes
Amber. 3. 40. Bruno. 4. 54. Cady. 5. 75. Drake. 6. 72.
Match each walker to their corresponding unit rate in miles per hour................................................. 3 3/4 mph, 3 mph, 3 1/2mph, 3 1/4 mph, 3 3/8 mph and 3 2/3mph
Answer:
Amber = 3 3/8 mphBruno = 3 1/3 mphCady =3 mphDrake = 3 3/4 mphStep-by-step explanation:
Consider the calculations in the table below with the respective columns being: Name | Laps | Time | Time(in hours) |Total Distance | Unit Rate
[tex]\left|\begin{array}{c|c|c|c|c|c}---&---&---&----&----&---\\Amber&3&40&\frac{40}{60}&3*\frac{3}{4}=2.25&2.25 \div \frac{40}{60}= 3\frac{3}{8} \\\\Bruno&4&54&\frac{54}{60}&4*\frac{3}{4}=3&3 \div \frac{54}{60}= 3\frac{1}{3}\\\\Cady&5&75&\frac{75}{60}&5*\frac{3}{4}=3.75&3.75 \div \frac{75}{60}= 3 \\\\Drake&6&72&\frac{72}{60}&6*\frac{3}{4}=4.5&4.5 \div \frac{72}{60}= 3\frac{3}{4} \end{array}\right|[/tex]
We can then match each walker to their respective unit rates in miles per hour.
Amber = 3 3/8 mphBruno = 3 1/3 mphCady =3 mphDrake = 3 3/4 mph2. The width of a rectangle is 12 inches less than its length. The perimeter of the rect-
angle is 56 inches. Find the length and width of the rectangle.
Answer:
[tex] P= 2*Lenght + 2*Width[/tex]
Since the perimeter is 56 inches we can solve for the lenght with this equation:
[tex] 56 in = 2*12in + 2*Length[/tex]
And solving for the length we got:
[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]
So then the lenght = 16 inhes and the width of 12 inches
Step-by-step explanation:
For a rectangle of width 12 inches and lenght y inches we know that the perimeter is given by:
[tex] P= 2*Lenght + 2*Width[/tex]
Since the perimeter is 56 inches we can solve for the lenght with this equation:
[tex] 56 in = 2*12in + 2*Length[/tex]
And solving for the length we got:
[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]
So then the lenght = 16 inhes and the width of 12 inches
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
1/2
Step-by-step explanation:
Find two points on the line
(2,0) and (4,1)
The slope is given by
m= (y2-y1)/(x2-x1)
=(1-0)/(4-2)
= 1/2
Assuming that $3u + 12v\neq0$, simplify $\dfrac{12u^3 + 48u^2v}{3u+12v}$.
Answer:
4u²
Step-by-step explanation:
[tex]\dfrac{12u^3 + 48u^2v}{3u+12v}=\dfrac{12u^2(u+4v)}{3(u+4v)}=\boxed{4u^2}[/tex]
Common factors cancel from numerator and denominator. The one factor that might make the expression undefined is given as non-zero, so no additional restrictions apply.
A shop has 4 types of sweets (chocolate, taffy, gummies, and cookies), 2 types of snacks (chips and crackers), and 3 types of drinks (sodas, juice, and sports drinks).
Mystery boxes are put together that randomly combine 1 sweet, 1 snack, and 1 drink.
What is the probability that a mystery box contains chocolate, chips, and juice?
Answer:
1/24
Step-by-step explanation:
1/4*1/2*1/3 = 1/24
at the last minute deal Don and Mary booked a 7 day cruise for a total of $670. If the normal price for a couple is $1340, what discount percent did Don ans Mary recieve?
Answer:50%
Step-by-step explanation:670/1340 = 1/2 = 50%
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
-3/4
Step-by-step explanation:
Find two points on the line
(0,1) and (-4,4)
We can use the slope formula
m = (y2-y1)/(x2-x1)
= (4 -1)/(-4 -0)
= 3/-4
= -3/4
What’s the correct answer for this?
Answer:
E:
Step-by-step explanation:
The equation of circles is
(x-a)²+(y-b)²=r²
Where
Center = (a,b) = (-6,-3) and r = 12
Now
The equation becomes
(x+6)²+(x+3)²=144
Use technology to find the quadratic regression curve through the given points. HINT [See Example 5.] (Round all coefficients to four decimal places.) (1, 4), (3, 6), (4, 5), (5, 2)
y(x) =
Answer:
The coefficients for the quadratic regression curve are
a = (-2/3) = -0.6667
b = (11/3) = 3.6667
c = 1 = 1.0000
y(x) = -0.6667x² + 3.6667x + 1.0000
Step-by-step explanation:
Quadratic regression curve gives a general expression of
y = ax² + bx + c
And the points on the curve include
(1, 4), (3, 6), (4, 5), (5, 2)
Taking the points one at a time and substituting them into general quadratic curve expression
(1, 4), x = 1, y = 4
y = ax² + bx + c
4 = a + b + c (eqn 1)
(3, 6), x = 3, y = 6
6 = a(3²) + b(3) + c
6 = 9a + 3b + c (eqn 2)
(4, 5), x = 4, y = 5
5 = a(4²) + b(4) + c
5 = 16a + 4b + c (eqn 3)
Combining the 3 equations and solving simultaneously
4 = a + b + c
6 = 9a + 3b + c
5 = 16a + 4b + c
From eqn 1, c = 4 - a - b
Substituting this into eqn 2 and 3, we have
6 = 9a + 3b + 4 - a - b
2 = 8a + 2b (*)
5 = 16a + 4b + 4 - a - b
1 = 15a + 3b (**)
8a + 2b = 2
15a + 3b = 1
a = (-2/3), b = (11/3)
c = 4 - a - b
c = 4 - (-2/3) - (11/3)
c = 1
Hence, the coefficients for the quadratic regression curve are
a = (-2/3) = -0.6667
b = (11/3) = 3.6667
c = 1 = 1.0000
y(x) = -0.6667x² + 3.6667x + 1.0000
Hope this Helps!!!
New York State's "Quick Draw" lottery moves right along. Players choose between one and 10 numbers from the range one to 80; 20 winning numbers are displayed on a screen every four minutes. If you choose just one number, your probability of winning is 20/80, or 0.25. Lester plays one number fourteen times as he sits in a bar. What is the probability that all fourteen bets lose
Answer:
0.0178
Step-by-step explanation:
For computation of probability that all fourteen bets lose first we need to find out the Probability of losing in 1 bet is shown below:-
Probability of losing in 1 bet = 1 - P(winning)
= 1 - 0.25
= 0.75
With the help of probability of losing in 1 bet we can find out the Probability of losing in 8 bets which is here below:-
= Probability of losing in 1 bet ^ Number of loosing bets
= 0.75 ^ 14
= 0.017817948
or
= 0.0178
Therefore for computing the probability that all fourteen bets lose we simply applied the above formula.
Find coordinates of the mid point AS if A is (-4,7) and 5,3
The right answer is (1/2 , 5)
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
if r is the radius of a circle and d is its diameter which of the following is an equivalent formula for the circumference c = 2 pie r
a C = pie d2
b C = pie rd
c C = pie d
d C = 2 pie d
Answer:
C
Step-by-step explanation:
C=2pier or pied
Answer:
a. C = 2πr
c. C= πd
both are correct
Jenn uses 6 cups of flour to bake 40 muffins. How many muffins can she can bake if she has 15 cups of flour?
Answer:
100 muffins
Step-by-step explanation:
We can use a ratio to solve
6 cups 15 cups
------------- = -----------
40 muffins x muffins
Using cross products
6x = 40*15
Divide each side by 6
6x/6 = 40*15/6
x =100
100 muffins
Answer:
100 muffins
Step-by-step explanation:
If she could bake 40 muffins with 6 cups, then she could bake 80 muffins with 12 cups. Then, we have 3 cups left over, which is half of 6, meaning she can only bake half of her regular amount with 3 cups, which would be 20. 80+20=100
40+40+20=100
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
You are given the equation [tex]f(x)=x+6[/tex] and [tex]g(x)=x^4[/tex]. When you combine G(F(x)) your equation would come out as [tex]g(f(x))=x^4(x+6)[/tex]. Once you distribute the equation you will get [tex]g(f(x))=(x+6)^4[/tex]
Therefore you answer choice would be B. [tex](x+6)^4[/tex]
Compute 8P2 *
16
O 56
O 28
O
none of these are correct
A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures wide. The biologist estimates she will need of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres. Round your answer to significant digits.
The complete question is;
A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 78.0 cm wide. The biologist estimates she will need 2600 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit in to the air tank. Write you answer in atmospheres
Answer:
10.5 atm
Step-by-step explanation:
Formula for Volume of a sphere is;
V = (4/3)πr³
r = 78/2 = 39 cm
V = (4/3)π(39)³
V = (4/3)*π*59319
V = 248475 cm³
Now, from conversions, 1000 cm³ = 1L
So,
V = 248475/1000
V = 248.5 L
This is the volume of the storage tank
If we assume that the 2600 L of air is measured at 1 atmosphere pressure, then we will obtain the following relationship:
From Boyles law,
P1 × V1 = P2 × V2
Thus;
(1 atm) × (2600 L) = (P2) × (248.5 L)
P2 = 2600/248.5
P2 = 10.463 atmospheres
Approximating to 3 significant figures is; P2 = 10.5 atm
Which of these shapes have rectangular cross sections when they are cut perpendicular to the base? Select three options.
-rectangular prism
-triangular prism
-cylinder
-cone
-square pyramid
-triangular pyramid
Answer:
A, B, and E
Step-by-step explanation:
Answer:
abe
Step-by-step explanation:
A recent survey found that 86% of employees plan to devote at least some work time to follow games during the NCAA Men's Basketball Tournament. A random sample of 100 employees was selected. What is the probability that less than 80% of this sample will devote work time to follow games?
Answer:
4.18% probability that less than 80% of this sample will devote work time to follow games
Step-by-step explanation:
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
[tex]p = 0.86, n = 100[/tex]
So
[tex]\mu = 0.86, s = \sqrt{\frac{0.86*0.14}{100}} = 0.0347[/tex]
What is the probability that less than 80% of this sample will devote work time to follow games?
This is the pvalue of Z when X = 0.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8 - 0.86}{0.0347}[/tex]
[tex]Z = -1.73[/tex]
[tex]Z = -1.73[/tex] has a pvalue of 0.0418
4.18% probability that less than 80% of this sample will devote work time to follow games
Suppose you have a job teaching swimming lesson and get paid $6 an hour you also have a job as a chasier and get pay $8 and hour if you cannot work more than 15 hours a week what are the number you f hours you can work at each job and still make at least $100
Answer:
You can work no more than 10 hours teaching, and must work at least 5 hours cashiering. The remaining hours can be worked at the other job until the goal is reached.
Step-by-step explanation:
The restrictions give rise to two inequalities. If we ...
let x represent teaching hours
let y represent cashiering hours
then the restrictions are ...
x + y ≤ 15 . . . . total hours cannot exceed 15
6x +8y ≥ 100 . . . . you want to earn at least $100
The solution set for these inequalities is a triangular area on a graph with vertices at ...
(x, y) = (10, 5), (0, 12.5), (0, 15)
You must work at least 5 hours cashiering, and the remainder of necessary time at teaching.
0.2x + (-0.9) + 1.7 = 9.6
0.2x + 0.8 = 9.6
X=
WHAT DOES x =
Answer:
x =44
Step-by-step explanation:
0.2x + (-0.9) + 1.7 = 9.6
Combine like terms
.2x +.8 = 9.6
Subtract .8 from each side
.2x +.8 -.8 = 9.6 -.8
.2x = 8.8
Divide each side by .2
.2x/.2 = 8.8/.2
x =44
Please answer this correctly
Answer:
0-4: Make it 2 units tall
5-9: Make it 5 units tall
10-14: Make it 1 unit tall
15-19: Make it 4 units tall
20-24: Make it 4 units tall
Step-by-step explanation:
0-4: 2, 2 (2 numbers)
5-9: 6, 7, 7, 8, 9 (5 numbers)
10-14: 14 (1 number)
15-19: 15, 16, 16, 18 (4 numbers)
20-24: 21, 23, 23, 24 (4 numbers)
Solve the system of equations by using substitution
Y=2x+3
Y=x+2
Since our first equation reads y = 2x + 3, we can substitute a 2x + 3
in for y in our second equation and then solve from there.
So we have 2x + 3 = x + 2.
Now subtract x from both sides to get x + 3 = 2.
Now subtract 3 from both sides to get x = -1.
To find y, plug -1 back into either equation.
I have chosen to plug it into the second.
So we have y = (-1) + 2 which simplifies to 1.
So our solution to this system is (-1, 1).