Answer:
Step-by-step explanation:
Given the expression [tex]log_81000 = log_210[/tex], to prove this expression is true using the properties of logarithm, we will follow the following steps.
Starting from the Left Hand Side:
[tex]log_81000\\[/tex]= log₈ 10³= log_ 2^3 (10³)= log₂10The amount of time t(in minutes) that it takes to put out a fire varies inversely with G, the volume of water used (in hundreds of gallons). When G is 2, t is 20. Find how long it takes to put out a fire when 500 gallons of water (G = 5) are used.
Answer:
50 minutes.
Step-by-step explanation:
You can use a ratio to solve:
[tex]t[/tex] : [tex]G[/tex]
20 : 2
10 : 1
[tex]x[/tex] : 5
[tex]x[/tex] must be 50 minutes since 100 gallons of water takes 10 minutes.
Name all the chords ...
Answer:
option 3 is the answer.
Elif is arranging 28 chairs in rows in a room. Each row must be the same
length. The room is wide enough to make a row of 9 chairs, but no more
The room is deep enough to make 8 rows, but no more. What are the
possible numbers of rows and chairs in each row that Elif can make?
Answer:
Hey there!
Elif can only arrange the chairs like: 4 by 7, and 7 by 4.
Hope this helps :)
In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The
longest and the shortest days of the year vary by 2 hours 53 minutes from the equinox.
In this year, the equinox falls on March 21. In this task, you'll use a trigonometric function
to model the hours of daylight hours on certain days of the year in New York City.
Identify the independent and dependent variables find amplitude and the period of the function create a trigonometric function that describes the hours of sunlight for each day of the year and then use the function you built to find how fewer daylight hours February 10 will have then March 21
Answer:
independent: day number; dependent: hours of daylight
d(t) = 12.133 +2.883sin(2π(t-80)/365.25)
1.79 fewer hours on Feb 10
Step-by-step explanation:
a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).
__
b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,
March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...
d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))
d(t) = 12.133 +2.883sin(2π(t-80)/365.25)
__
c) d(41) = 10.34, so February 10 will have ...
12.13 -10.34 = 1.79
hours less daylight.
The number 3. I 4063 written correct to 3 decimal places is
Answer:
3.141
Step-by-step explanation:
From the decimal point, count three no. s to the right. If the no. after the three no. s is more than five, add one to third no. if not more than five then third no. remains as it is
I need help with this
help me out if you know the answer.
Answer:
The answer is
[tex]$ (3x^2 - 12x + 43) + \frac{-190}{(x+4)} $[/tex]
Where
Remainder = -190
quotient = [tex]3x^2 - 12x + 43[/tex]
Step-by-step explanation:
The dividend is given as
[tex]3x^3 - 5x -18[/tex]
The divisor is given as
[tex]x + 4[/tex]
Using the long division,
Multiply [tex](x + 4)[/tex] by [tex]3x^2[/tex]
Remainder:
[tex]-12x^2 - 5x -18[/tex]
Multiply [tex](x + 4)[/tex] by [tex]-12x[/tex]
Remainder:
[tex]43x - 18[/tex]
Multiply [tex](x + 4)[/tex] by [tex]43[/tex]
Remainder:
[tex]-190[/tex]
Therefore, the answer is
[tex]$ (3x^2 - 12x + 43) + \frac{-190}{(x+4)} $[/tex]
Where
Remainder = -190
quotient = [tex]3x^2 - 12x + 43[/tex]
The days of training a new employee needs are normally distributed with a population standard deviation of 3 days and an unknown population mean. If a random sample of 23 new employees is taken and results in a sample mean of 18 days, use a calculator to find a 90% confidence interval for the population mean.
Answer:
90% confidence interval for the population mean
(16.971 , 19.029)
Step-by-step explanation:
Step(i):-
Given mean of the sample x⁻ = 18 days
Standard deviation of the Population 'σ' = 3 days
Given sample size 'n' =23
Step(ii):-
90% confidence interval for the population mean is determined by
[tex]((x^{-} - Z_{0.10} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.10} \frac{S.D}{\sqrt{n} } )[/tex]
Critical value Z = 1.645
[tex]((18 - 1.645 \frac{3}{\sqrt{23} } , 18+ 1.645 \frac{3}{\sqrt{23} } )[/tex]
(18 -1.029 , 18 + 1.029)
(16.971 , 19.029)
final answer:-
90% confidence interval for the population mean
(16.971 , 19.029)
in triangle ABC shown below,
BD/BA = BE/BC
Which reason can be used to fill in the numbered blank space?
a. ABC ~ BED
SAS similarity postulate
b. ABC ~ BED
SSS similarity theorem
c. ABC ~ DBE
SAS similarity postulate
d. ABC ~ DBE
SSS similarity theorem
Answer:
Option C
Step-by-step explanation:
One pair of corresponding sides are proportional (BA-BD, BC-BE)
The included angles are equal (angle B)
=> SAS similarity
what is the surface area of the prism shown to the left?
(idk the answer i guessed)
Answer:
828
Step-by-step explanation:
Missing leg of triangle:
√15²-12²= √225-144=√81=9
Triangle faces= 2*1/2*12*9= 108
Base= 20*9= 180
Front face= 20*15= 300
Back face= 20*12= 240
Total= 108+180+300+240= 828
Second choice
What is the volume of this aquarium?
Answer:
9,000 inches^3
Step-by-step explanation:
The first part is 20 x 20 x 20, which equals 8,000
The second part is 10 x 10 x 10, which is 1,000
1,000 + 8,000 = 9,000
Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integration.) dy dt = 27t8
Answer:
[tex]y=3t^9+C[/tex]
Step-by-step explanation:
Given: [tex]\dfrac{dy}{dt}=27t^8[/tex]
We want to obtain the general solution of the given differential equation.
[tex]dy=27t^8$ dt\\$Take the integral of both sides\\\int dy =\int 27t^8$ dt$\\y=\dfrac{27t^{8+1}}{8+1} +C$, (where C is the constant of integration)$\\y=\dfrac{27t^{9}}{9} +C\\\\y=3t^9+C[/tex]
The general solution of the differential equation is: [tex]y=3t^9+C[/tex]
CHECK:
[tex]\dfrac{d}{dt} y=\dfrac{d}{dt}(3t^9+C)=\dfrac{d}{dt}(3t^9)+\dfrac{d}{dt}(C)\\\\\text{Since derivative of a constant is zero}\\\\\dfrac{dy}{dt}=27t^{9-1}\\\dfrac{dy}{dt}=27t^8[/tex]
Five years ago the age of father was twice as old as the age of daughter. The sum of present ages of the father and daughter is 55 years then find their present ages.
Answer:
Daughter = 20 years oldFather = 35 years oldStep-by-step explanation:
Solution,
Five years ago,
Daughter's age = X - 5
Father's age = 2 ( X - 5 ) = 2x - 10
Present age,
Daughter's age = X years
Father's age = 2x - 5 years
According to Question,
X + 2x - 5 = 55
or, 3x - 5 = 55
or, 3x = 55+5
or, 3x = 60
or, X = 60/3
X = 20
The present age of daughter is 20
Again,
present age of father= 2x - 5
= 2* 20 - 5
= 40 - 5
= 35
Hope this helps...
Good luck on your assignment...
Consider the initial value problem y'' + 49 y = cos(7t), y(0) = 9, y'(0) = 6. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). cos (7 t)/s^2 b. Solve your equation for Y(s). Y(s) = Laplace {y(t)}}=_________ c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = _____________
Answer:
35/49/50
Step-by-step explanation:
3.5/7.8/4.9=50
Identify the range of the function shown in the graph.
Answer:
B
Step-by-step explanation:
The range is all values of y. Y goes from -1 to 1. Please mark brainliest.
Answer:
see below
Step-by-step explanation:
The domain of the function is the possible x values
The domain is all real values since x can be any number
The range of the function is the possible y value
The values of y go from -1 to 1 so
-1 ≤y≤1
Determine whether each pair of figures is similar. Justify your answer. DEF is not similar to BAC . Corresponding angles are not the same. DEF-BAC because the corresponding angles of each triangle are congruent. The ratio of the corresponding sides is 1/2 . DEF-ABC because the corresponding angles of each triangle are congruent. The ratio of the corresponding sides is 2. DEF is not similar to BAC . The ratios of the corresponding sides are not the same.
Answer:
Option (2)
Step-by-step explanation:
Two triangle are similar when,
1). Two or more than two angles of the given triangles are equal in measure.
2). Ratio of the corresponding sides are same.
In the triangles ΔDEF and ΔBAC,
m(∠A) = m(∠E) = 58°
m(∠B) = m(∠D) = 53°
m(∠C) = m(∠F) = 69°
And ratio of the corresponding sides,
[tex]\frac{\text{EF}}{\text{AC}}=\frac{\text{DF}}{\text{BC}}=\frac{\text{DE}}{\text{AB}}[/tex]
[tex]\frac{2.6}{5.2}=\frac{2.8}{5.6}=\frac{3.1}{6.2}[/tex]
[tex]\frac{1}{2}=\frac{1}{2}=\frac{1}{2}[/tex]
Therefore, ΔDEF ~ ΔBAC
Option (2) will be the answer.
A business offers educational tours to Patagonia, a region of South America that includes parts of Chile and Argentina. The profit P for x number of persons is P(x) = −25x^2 + 1250x − 5000. The trip will be rescheduled if the profit is less than $7500. How many people must have signed up if the trip is rescheduled?
Answer:
13.82 or 14 people
Step-by-step explanation:
Step 1: Set equation equal to 7500
7500 = -25x² + 1250x - 5000
Step 2: Solve
0 = -25x² + 1250x - 12500
0 = -25(x² - 50x + 500)
0 = x² - 50x + 500
When you use the quadratic formula, you should get 13.82, rounded to 14 people as your answer.
Alternatively, we can graph the expression and see where $7500 for x people is.
We are standing on the top of a 320 foot tall building and launch a small object upward. The object's vertical altitude, measured in feet, after t seconds is h ( t ) = − 16 t 2 + 128 t + 320 . What is the highest altitude that the object reaches?
Answer:
The highest altitude that the object reaches is 576 feet.
Step-by-step explanation:
The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be [tex]h(t) = -16\cdot t^{2} + 128\cdot t + 320[/tex], the first and second derivatives are, respectively:
First Derivative
[tex]h'(t) = -32\cdot t +128[/tex]
Second Derivative
[tex]h''(t) = -32[/tex]
Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:
[tex]-32\cdot t +128 = 0[/tex]
[tex]t = \frac{128}{32}\,s[/tex]
[tex]t = 4\,s[/tex] (Critical value)
The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:
[tex]h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320[/tex]
[tex]h(4\,s) = 576\,ft[/tex]
The highest altitude that the object reaches is 576 feet.
Solve the system of linear equations.
Answer:
work is shown and pictured
Suppose you are interested in estimating the proportion of Florida State University students who make use of the university's mental health services. You take a sample of 300 students, and find that 47 made use of the university's mental health services. Which of the following is a 95% confidence interval for the true proportion of Florida State University students who make use of the university's mental health services (rounded to two decimal places)? a. 16.84 b. 12.20 c. 10.21 d. 45.57
Answer:
The 95% confidence interval for the true proportion of Florida State University students who make use of the university's mental health services is (0.12, 0.20). Option b.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 300, \pi = \frac{47}{300} = 0.1567[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1567 - 1.96\sqrt{\frac{0.1567*0.8433}{300}} = 0.1156[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1567 + 1.96\sqrt{\frac{0.1567*0.8433}{300}} = 0.1978[/tex]
Rounded to two decimal places: (0.12, 0.20)
The 95% confidence interval for the true proportion of Florida State University students who make use of the university's mental health services is (0.12, 0.20). Option b.
A survey of 700 non-fatal accidents showed that 143 involved faulty equipment. Find a point estimate for p, the population proportion of accidents that involved faulty equipment. Group of answer choices
Answer:
The point estimate for p is 0.2043.
Step-by-step explanation:
The point estimate for the population proportion of accidents that involved faulty equipment is the number of acidents which involved faulty equipment divided by the number of accidents surveyed.
In this question:
700 accidents surveyed
143 involved faulty equipment
143/700 = 0.2043
The point estimate for p is 0.2043.
Suppose 27 cars start at a car race. In how many ways can the top 3 cars finish the race?
The number of different top three finishes possible for this race of 27 cars is
(Use integers for any number in the expression.)
Answer:
2925
Step-by-step explanation:
27 choose 3
(27!) / (24!3!)
the 24! cancels leaving the numerator with 27 x 26 x 25
(27 x 26 x 25) / (3 x 2 x 1)
Canceling out we get
9 x 13 x 25 which works out to be
2925!
Answer:
What expression? Anyways it is 17,550 different ways.
what is 3x3x4/45 does anyone know the answer
Answer:
4/5 or 0.8
Step-by-step explanation:
3*3*4/45
3*3=9
9*4=32
32/45=4/5
Hope it helps ;)
━━━━━━━☆☆━━━━━━━
▹ Answer
0.8 (4/5 or 8 × 10⁻¹)
▹ Step-by-Step Explanation
3 × 3 × 4 ÷ 45
3² × 4 ÷ 45
9 × 4 ÷ 45
36 ÷ 45
= 0.8 (4/5 or 8 × 10⁻¹)
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
A retail store sells two types of shoes, sneakers and sandals. The store owner pays $8 for the sneakers and $14 for the sandals. The sneakers can be sold for $10 and the sandals can be sold for $17. The owner of the store estimates that she won't sell more than 200 shoes each month, and doesn't plan to invest more that $2,000 on inventory of the shoes. Let x= the number of sneakers in stock, and y=the number of sandals in stock. Write an equation to show the profit she will make on sneakers and sandals. P = [answer0]
Answer:
The equation that shows the profit: P = 2x + 3y
Step-by-step explanation:
The number of sneaker = x
The number of sandals = y
Cost of sneaker = 8 dollars.
Cost of sandals = 14 dollars.
Selling price of sneaker = $10
Selling price of sandals = $17
Total revenue = $10x + $17y
Total cost = $8x + $14y
Profit (P) = Total revenue - Total cost.
Profit = ($10x + $17y) – ($8x + $14y)
P = 10x +17y – 8x – 14y
P = 2x + 3y
Identify the 3D shape shown below.
Answer:
triangular prisim
Step-by-step explanation:
this is a triangular prisim because if you can see that the shape is a triangle and then is put into 3D. A cone is a circular shape. A rectangular prisim has a rectangular shape.
answer is
c) triangular prism
45 points! Yay An investment may earn interest using a simple interest rate or a compound interest rate. This expression can be used to find the value of an investment that is earning simple interest: P(1+rt) This expression can be used to find the value of an investment that is earning compound interest: P(1+r)t Use the drop-down menus to complete the statements about simple and compound interest. For an investment earning(simple interest,compound interest) , the interest is applied each year to the principal and to any interest that already accrued. For an investment earning(simple interest, compojnd interest) , the interest is applied each year only to the principal. Please help I'm literally the dumbest person i know •,-,•
Answer:
1. Compound Interest
2. Simple Interest
Step-by-step explanation:
Simple Interest multiplies the interest rate on the principal rate by the number of days.
Compound Interest multiplies the interest rate on the principal rate and existing rate by periods.
Answer:
:)
Step-by-step explanation:
The public radio show "A Prairie Home Companion," features news from the fictional town of Lake Wobegon, MN, home to many Norwegian bachelor farmers, and where "all the women are strong, all the men are good looking, and all the children are above average." Suppose average means average for the town. Such a town could not possibly exist, because (select all that apply)
a. not all women are strong
b. not all the children can be above average
c. not all Norwegian bachelor farmers are good looking
d. half the children must be below average
Answer:
b. not all the children can be above average
d. half the children must be below average
Step-by-step explanation:
In theory, all women could be strong and all men could be good looking, however, since the average is calculated based on the town children, it is not possible for all children to be above average.
Assuming a normal distribution, half the children must be at or below average, while the other half must be at or above the average.
Therefore, the correct answers are:
b. not all the children can be above average
d. half the children must be below average
Answer:
Second and last options are correct choices.
Step-by-step explanation:
If all the children are above average, then the average should not include the average of the children. Because it is impossible for a data set to be have values greater than it's average.
Best Regards!
According to the New York Stock Exchange, the mean portfolio value for U.S. senior citizens who are shareholders is $183,000. Assume portfolio values are normally distributed. Suppose a simple random sample of 51 senior citizen shareholders in a certain region of the United States is found to have a mean portfolio value of $198,000, with a standard deviation of $65,000.
a. From these sample results, and using the 0.05 level of significance comment on whether the mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation, by using the critical value method. Establish the null and alternative hypotheses.
b. What is your conclusion about the null hypothesis?
Answer:
The test statistic value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation
Step-by-step explanation:
Step(i):-
Given mean of the population (μ) = $183,000
Given mean of the sample (x⁻) = $198,000
Given standard deviation of the sample (S) = $65,000.
Mean of the sample size 'n' = 51
level of significance α = 0.05
Step(ii):-
Null hypothesis : H₀ : There is no significance difference between the means
Alternative Hypothesis :H₁: There is significance difference between the means
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]t = \frac{198,000- 183,000 }{\frac{ 65,000}{\sqrt{51} } }[/tex]
t = 1.64
Step(iii)
Degrees of freedom ν = n-1 = 51-1 =50
t₀.₀₅ = 2.0086
The calculated value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
Final answer:-
There is no significance difference between the means
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation
PLEASE HELP!!(PIC INCLUDED)
Which of the following steps were applied to ABCD to obtain A'B'C'D?
A. shifted 3 units right and 2 units down
B. shifted 4 units right and 2 units down
C. shifted 2 units right and 3 units down
D. shifted 3 units right and 1 unit down
Answer:
A. Shifted 3 unit right and 2 unit down
Step-by-step explanation:
Let's determine the reason for the answer.
We will use a reference point, only one point to determine the reason.
Because the both shape are identical.
Let's use point A
The position of A is 2 on the y axis and 1 on the x axis
While the position of A' is 0 on the y axis and 4 on the X asis
Let's know how many units where moved from the position.
A' -A
For X axis
4-1= 3
For y axis
0-2= 2(we need only the magnitude)
So its 2 units Down and 3 unit right
a piece of rope is 40 feet long it is cut into three pieces. One piece is 25 feet longer than the shortest piece. The third piece is three times as long as the shortest piece find the length of the third piece?
Answer:
9 ft
Step-by-step explanation:
Let x represent the shortest piece. Then the sum of lengths is ...
x + (x +25) +3x = 40
5x = 15
x = 3
3x = 9
The third piece is 9 feet long.
_____
Check
The pieces are 3 ft, 28 ft, 9 ft, so total 40 ft, as required.
How many combinations of players can a coach have if he needs to pick 2 out of a total of 4?
Answer:
the coach will have a combination of 2 players since there are initially 4 players on ground and he's picking two from them.
