Use the change-of-base property for logarithms to write
logₓ(16) log₂(x) = (ln(16) / ln(x)) (ln(x) / ln(2)) = ln(16)/ln(2) = log₂(16)
Then since 2⁴ = 16, we hvae
log₂(16) = log₂(2⁴) = 4 log₂(2) = 4
Mary spent $4 more than 1/8 of her original amount of money on a bag. She then
Spent $12 more than 2/3 of her remaining money on groceries.Given that Mary had $24 left,how much did the bag cost?
Answer:
464 $
Step-by-step explanation:
How many numbers multiple of 3 are in the range [2,2000]?
Answer: so there are 666 multiples of 3 between 2 and 2000.
Step-by-step explanation:
the smallest number = 3 which is 3*1. The largest number is = 1998 = 3*666
multiples of 3 between {2,2000} = 666-1+1 = 666
A local rectangular shaped pool used by lap swimmers has dimensions 25 yd by 30 yd and is 5.1 feet deep. Find the cost for filling the pool if the city charges $1.50 per 1000 gallons. Use the conversion 1 gallon
Answer:
the cost of filling the pool is $386.3
Step-by-step explanation:
Given;
dimension of the rectangular pool, = 25 yd by 30 yd by 5.1 ft
covert the given dimensions to feet;
1 yd = 3 ft
25 yd = 25 x 3 ft = 75 ft
30 yd = 30 x 3 ft = 90 ft
The volume of the rectangular pool in cubic feet (ft³);
Volume = 75 ft x 90 ft x 5.1 ft
Volume = 34,425 ft³
Convert the volume to gallons;
1 ft³ = 7.481 gallons
10,125 ft³ = 34,425 x 7.481 gallons
= 257,533.425 gallons
The cost per a 1000 gallons is $1.50, then cost of the 257,533.425 gallons is calculated as;
[tex]cost = \frac{\$ 1.50}{1000 \ gallons} \times 257,533.425 \ gallons = \$ 386.3[/tex]
Therefore, the cost of filling the pool is $386.3
Use the distributive property to find the product of the rational number.
5/2 (- 8/5 + 7/5)
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Answer:
-1/2
Step-by-step explanation:
The factor outside parentheses multiplies each term inside.
5/2(-8/5 +7/5)
= (5/2)(-8/5) +(5/2)(7/5)
= -8/2 +7/2 = -1/2
Give a vector parametric equation for the line through the point (−2,−4,0) that is parallel to the line ⟨−2−3t,1−4t,−5t⟩:
The tangent vector for the given line is
T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩
On its own, this vector points to a single point in space, (-3, -4, -5).
Multiply this vector by some scalar t to get a whole set of vectors, essentially stretching or contracting the vector ⟨-3, -4, -5⟩. This set is a line through the origin.
Now translate this set of vectors by adding to it the vector ⟨-2, -4, 0⟩, which correspond to the given point.
Then the equation for this new line is simply
L(t) = ⟨-3, -4, -5⟩t + ⟨-2, -4, 0⟩ = ⟨-2 - 3t, -4 - 4t, -5t⟩
The vector parametric equation for the line through the point is [tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex].
GivenGive a vector parametric equation for the line through the point (−2,−4,0) that is parallel to the line ⟨−2−3t,1−4t,−5t⟩.
What is a parametric equation vector?Parametric equations of the line segment are defined by its endpoints.
To find the vector equation of the line segment, we’ll convert its endpoints to their vector equivalents.
Two lines are parallel if they have the same direction, and in the parametric form, the direction of a line is always the vector of constants that multiply t (or the parameter).
The vector equation of a line is given by:
[tex]\rm v = r_0+tv[/tex]
Where v is the direction vector and [tex]\rm r_0[/tex] is a point of the line.
The tangent vector for the given line is
T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩
Here,
[tex]\rm r_0 = (-2,-4,0) \ and \ v=(-3, \ -4, \ -5)t\\\\[/tex]
Then,
[tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex]
x = -2-3t, y = -4-4t, and z = 0-5t
To know more about the Parametric equation click the link given below.
https://brainly.com/question/14701215
Solve the word problems. The price of a bed was $2600. MDM Yap bought the bed and had to pay an additional 7% GST. (a) What was the amount of GST she had to pay? (b) What was the price of the bed including GST?
Answer:
Step-by-step explanation:
Help me with this please
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Answer:
B. √6
Step-by-step explanation:
The circles are not tangent to one another. If they were, the distance between their centers would be the sum of their radii: 1 +1 = 2.
__
The center of the first circle is (√3, √3), and the center of the second is the origin. The distance between these two centers is given by the distance formula:
d = √((x2 -x1)^2 +(y2 -y1)^2)
d = √((√3 -0)^2 +(√3 -0)^2) = √(3+3) = √6 . . . . matches choice B
Please answer ASAP!!!!
Answer:
0
Step-by-step explanation:
0
In an accelerated failure test, components are operated under extreme conditions so that a substantial number will fail in a rather short time. In such a test involving two types of microchips, 580 chips manufactured by an existing process were tested, and 125 of them failed. Then, 780 chips manufactured by a new process were tested, and 130 of them failed. Find a 90% confidence interval for the difference between the proportions of failures for chips manufactured by the two processes. (Round the final answers to four decimal places.) The 90% confidence interval is
Answer:
The 90% confidence interval is (0.0131, 0.0845).
Step-by-step explanation:
Before finding the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
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.
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]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Old process:
125 out of 580, so:
[tex]p_O = \frac{125}{580} = 0.2155[/tex]
[tex]s_O = \sqrt{\frac{0.2155*0.7845}{580}} = 0.0171[/tex]
New process:
130 out of 780. So
[tex]p_N = \frac{130}{780} = 0.1667[/tex]
[tex]s_N = \sqrt{\frac{0.1667*0.8333}{780}} = 0.0133[/tex]
Distribution of the difference:
[tex]p = p_O - p_N = 0.2155 - 0.1667 = 0.0488[/tex]
[tex]s = \sqrt{s_O^2+s_N^2} = \sqrt{0.0171^2 + 0.0133^2} = 0.0217[/tex]
Confidence interval:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.0488 - 1.645*0.0217 = 0.0131[/tex]
The upper bound of the interval is:
[tex]p + zs = 0.0488 + 1.645*0.0217 = 0.0845[/tex]
The 90% confidence interval is (0.0131, 0.0845).
Help please ……………….zzzz
1) I think 15 choose (d)
2) The choose (C) -4fg+4g
3) The choose (d) 3xy/2
4) The choose (a) ab/6
5) The choose (C) 2p+4q-6
6)
[tex]\pi {r}^{2} h = 3.14 \times {3}^{2} \times 1.5 = 42.39 {m}^{3} = 42.390 {m}^{3} [/tex]
Point 6 I think there is an error because the unit m must be m³ because it is r² (m²) and h(m) becomes m³.
I hope I helped you^_^
solve for x . please help also don’t forget to show work
Answer:
X-4x+11=8
-3x+12-8=0
-3x+4=0
3x=4
X=4/3
Answer:
x = 4/3 or 1.3
Step-by-step explanation:
Combine like terms
8 = -3x + 12
Move the terms
3x = 12 - 8
Calculate
3x = 4
Divide both sides by 3
x = 4/3
or
x = 1.3
Hey good morning I need help ASAP thank you guys
Answer:
B. x = 2.77
Step-by-step explanation:
3^x = 21
You first look for a base for 21 that is 3 to the power of something.
21 = 3^2.77
So 3^x = 2^2.77
They have the same base so
x= 2.77
Evaluate the expression when x = 12/7
The value of the expression when x equals is ???
PLEASE HELP!!
Answer:
82
Step-by-step explanation:
1/3( x+9/7) + 3^4
Let x = 12/7
1/3( 12/7+9/7) + 3^4
PEMDAS says parentheses first
1/3( 21/7) + 3^4
1/3(3) +3^4
Then exponents
1/3(3)+81
Then multiply
1+81
82
please help me
no links or files
thank you !
Jane is saving to buy a cell phone. She is given a $100 gift to start and saves $35 a month from her allowance. So after one month, Jane has saved $135. Does it make sense to represent the relationship between the amount saved and the number of months with one constant rate? Why or why not? Explain your answer.
Jane is given a $100 gift to start and saves $35 a month from her allowance.
After 1 month, Jane has saved
After 2 months, Jane has saved
After three months, Jane has saved
and so on
In general, after x months Jane has saved
This means that it makes sense to represent the relationship between the amount saved and the number of months with one constant rate (in this case the constant rate is 35). It makes sense because the amount of money increases by $35 each month. Since the amount of increase is constant, we get constant rate. Also the initial amount is known ($100), so there is a possibility to write the equation of linear function representing this situation.
Step-by-step explanation:
I need this please pleaseeee nowww
Answer:
y = 3x - 5
Step-by-step explanation:
Slope = 3
x-intercept (what the value of y is when its 0) = -5 so y = 3x - 5
Answer:
y = 3x - 5
Step-by-step explanation:
Find the slope of the line between (0,−5)(0,-5) and (3,4)(3,4) using m=y2−y1x2−x1m=y2-y1x2-x1, which is the change of yy over the change of xx.
m=3m=3
Use the slope 33 and a given point (0,−5)(0,-5) to substitute for x1x1 and y1y1 in the point-slope form y−y1=m(x−x1)y-y1=m(x-x1), which is derived from the slope equation m=y2−y1x2−x1m=y2-y1x2-x1.
y−(−5)=3⋅(x−(0))y-(-5)=3⋅(x-(0))
Simplify the equation and keep it in point-slope form.
y+5=3⋅(x+0)
Add xx and 00.
y+5=3xy+5=3x
Subtract 55 from both sides of the equation.
y=3x−5
I need help figuring out this equation
270 degrees is at the bottom of the unit circle, and it splits the 3rd and 4th quadrants.
Its terminal point is (0, -1).
Hope this helps!
Answer:
A. (0, -1)
Step-by-step explanation:
This question requires a chart to answer. The chart is inserted in the answer.
270 degrees is all the way at the bottom, at South which shows that 270 degrees is at (0, -1).
Meaning, the answer is A, (0, -1).
Hope this helped.
Write the inequality shown in this graph.
Answer:
y > -1/2 x + 4
Step-by-step explanation:
Equation of a line : (y-y1)/(y2-y1) = (x-x1)/(x2-x1)
(y-4)/(2-4)= (x-0)/(4-0)
(y-4)/-2 = x/4
(-y+4)/2 = x/4
-y+4 = 1/2 x
-y = 1/2 x - 4
y = -1/2 x + 4
the solutions of the inequality are the points above this line, so
y > -1/2 x + 4
Two professors are applying for grants. Professor Jane has a probability of 0.64 of being funded. Professor Joe has probability 0.28 of being funded. Since the grants are submitted to two different federal agencies, assume the outcomes for each grant are independent.
Required:
a. What is the probability that both professors get their grantsfunded?
b. What is the probability that at least one of the professors will befunded?
c. What is the probability that Professor Jane is funded but ProfessorJoe is not?
d. Given at least one of the professors is funded, what is theprobability that Professor Jane is funded but Professor Joe is not?
Find the measure of ZJ, the smallest angle in a triangle
with sides measuring 11, 13, and 19. Round to the
nearest whole degree.
O 30°
O 34°
o 42°
O 47°
At what rates did she invest?
$1400 invested at ____%
$900 invested at ____%
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Answer:
$1400 at 8%$900 at 10%Step-by-step explanation:
The 1-year interest is simply the invested amount times the interest rate.
Let r represent the lower interest rate. Then r+0.02 is the higher rate, and the total interest earned is ...
1400r + 900(r +.02) = 202
2300r +18 = 202 . . . . . . . . . .simplify
2300r = 184 . . . . . . . . . .subtract 18
r = 184/2300 = 0.08 = 8% . . . . . . divide by the coefficient of r
$1400 was invested at 8%.
$900 was invested at 10%.
Which point on the number line shows the graph
Answer:
B
Step-by-step explanation:
You need 675 mL of a 90% alcohol solution. On hand, you have a 25% alcohol mixture. How much of the 25% alcohol mixture and pure alcohol will you need to obtain the desired solution?
Answer:
90 ml of the 25 percent mixture and 585 of pure alcohol
Step-by-step explanation:
Firstly, you should find the quantity of alcohol in the desired mixture.
675:100*90= 675*0.9= 607.5
Firstly, define all the 25 percents mixure as x, the pure alcohol weight is y.
1. x+y= 675 (because the first and the second liquid form a desired liquid).
Then find the equation for spirit
The first mixture contains 25 percents. It is x/100*25= 0.25x
When the second one consists of pure alcohol, it contains 100 percents of spirit, so it is x.
2. 0.25x+y=607.5
Then you have a system of equations ( 1.x+y= 675 and 2. 0.25x+y= 607.5)
try 2-1 to get rid of y
x+y- (0.25x+y)= 675-607.5
0.75x= 67.5
x= 90
y= 675-x= 675-90= 585
It means that you need90 ml of the 25percents mixture and 585 0f pure alcohol
X ^2 + 2x + y’ + 6y = 15
Step-by-step explanation:
x^2+2x+7y=15
7y=15-x^2-2x
y=15/7-1/7x^2-2/7x , x ∈ all real numbers
What is the equation of the parabola shown in the graph?
Answer:
[tex]-\frac{x^{2} }{4}[/tex] -2x - 7
Step-by-step explanation:
Never seen a phone with 3 cameras before or something but ok.
Took a while to use brainly's insert character thingie since fractions and the exponent kinda threw me off.
18 Geometry question: Use an algebraic equation to find the measure of each angle that is representative in terms of X
Answer:
12x - 28° = 116°
7x + 32° = 116°
Step-by-step explanation:
12x - 28° and 7x + 32° are vertical angles. Vertical angles are congruent.
Therefore, to find the measure of each angle, we have to set each equation equal to each other as follows:
12x - 28° = 7x + 32°
Collect like terms
12x - 7x = 28 + 32
5x = 60
Divide both sides by 5
5x/5 = 60/5
x = 12
✔️12x - 28°
Plug in the value of x
12(12) - 28
= 144 - 28
= 116°
✔️7x + 32°
7(12) + 32
= 84 + 32
= 116°
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course: 16, 21, 22, 12, 22
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The critical value used is [tex]T_c = 2.132[/tex]
The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).
Step-by-step explanation:
Before building the confidence interval, we need to find the sample mean and the sample standard deviation.
Sample mean:
[tex]\overline{x} = \frac{16+21+22+12+22}{5} = 18.6[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(16-18.6)^2+(21-18.6)^2+(22-18.6)^2+(12-18.6)^2+(22-18.6)^2}{4}} = 4.45[/tex]
Confidence interval:
We have the standard deviation for the sample, so the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 5 - 1 = 4
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.132. The critical value used is [tex]T_c = 2.132[/tex]
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.132\frac{4.45}{\sqrt{5}} = 4.243[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 18.6 - 4.243 = 14.357
The upper end of the interval is the sample mean added to M. So it is 18.6 + 4.243 = 22.843.
The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).
You and your friends have tickets to attend a music concert. While standing in line, the promoter states he will give a gift card for a free album download to each person that is a multiple of 2. He will also give a backstage pass to each fourth person and floor seats to each fifth person. Which person will receive the free album download, backstage pass, and floor seats? Explain the process you used to determine your answer.
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Answer:
20th
Step-by-step explanation:
The person will receive all gifts if the are all of a multiple of 2, a multiple of 4, and a multiple of 5. Since 4 is already a multiple of 2, the person who will receive all is the one who is a multiple of 4 and 5.
20 is 4×5, so is a multiple of both numbers. There is no smaller number that is a multiple of both 4 and 5.
The 20th person will receive all gifts.
_____
The value we have determined here is called the "least common multiple" (LCM). It is the product of the unique prime factors of the numbers of interest, raised to the highest power that appears in any of the numbers.
2 = 2¹
4 = 2²
5 = 5¹
LCM(2, 4 5) = 2² × 5¹ = 20
A woman is 42years old. Her daughter is 1/3 of her age. Three years ago the sum of her age was
Answer:
50
Step-by-step explanation:
So we know that 42/3=14.
3 years before was:
14-3=11
42-3=39
The sum of 11+39 is 50
if x-y =2 and xy=15, find the value of x cube - y cube.
Answer:
5³ = 125 : -3³ = -27Step-by-step explanation:
let x= 5 and y= 3x - y = 25 - 3 = 2xy = 155 × 3 = 15x³ = ? : -y³ = ?5³ = 125 : -3³ = -27[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
find the squre of 17
[tex] \sqrt{17} [/tex]
