Answer:
x = -6
Step-by-step explanation:
-2/3x + 9 = 4/3x - 3
First we need to simplify to where we have x on one side and a constant (number not connected to a variable) on the other side.
Subtract 4/3x from both sides:
-2/3x + 9 - 4/3x = -3
-6/3x + 9 = -3
Now subtract 9 from both sides:
-6/3x + 9 - 9 = -3 - 9
-6/3x = -12
Now turn -6/3 into a whole number to make things more simple:
-6/3 = -2
-2x = -12
Now divide both sides by -2 to get x by itself
-2x/-2 = -12/-2
x = -6
A motorboat can maintain a constant speed of 13 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 63 minutes; the return trip takes 15 minutes. What is the speed of the current?
Answer:
8 mph
Step-by-step explanation:
The speed in each direction is the speed of the boat with the speed of the current appropriately added. If x is the speed of the current, the upstream speed is 13-x; the downstream speed is 13+x.
The ratio of times is inversely proportional to the ratio of speeds, so we ahve ...
15/63 = 5/21 = (13-x)/(13+x)
5(13 +x) = 21(13 -x) . . . . . . . cross multiply
26x = 13(21 -5) = 13·16
x = 13·16/26 = 16/2 = 8
The speed of the current is 8 miles per hour.
Please answer this correctly
Answer:
169.5 yd²
Step-by-step explanation:
See attachment.
In situations like this, ALWAYS (!) make as sketch.
Divide the areas by adding dotted lines on sensible places, and write in the missing numbers for the correct distances.
The only possible difficult one is the triangle, which is the half of a rectangle. So you are dealing with a series of areas of rectangles. That is really easy if you understand what you are doing.
Total area =
area 1 + area 2 + area 3 + area 4
10*4 + 4*7 + 3*13 + (0.5 * 7*17)
40 + 28 + 42 + 59.5
Total area = 169.5 yd²
1/216^-2/3 + 1/256^-3/4 + 1/243^-1/5
Answer:
103
Step-by-step explanation:
[tex]\dfrac{1}{216}^{-2/3}+\dfrac{1}{256}^{-3/4}+\dfrac{1}{243}^{-1/5}= \\\\\\\sqrt[3]{216^2}+\sqrt[4]{256^3}+\sqrt[5]{243}=\\\\\\6^2+4^3+3=\\\\\\36+64+3=\\\\\\103[/tex]
Hope this helps!
if log3(x+1) - log3x=2, then x = ?
Answer:
x= 1/8
Step-by-step explanation:
The aspect ratio of a rectangular shape is it's length divided by it's width (L/W). If the aspect ratio of a chalkboard is 4:3 and the width is 5 in, what is the length of the chalkboard? A. 6.67 in B. 9.33 in C. 12 in D. 14 in
Answer:
A. 6.67 in
Step-by-step explanation:
length/width = 4/3 = x/5
Multiply by 5:
5(4/3) = x = 20/3 = 6 2/3
The length of the chalkboard is 6.67 inches.
Nadeen is at an arcade. She started with 18 tokens. Each game costs 3 tokens. So far, Nadeen has played 2
games.
Answer:
see below
Step-by-step explanation:
I think you are asking how many tokens she has left. She has 18 - 3 * 2 = 18 - 6 = 12 tokens left. She can play 12/3 = 4 more games.
What is the gcf of 96x5 and 64x2
Answer:
The GCF is going to be 32
Answer:
32x^2
Step-by-step explanation:
B on edge
if a propane tank has the shape of a cylindrical tank with a height of 4.2m and a radius of 1.3m how many cubic metres of propane is in the tank if it's only 50% full
Answer:
11.1 cm³
Step-by-step explanation:
V=πr²h / 2 (for half full)
V = (3.14)(1.3)²(4.2)/2
V = 11.1 cm³
A new post-surgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven others (the controls) receive the standard treatment. The recovery times, in days, are given below.
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
Required:
Find a 98% confidence interval for the difference in the mean recovery times between treatment and control.
Answer:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
Step-by-step explanation:
For this case we have the following info given:
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
We can find the sample mean and deviations with the the following formulas:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s =\sqrt{\frac{\sum_{i=1}^n (X_i- \bar X)^2}{n-1}}[/tex]
And repaplacing we got:
[tex] \bar X_T = 17.714[/tex] the sample mean for treatment
[tex] \bar X_C = 28.714[/tex] the sample mean for treatment
[tex] s_T= 4.461[/tex] the sample deviation for treatment
[tex] s_C= 7.387[/tex] the sample deviation for control
[tex]n_T= n_C= 7[/tex] the sample size for each sample
The degrees of freedom are given by:
[tex] df= 7+7-2= 12[/tex]
The confidence interval for the difference of means is given by:
[tex] (\bar X_T -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_T}{n_T} +\frac{s^2_C}{n_C}}[/tex]
The confidence is 98% so then the significance is [tex]\alpha=0.02[/tex] and [tex] \alpha/2 =0.01[/tex]. Then the critical value would be:
[tex] t_{\alpha/2}=2.681[/tex]
And replacing we got:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
The cottage inside the pen is a shape of a cylinder.
Answer:
Cylinder
As u can see the shape it's like a cylinder
3. Set up an equation and use it to solve for x.
51°
(5x + 1)
Answer:
51 = 5x+1
x = 10
Step-by-step explanation:
The angles are vertical angles which means they are equal
51 = 5x+1
Subtract 1 from each side
51-1 = 5x+1-1
50 = 5x
Divide each side by 5
50/5 = 5x/5
10 =x
Answer:
10
Step-by-step explanation:
51 = 5x + 1
5x = 51 - 1
5x = 50
x = 10
Hope this helps!
I’ll give the bralyist to the first correct answer
Let f be defined as shown.
What is f1 (-7)?
Answer:
The answer is 2
From the function when the input is 2 the output is -7. The inverse reverses the order so the input will be -7 and the output will be 2.
Which of the following expressions represents "the sum of n and the sum of 8 and 6"? n(8 + 6) n + (8 + 6) (n + 6)8
Mr. Hobbs took out a loan of $12,000 for 4 years at a simple annual
interest rate of 7%. How much interest did he pay?
Answer:
Step-by-step explanation:
I= P*r*t
I = 12000* 7% *4
Total interest paid was $3360.
Answer: $3,360
Step-by-step explanation:
What is true about the number 3.872? Check all that apply.
The 8 is in the tens place.
The 7 is in the hundredths place.
The 3 is in the ones place.
This number is read as "three and eight seventy-two hundredths."
3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001).
Answer:
The 7 is in the hundredths place.
The 3 is in the ones place.
3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001).
Step-by-step explanation:
Given the number 3.872, to check all the given options that are true apply to the number, let's take a look at each position occupied by each digit. In order words, let's consider their place value.
Thus,
The 3 is in the ones place and as such has a value of 3.
8 is in the tenths place having a place value of 0.8 (⁸/10)
7 is in the hundredths place having a place value of 0.07 (⁷/100)
2 is in the thousandths place having a place value of 0.002 (²/1000)
Going by these, the following statements are true :
"The 7 is in the hundredths place."
"The 3 is in the ones place."
"3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001)."
The number is pronounced as three and eight hundred seventy-two thousandths rather than the option given.
Therefore, only 3 if the options are correct
Answer: The 7 is in the hundredths place.
The 3 is in the ones place.
3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001).
Step-by-step explanation:
In the question, 3 is in the ones place. The first number after the decimal point is the tenths. In the question, the place value of 8 is 8 tenths; 7 is in the hundredths place.
3.872 = (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001)
= 3 + 0.8 + 0.07 + 0.002
= 3.872
The number is pronounced as three and eight hundred seventy-two thousandths
Express the following ratio in its simplest form.
4:12
Answer:
3:12
Step-by-step explanation:
Answer:
1:3
Step-by-step explanation:
Think 4:12 as a fraction for a moment, it would be 4/12. Now completely simplify 4/12, you get 1/3. Now put 1/3 as a ratio, it would be 1:3.
Please mark BRAINLIEST, thanks!
A shopkeeper buys 1 dozen of pens at Rs 15 each and sells them at Rs 18
ch. Find his profit and profit percent.
Answer:
20%
Step-by-step explanation:
Cost price (C. P.) of each pen = ₹ 15
Selling price (S. P.) of each pen = ₹ 18
Profit = S. P. - C. P. = 18 - 15 = ₹3
[tex]profit \: percent \\ \\ = \frac{profit}{c.p.} \times 100 \\ \\ = \frac{3}{15} \times 100 \\ \\ = \frac{3}{3} \times 20 \\ \\ = 20\%[/tex]
For a particular disease, the probability of having the disease in a particular population is 0.04. If someone from the population has the disease, the probability that she/he tests positive of this disease is 0.95. If this person does not have the disease, the probability that she/he tests positive is 0.01. What is the probability that a randomly selected person from the population has a positive test result
Answer:
4.76% probability that a randomly selected person from the population has a positive test result
Step-by-step explanation:
We have these following probabilities:
4% probability of having the disease.
If a person has a disease, 95% probability of a positive test.
100-4 = 96% probability a person does not have the disease.
If a person does not have the disease, 1% probability of a positive test.
What is the probability that a randomly selected person from the population has a positive test result
95% of 4% and 1% of 96%. So
p = 0.95*0.04 + 0.01*0.96 = 0.0476
4.76% probability that a randomly selected person from the population has a positive test result
A 2-pack of scented candles costs $0.95. What is the unit price, rounded to the nearest cent?i mark the 1st answer brainliest
Step-by-step explanation:
Cost of 2 pack = 0.95
Cost of 1 pack = 0.95 ÷ 2 = 0.475
Unit price = 0.475
A designer makes a model of a patio using 1/2 inch square tiles each 1/2 inch square tiles = 4 square feet what area is represented by the 8 x 6 model
Answer:
[tex]192ft^2[/tex]
Step-by-step explanation:
The model of a patio was made by
using 1/2 inch square title=4 square feet.
area represented by the 8 *6 model can be calculated as follows;
FIRSTLY, the number of tiles in the 8 *6 model can be calculated by multiplying it i.e
8 *6 model =[tex]48 tiles[/tex]
Hence there are 48 tiles in 8 *6 model
It was given that 1/2 inch square title=4
square feet.
So to calculate the total Area occupied by the 48 tiles
[tex]Area=1/2×48[/tex]
[tex]Area=24inches^2[/tex]
If [tex]1/2inches^2=4ft^2[/tex] ( from the question)
Let X represent [tex]24inches^2[/tex]
Then, [tex]24inches^2=Xft^2[/tex]
Cross multiply
[tex]4×24=X×1/2
X=4×24×2
X=[tex]192ft^2[/tex]
[tex]24inches^2=[tex]192ft^2[/tex]
Therefore, the area represented by the 8 *6 model is [tex]192ft^2[/tex]
What is an equivalent function to f(x)=(x-2)^3
Answer:
x^3-6x^2-4x-8
Step-by-step explanation:
First you would multiply (x-2) by itself (x-2) to get
x^2-2x-2x+4
then you would combine like terms
x^2-4x+4
Then you would multiply that by x-2
(x^2-4x+4)(x-2)
x^3-2x^2-4x^2-8x+4x-8
then you combine like terms
x^3-6x^2-4x-8
Please answer this correctly
Answer:
Pennies: 20%
Nickels: 36%
Dimes: 18%
Quarters: 21%
Step-by-step explanation:
Pennies: [tex]\frac{125}{125+180+90+105} =\frac{125}{500} =\frac{25}{100}[/tex] or 20%
Nickels: [tex]\frac{180}{125+180+90+105} =\frac{180}{500} =\frac{36}{100}[/tex] or 36%
Dimes: [tex]\frac{90}{125+180+90+105} =\frac{90}{500} =\frac{18}{100}[/tex] or 18%
Quarters: [tex]\frac{105}{125+180+90+105} =\frac{105}{500} =\frac{21}{100}[/tex] or 21%
Round 8326 to the nearest hundred
Answer:
The answer is 8300.
Step-by-step explanation:
1) We round the number up to the nearest hundred, if the last two digits in the number are 50 or above.
2) We round the number down to the nearest 100 if the last two digits in the number are 49 or below.
3) If the last two digits are 00, then we do not have to do any rounding because it is already to the hundred.
what are 80 percent of 500
Answer: 400
Step-by-step explanation:
500 x 0.80 = 400
Answer:
400
Step-by-step explanation:
Of means multiply
80% * 500
Change to fraction form
80/100 * 500
Rewriting to reduce
80 * 500/100
80 * 5
400
a cone has the diameter of 3 inches. the cone holds 12 cubic inches of water. to the nearest inch, what is the height of the cone?
Answer:
The height is about 5 inches.
Step-by-step explanation:
The volume for a cone is [tex]\frac{1}{3}[/tex] × π × r² × h
The radius of the cone is 1.5
12= [tex]\frac{1}{3}[/tex] × π × 1.5² × h
12= [tex]\frac{1}{3}[/tex] × π × 2.25 × h
12=0.75×π×h
Divide both sides by 0.75
16=π×h
Divide both sides by π
5≈h
The height is about 5 inches.
A high school track is shaped as a rectangle with a half circle on either side.Jake plans on running four laps. How many meters will Jake run? Use 3.14 for Pi.
Answer:
if you go around a track one time thats 400 meters but if you go around 4 times thats 1600 meters, you dont need to use 3.14 pi for this " no offense", i do track and field myself and i do the short distance, which is 100 meters and 200 meter but for for long distance runners they go around the track 4- 8 times so it is 1600 meters is ur answer. and when u go around 8 times, thats 3200 meters.
Step-by-step explanation:
Angle EFB is 108º
a)Find the size of angle x.
b) which one of these justifies your answer?
A-corresponding angles
B- Alternate angles
C- vertically opposite angles
Answer:
c of what im sure about
Step-by-step explanation:
3. What would you expect the relationship between the length of a baby at birth and
the month in which the baby was born to be?
A positive correlation
B negative correlation
C no correlation
What’s the degree of the rotation?
Answer: The answer is C 90
Step-by-step explanation: Rotations is ¼ and the Radians is π/2
the time taken by a student to the university has been shown to be normally distributed with mean of 16 minutes and standard deviation of 2.1 minutes. He walks in once a day during term time, 180 days per year, and leaves home 20 minutes before his first lecture. a. Find the probability that he is late for his first lecture. b. Find the number of days per year he is likely to be late for his first lecture.
Answer:
a) 2.84% probability that he is late for his first lecture.
b) 5.112 days
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 16, \sigma = 2.1[/tex]
a. Find the probability that he is late for his first lecture.
This is the probability that he takes more than 20 minutes to walk, which is 1 subtracted by the pvalue of Z when X = 20. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 16}{2.1}[/tex]
[tex]Z = 1.905[/tex]
[tex]Z = 1.905[/tex] has a pvalue of 0.9716
1 - 0.9716 = 0.0284
2.84% probability that he is late for his first lecture.
b. Find the number of days per year he is likely to be late for his first lecture.
Each day, 2.84% probability that he is late for his first lecture.
Out of 180
0.0284*180 = 5.112 days