Answer:
The capacity of the mug = [tex]1\frac{1}{3}[/tex] cups
Step-by-step explanation:
Given - A mug is 1/8 full. The mug contains 1/6 of a cup of water.
To find - Find the capacity of the mug. Write the answer as a fraction or mixed number
Proof -
Let the capacity of water = x
Given that,
A mug is [tex]\frac{1}{8}[/tex] full of water
⇒Total cups of water in the mug = [tex]\frac{1}{8} x[/tex]
Now,
Given that, The mug contains [tex]\frac{1}{6}[/tex] of a cup of water.
∴ we get
[tex]\frac{1}{8} x[/tex] = [tex]\frac{1}{6}[/tex]
⇒x = [tex]\frac{1}{6}[/tex] × 8
= [tex]\frac{8}{6}[/tex]
= [tex]\frac{4}{3}[/tex] = [tex]1\frac{1}{3}[/tex]
⇒x = [tex]1\frac{1}{3}[/tex]
∴ we get
The capacity of the mug = [tex]1\frac{1}{3}[/tex] cups
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 620 babies were born, and 341 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?
Answer:
Based on the confidence interval, the method appears to not bring expected results
Step-by-step explanation:
The given parameters are;
The number of babies in the study, n = 620 babies
The number of girls in the study sample = 341 girls
The proportion of girls in the study sample, [tex]\hat p[/tex] = 341/620 = 0.55
At 99% confidence level, we have the critical z = 2.576;
The confidence interval is given by the following formula;
[tex]CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p} \cdot (1-\hat{p})}{n}}[/tex]
Plugging in the values of the variables, we get;
[tex]CI=0.55\pm 2.576\times \sqrt{\dfrac{0.55 \times (1-0.55)}{620}} \approx 0.55 \ \pm 5.14680 \times 10^{-2}[/tex]
Therefore, 0.498532 < p < 0.601468
Based on the result of the confidence interval, we can be 99% sure that the true mean is between 0.498532 and 0.601468, therefore, given that the range includes a true mean of 0.5 or 50% probability of conceiving a girl, which is the percentage predicted by genetics, the method appears ineffective
Find the CIRCUMFERENCE of the circle.
Answer:
C=2πr
Step-by-step explanation:
Its on the wall of my math class
90 minutes in fraction hour?
Answer:
1.5 Hours
Step-by-step explanation:
So, 90 minutes is between 1 hour and 2 hours (2 x 60 = 120 minutes). It is exactly half way between, hence 90 minutes is 1 and 1 half hours (or less formally, 1 and a half hours).
or
90 Minutes = 1.5 Hours = 1 Hour and 30 Minutes. Minutes to hours Time Converter 90 hours to minutes. This conversion of 90 minutes to hours has been calculated by multiplying 90 minutes by 0.0166 and the result is 1.5 hours.
HELPPPPPP!!!
find each missing length. give all answers in the simplest radical form.
Answer: 67.082
Step-by-step explanation: 67.1
HELP HELP HELP PLS
What is the common denominator between 5/7 and 2/6?
What should the renamed numerators be? (Just type the numerator, not the entire fraction).
Answer:
21 is common denominator.
15 and 7 are the corresponding numberators.
Step-by-step explanation:
You multiply the 7 and 6, then apply to the fractions, and slowly reduce until you find a good match.
Answer:
30 and 14
Step-by-step explanation:
5/7 = times by 6 to get 30/42
2/6 = times by 7 to get 14/42
ducks and pigs are in a barn. There a total of 20 animals with 56 legs all together. How many of each animal are in the barn?
Answer:
Ducks- 8
Pigs- 12
Step-by-step explanation:
56 divided by 8 is 12 and 12 plus 8 is 20.
Kayla is framing a square painting with side lengths of x+5 inches. The total area of the painting and the frame has a side length of 3x-6 inches. The material for the frame will cost 0.07 per square inch
Complete question :
Kayla is framing a square painting with side lengths of x+5 inches. The total area of the painting and the frame has a side length of 3x-6. inches. Write an expression for the area of the frame. Then find the cost of the material for the frame if x = 16. The material for the frame will cost 0.07 per square inch
Answer:
8x² - 46x + 11 ;
$92.61
Step-by-step explanation:
Side length of square painting = x + 5
Area of square painting = (x +5)²
Side length of Total area of square painting + frame = 3x - 6
Total area = (3x - 6)²
Area of frame :
(3x - 6)² - (x +5)²
(3x - 6)(3x-6)
9x² - 18x - 18x +. 36 = 9x² - 36x + 36
(x +5)(x+5) = x²+5x+5x+25 = x² + 10x + 25
9x² - 36x + 36 - (x² + 10x + 25)
9x² - 36x + 36 - x² - 10x - 25
8x² - 46x + 11
Area of frame = 8x² - 46x + 11
8(16^2) - 46(16) + 11
= 1323 in²
1323 * 0.07 = $92.61
What is another way to write x2.x4?
Answer:
If x2.x4 and x2= 2x, x4=4x, while . means multiplication. therefore it can be written as 2x × 4x
Assignment: Wed : Finding Unit Rates (7.RP.1, 7. RP.2, 7.RP.2a
Problem ID: PRABDPF7
In
1
10
of an hour, Jane can clean
5
8
of a window.
What is her unit rate in windows per hour?
The Utah Middle School Math Project
The
Answer:
5
Step-by-step explanation:
You earn $36 over a weekend shoveling snow. It snows again on Monday night, and after another afternoon of snow shoveling you now have $42 total dollars. How much money did you eam on Monday( include equation)
find the different pen! ⬇️
182
Having good study habits will help you learn more.
TrueFalse
Answer:
Ture
Step-by-step explanation:
I have experience and i answered this question before
Answer:
True.
Step-by-step explanation:
Studying helps implant the knowledge into your brain, allowing you to remember it, and succeed in that subject of knowledge, thus having good study habits will help you learn more!
If the measure of arc RT = 80 degrees and the measure of arc US = 40 degrees, what is the m<2?
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=38(1.108)^x
Step-by-step explanation:
We are given this function:
y=8700* (1.04)^{4}y=8700∗(1.04)
4
8700 is the initial amount.
1.04 shows the change of original amount. This is decimal form of percentage. We need to transform it into regular percentage.
1.04 * 100% = 104%
Now we observe this number. If it is greater than 100% we have growth, if it is lower than 100% it is decay, and if it is equal to 100% than there is no change.
In our case this number is greater than 100% so we have growth. To determine the percentage rate we must substract 100% as it represents the original amount.
104% - 100% = 4%
This would be our solution if we don't have an exponent.
We have exponent so first step is to calculate the number and then we repeat the steps from above.
1.04^{4} = 1,169858561.04
4
=1,16985856
1,16985856 * 100% ≈ 116,99%
116.99% - 100% = 16.99%
So, final solution is growth of 16.99%
We are given this function:
y=8700* (1.04)^{4}y=8700∗(1.04)
4
8700 is the initial amount.
1.04 shows the change of original amount. This is decimal form of percentage. We need to transform it into regular percentage.
1.04 * 100% = 104%
Now we observe this number. If it is greater than 100% we have growth, if it is lower than 100% it is decay, and if it is equal to 100% than there is no change.
In our case this number is greater than 100% so we have growth. To determine the percentage rate we must substract 100% as it represents the original amount.
104% - 100% = 4
This would be our solution if we don't have an exponent.
We have exponent so first step is to calculate the number and then we repeat the steps from above.
1.04^{4} = 1,169858561.04
4
=1,16985856
1,16985856 * 100% ≈ 116,99%
116.99% - 100% = 16.99%
So, final solution is growth of 16.99%
Find the volume of a right circular cone that has a height of 4.4 in and a base with a diameter of 3.3 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
12.5 in squared 3
Step-by-step explanation:
Answer:
12.5!
Step-by-step explanation:
Plz help I need this for my grade report cards are coming out
Answer:1.5
1st box: 0.75
2nd box: 1.5
3rd box: 3
4th box: 28
Step-by-step explanation:
First I got the 4th box. I found out 3.5x2=7, and 7x2=14. So I know the pattern is multiply by 2.
Then I got the 3rd box. I used a proportion. (14x6)/28= 3
Then the 2nd box. I did (3x7)/14=1.5
Lastly, I did the 1st box. (1.5x3.5)/7= 0.75
I hope that helped :)
Answer:
1.19
69.9
Per
6 have a great day
Yesterday, you sent 25 text messages. You said that 20% of those messages were to your best friend. How many text messages did you send to your best friend yesterday?
Answer:
5 text messages
Step-by-step explanation:
Given data
The total number of text= 25
20% of the text message were to your best friend
Let us find 20% of 25
=20/100*25
=0.2*25
=5
Hence the number of text sent to your best friend is 5 text messages
Given g(x) = -x – 4, solve for 2 when g(x) = -4.
How many learners can enrol if there are 12 teachers and a ratio of teachers to learners is 30:1
Answer:
360 learners
Step-by-step explanation:
One way to solve these types of problems is that you could set up a proportion
learners/teachers = learners/teachers
Let x = no. of learners to enrol
30/1 = x/12
12(30) = x
x = 360 learners
Just number 14 pleaseee
9514 1404 393
Answer:
Step 2 is where the error lies.
The solution is x > 6
Step-by-step explanation:
The rules for solving inequalities are substantially similar to the rules for solving equations. If you perform the same operation on both sides of the comparison, the value of the variable does not change. (The exception is when that operation is an "order-reversing" operation. See comment below.)
Kahal's steps would be expected to be the same ones you would use:
Step 1: 4x -4 > 20 . . . given
Step 2: 4x > 24 . . . add 4 to both sides
Step 3: x > 6 . . . . . divide by 4
We note that our Step 2 is different from Kahal's Step 2. In Step 2 is where his mistake was made. He added 4 to one side and subtracted 4 from the other side.
__
Exception (order-reversing operations)
The operation you will usually run across in high-school algebra that will reverse ordering is multiplication (or division) by a negative number. Consider, for example, ...
1 < 2
-1 > -2 . . . . . both sides of the inequality multiplied (or divided) by -1
Notice that the order has been reversed: the larger magnitude number is now "less than".
The perimeter of a regular hexagon is 78 cm .What will be the length of each side?
Answer:
13 cm
Step-by-step explanation:
78/6=13
Answer:
13cm
Step-by-step explanation:
regular means the sides are equala hexagon has 6sides78/6=13A rectangle has vertices located at (–4, 4), (2, 4), (2, –4) and (–4, –4). What is the length of a diagonal of the rectangle?
Answer:
A diagonal of this rectangle has length 10.
Step-by-step explanation:
The vertices (-4, 4) and (-4, -4) have the same x-coordinate (-4) and different y-coordinates (4 and -4). These two points are the endpoints of a vertical side of the rectangle which has length 4 - (-4) = 8.
Similarly, the vertices (2, -4) and (-4, -4) have the same y-coordinate (-4) but different x-coordinates (2 and -4). To find the horizontal dimension of the rectangle, we calculate 2 - (-4), which comes out to 6.
Thus, the width of the rectangle is 6 and the length is 8.
Using the Pythagorean Theorem, we find the length of a diagonal as follows:
d = √(6^2 + 8^2) = √(36 + 64) = √100 = 10.
A diagonal of this rectangle has length 10.
If twice a number is 10, what is that number?
Answer:
2x = 10
x = 10 / 2
therefore, x can be 5
Step-by-step explanation:
check
2*5 = 10
BRAINLIEST ARMYYY
A line passes through the points (-3,0) and (2,5). Find its equation in general
form.
Factor completely:
x³ - 9x
Answer:
x(x+3)(x-3)
Step-by-step explanation:
Factor out common term x
=x(x^2-9)
Factor x^2-9;
(x+3)(x-3)
=x(x+3)(x-3)
Answer:
x(x + 3)(x - 3)
Step-by-step explanation:
What we're given is a difference of squares multiplied by x. If we start by factoring x out, we can simply expand the binomial:
x³ - 9x
= x(x² - 9)
= x(x + 3)(x - 3)
Any time you see an expression in the format a² - b², that is called a difference of squares, and can always be expanded out to (a + b)(a - b). In this case, a is x, and b is 3.
A complex shape made of two rectangles. The bottom rectangle has measurements 3 meters by 4 meters. The top rectangle has measurements 3 meters by 2 meters plus 4 meters plus 2 meters. Side A B is opposite of the side with measurements 2 meters, 4 meters, 2 meters. What is the distance from point A to point B? 8 m What is the perimeter of the shape?
The length of the side opposite to points A and B is 8 m
The perimeter of the shape is 18 m.
What is the distance from point A to point B?The length of the side opposite to points A and B, is 2 meters and 4 meters and 2 meters.
Length of AB = 4 m + 2 m +2 m = 8 m.
The perimeter of the complex shape by adding the lengths of all its sides;
Perimeter = length of AB + length of BC + length of CD + length of DA
Length of BC = length of the bottom side of the top rectangle = 3m
Length of CD = length of the top side of the top rectangle = 3 m.
Length of DA = length of the bottom side of the bottom rectangle = 4 m.
The perimeter of the complex shape is calculated as follows;
Perimeter = 8 m + 3 m + 3 m + 4 m
Perimeter = 18 m.
Learn more about perimeter here: https://brainly.com/question/19819849
#SPJ1
if the simple interest on 2000 for 4 years is 4000 then what is the interest rate
Answer:
Principal = Rs 2000
Time = 4 years
Interest = Rs 400
Now, Interest= Principal×Rate×Time/100
400= 2000×R×4/100
R= 400×100/2000×4
Step-by-step explanation:
Hope it is helpful....
Solve for x.
3/4(8x-12) = 2/3(6x+12)
In order for a rhombus to be proven using either its sides or angels, it must first be proven to be a
Answer:
It must be proven to be a quadrilateral
Step-by-step explanation:
The question is straightforward, and it requires a direct answer.
A rhombus has four sides and as such it means it is a type of quadrilateral.
So, before a shape is proven to be a rhombus, it has to first be proven to be a quadrilateral.
A football field measures at 100 yards with 2 end zones. There are 2 end zones. Each end-zone is 10 yards long. What is the total length of the football field in feet?
Answer:
360 feet.
Step-by-step explanation:
If there are 2 end zones each measuring 10 yards long then that means that both together measure 20 yards long. We add this to the 100 yards of the field and we get a total length of 120 yards. Now we can simply turn this into feet, we know that ...
1 yard = 3 feet
120 yards = x feet
120 * 3 = x
360 feet = x
Finally, we can see that the length of the football field is 360 feet.
Adult tickets to a basketball game cost $5. Student ticket cost $1. A total of 2,814 was collected on the sale of 1,150 ticket. How many of each type of ticket were sold?
Answer:
Adult: 333 tickets, Student: 1664 tickets