In 100g of 15% sugar syrup, there is 15g of sugar.
Sugar SyrupSugar syrup is a thick viscous liquid that mostly contains water and dissolved sugar in it. therefore, a 20% sugar syrup means having a 20:80 ratio of sugar and water in a unit of sugar syrup.
Given to us,100g of sugar syrup 15% sugar,
Now, 15% of sugar means having a 15:85 ratio of sugar and water in 100g of sugar syrup. Let the sugar in 100g of sugar syrup be x. so, the water in the syrup is (100-x), therefore,
[tex]\bold{\dfrac{15}{85} = \dfrac{sugar}{water}}[/tex]
Substituing the values we get,
[tex]\dfrac{15}{85} = \dfrac{x}{100-x}\\\\15\times(100-x) = 85x\\1500 - 15x = 85x\\1500 = 85x +15x\\1500 = 100 x\\\\x = \dfrac{1500}{100}\\\\x = 15[/tex]
Hence, In 100g of 15% sugar syrup, there is 15g of sugar.
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The line plots shows the number of hours two different age groups of teenagers spent online the previous week.
Select from the drop-down menus to complete each statement.
The range is? is the same for both
is greater for data set 1
is greater for data set 2
The mean? is the same for both
is greater for data set 1
is greater for data set 2
Answer:
is greater for data set 2 ; is greater for data set 2
Step-by-step explanation:
The range is found by subtracting the highest and lowest value. The range of the first plot would be
34-21 = 13.
The range of the second plot would be
36-12 = 24.
The mean is found by adding together all of the data points and dividing by the number of data points. For the first plot, the sum of the data is 274 and there are 10 data points; this makes the mean 274/10 = 27.4.
For the second plot, the sum of the data is 280.5 and there are 10 data points; this makes the mean 280.5/10 = 28.05.
The range is greater for data set 2.
Then mean is greater for data set 2.
What is Mean?Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.
Consider the data plot for 13 to 15 years olds.
Mean = Average of the values
= (21 + 24 + 26 + 27 + 27 + 28 + 28 + 28 + 31 + 34) / 10
= 27.4
Range = Maximum value - Minimum value
= 34 - 21
= 13
Consider the data plot for 16 to 18 years olds.
Mean = Average of the values
= (12 + 21 + 28 + 28 + 28 + 28 + 30.5 + 34 + 35 + 36) / 10
= 28.05
Range = Maximum value - Minimum value
= 36 - 12
= 24
Hence the range and mean are greater for data set 2.
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HELP PLEASE AND ANSWER WITH STEPS thank you so much
a number cube is rolled 24 times.how many times will a number be less than tree be expected to be rolled?
The number of the times cube is rolled for getting less than three is 8.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability of getting less than three = 2 / 6 = 1 / 3
The number of the times cube rolled is,
Pn = ( 1 / 3 ) x 24 = 8
Therefore, the number of the times cube is rolled for getting less than three is 8.
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Given: a = 640, A = 70°, B = 52° in triangle ABC ; find b. Round answers to the nearest whole number
Answer: 537
Step-by-step explanation:
Given: a = 640 A =70° B =52°
Whenever two angles and one side of a triangle is given, we can always use the sine formular to find the other side
Using the sine formula;
sin A / a = sin B /b
sin70° / 640 = sin 52° / b
cross multiply
bsin70° = 640sin52°
To get b, we divide bothside by
sin 70°
b = 640sin52° / sin 70°
b = 504. 327 / sin70°
b = 536. 693
b = 537 to the nearest whole number
Write an Inequality for the following situation
No more than 8 books are in your bag
It says "No more than 8 books are in your bag". Here "Not more than" a specific number would be a set of all values that are "less than or equal" to given number.
So let's consider 'n' represents the number of books in the bag and we know this number can not be a negative value i.e. n is "greater than or equal" to 0.
Also n is "less than or equal" to 8 as given in the question.
Hence, the inequality would be 0 ≤ n ≤ 8.
the slope of the containing the point (-2,3) and (-3,1) is
While bowling with friends, Brandy rolls a strike in 5 out of 10 frames. What is the experimental probability that Brandy will roll a strike in the first frame of the next game? Enter your answer as a simplified fraction.
The experimental probability of Brandy rolling a strike in the first frame of the next game is 1/2.
Explanation:To find the experimental probability that Brandy will roll a strike in the first frame of the next game, we need to divide the number of times Brandy rolled a strike in the first frame by the total number of frames. In this case, Brandy rolled a strike in 5 out of 10 frames, so the experimental probability is 5/10, which simplifies to 1/2.
find the nonpermissible replacement for a in this expression 7/6a
Geometry Circle - Find the Midsing Angle
Lisa has 1 set of 12 cars and she gives her sister 3cars. What fraction of Lisa's set did she give her sister
if f(x)=8x+6, what is f(-1)
how farare 27and -54 apart on the number line
How far are 27 and -54 apart on the number line?
Solution:
If we see on the number line , 27 is 27 units apart from 0 and it is 27 units to the right of 0
And, -54 is 54 units apart from 0 and it is 54 units to the left of 0. So, -54 is in opposite direction with respect to 27.
So, To find how far is 27 from -54 we must add 27 and 54
As, 27+54=81
So, -54 and 27 are 81 units away from each other.
Answer:81 units
Please see the number line attached.
the mean temperature during the winter in the arctic tundra is -34°c. you can convert degrees celsius to degrees fahrenheit by using the formula f=9/5c+32. what is the mean temperature in degrees fahrenheit?
The base of a triangular prism is an isosceles right triangle with a hypotenuse of
√50 centimeters. The height of the prism is 8 centimeters. Find the surface area of the triangular prism. Round your answer to the nearest tenth.
HELP PLZ; 20 POINTS
At a fair, each person can spin two wheels of chance. The first wheel has the numbers 1, 2, and 3. The second wheel has the letters A and B. (a) List all the possible outcomes of the compound event. (b) If you spin both wheels, what is the probability that you get either a 1 or an A? Explain. Answer:
(a) All the possible outcomes of the compound event are {(1, A), (1, B), (2, A), (2, B), (3, A), (3, B)}
(b) Probability is 2/3.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
Given that,
At a fair, each person can spin two wheels of chance.
The first wheel has the numbers 1, 2, and 3.
The second wheel has the letters A and B.
(a) 1 can be followed by A and B, 2 can be followed by A and and B and so is 3.
Possible outcomes = {(1, A), (1, B), (2, A), (2, B), (3, A), (3, B)}
(b) Total possible outcomes = 6
Number of outcomes which has either 1 or A = 4
Probability = 4/6 = 2/3
Hence the required probability is 2/3.
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Jake has a teepee that is cone shaped it has a height of 9 feet and a diameter of 8 feet find the volume of the teepee in terms of Pi.
PLEASE HELP..... I WILL GIVE BRAINLIEST!!
factorise 36n(squared) divide by 25 minus 1
Answer:
[tex]( \frac{36n^{2} }{25} - 1) [/tex] factors to become [tex]( \frac{6}{5}n - 1)( \frac{6}{5}n + 1) [/tex]
Explanation:
The binomial [tex]( \frac{36n^{2} }{25} - 1) [/tex] is what is called a difference of two squares which can be identified by the equation being in the form (a² - b²) where both terms can be square-rooted.
Because the equation is a difference of two squares, its factors will be in the form: (a - b)(a + b).
With a² = [tex]\frac{36n^2}{25}[/tex] and b² = 1, we can find the square root of both and plug them into the above factor form.
√(36n² / 25) = 6n/5
√1 = 1
So the factors are [tex](\frac{6}{5}n -1)(\frac{6}{5}n +1)[/tex]
the sum of four times a number and 17 is 33. Find the number, please? I really need help!!
Hector has a $5 off coupon at Brenda's Bagels. Bagels cost $8.99 per dozen. Write an equation that models the total amount of money (y) Hector owes if he buys (x) dozen bagels.
Marie draws a marble out of a bag. It is either red or green. She records the color and then puts the marble back in the bag.
She repeats this process 80 times to get the following results:
Red:30
Green : 50
Because Marie knows that there are 5 marbles in the bag she knows that the probability of choosing a red marble must be either 1/5,2/5,3/5,4/5, or 5/5. Based on her data which of these models is most probable?
*THIS QUESTION IS WORTH 30 POINTS*
Answer:
2/5 thx for the points
Step-by-step explanation:
If (tan^3 theta -1) / (tan theta - 1) - sec^2 theta +1 = 0, find cot theta.
a. -1 b.0 c. 1 d. sec theta
Answer:
Option A. [tex]cot\theta = -1[/tex]
Step-by-step explanation:
[tex]\frac{tan^{3}\theta -1}{tan\theta -1}-sec^{2}\theta +1=0[/tex]
we have to the value of [tex]cot\theta[/tex]
We further solve the equation
[tex]\frac{(tan\theta -1)(tan^{2}\theta +1+tan\theta )}{(tan\theta -1)}-sec^{2}\theta+1=0[/tex] [a³- b³= (a-b)(a² + b²+ ab)]
[tex]sec^{2}\theta +tan\theta -sec^{2}\theta +1=tan\theta +1=0[/tex]
[tex]\frac{1}{cot\theta }=-1[/tex]
[tex]cot\theta = -1[/tex]
Therefore Option A. [tex]cot\theta = -1[/tex] is the answer.
A bag contains 45 marbles of various colours. Lena draws 48 times, each time replacing the marble before drawing again. She gets a total of 16 red marbles. Which is the best prediction of how many red marbles are in the bag?
A) 3
B) 13
C) 15
D) 16
Help as soon as possible!!!!
Question 2 Unsaved Cat is 5 less than twice Dog's age. Cat is 11 years old. Find Dog's age.
Let the dog's age be called x.
From the given statement, the following equation can be framed
Cat's age = 2*x -5
We are given to know that Cat's age is 11 years
So, we have:
11 = 2x -5
2x = 16
x = 16/2
x = 8
Dog's age = 8 years
A cylinder shaped drum is used to store used motor oil. The drum has a height of 3 ft and a radius of 1.5 ft
PLEASE HELP! @) POINTS
Describe the relationship between the probability of an event and its complement. If the probability of an event is 0.3, what is the probability of its complement?
1. The probability P of an event and its complement P' are mutually exclusive and add up to 1
2. If the probability of an event is 0.3, then the probability of its complement is 0.7. (1 - 0.3 = 0.7)
a circle has an area of 81 3.14 units . what is the diameter in terms of 3.14a circle has an area of 81 Pi square units what is the diameter of the circle
Answer:
18 units
Step-by-step explanation:
[tex]\pi r^2=81\pi[/tex]
Solve for [tex]r[/tex]:
[tex]\pi r^2=81\pi \\r^2=81\\r=9[/tex]
Knowing diameter is 2*r, we can apply the formula to find diameter
[tex]d=2*r\\d=2*9\\d=18[/tex]
an equation of the horizontal line that passes through the point (-2,5)
y = 5 is the equation of the horizontal line that passes through the point (-2,5).
Mathematically, an equation is a statement that two expressions are equal. The expressions on either hand of the equals sign are termed the left-hand side and the right-hand side of the equation. The equals sign is perused as" is equal to" or" equals".
An equation comprises variables, numbers and comparison sign.
As the ordinate of the given point is 5 then y = 5 is the horizontal line that passes through (-2,5).
Thus, the equation that passes through the point (-2,5) and is the horizontal line is y = 5.
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Jenny has $25 and she earns $10 for each lawn that she mows. Jenny wants to buy a concert ticket that costs $65.
Enter the minimum number of lawns Jenny needs to mow to be able to buy the concert ticket.