Answer:
[tex]17 \le t \le 28[/tex]
Step-by-step explanation:
Given
[tex]t = 22\frac{1}{2}[/tex] --- average time
[tex]\triangle t = 5\frac{1}{2}[/tex] --- the variation
Required
The inequality to represent the scenario
To do this, we simply add and subtract the variation from the average time.
i.e.
[tex]t \± \triangle t[/tex]
So, the inequality is:
[tex]22\frac{1}{2} - 5\frac{1}{2} \le t \le 22\frac{1}{2} + 5\frac{1}{2}[/tex]
Solve:
[tex]17 \le t \le 28[/tex]
2) Three people shared some money in a
ratio of 4:3:5. The second person got
£21 as a result. How much money did
they share?
Answer:
£ 84
Step-by-step explanation:
Let :-
Total amount be x .Given ratio :-
4 : 3 : 5 .→ Sum of ratios = 4 + 3 + 5 = 12 .
According to Question :-
→ 3/12 × x = £21
→ x = £21 × 12/3
→ x = £ 84 .
Answer:
£84.
Step-by-step explanation:
There are 4 + 3 + 5 = 12 parts.
The second person got 3 parts so we can write:
3/12 x = 21 where x is the required amount of money
x = 21 * 12/3
= 21 * 4
= £84.
Tony sold t-shirts and hats at the festival. He made a $4 profit for each t-shirt he sold. He also made a profit of $34 from selling hats. If he made a total profit of $106, how many t-shirts did he sell?
Answer:
18 T-shirts
Step-by-step explanation:
$4×18= $72 $72+$34=$106
If Kiri has 17 part-time members this month, how many full-time members does she need according to your equation?
Answer:
5050 = 225f + 125p
If p = 17 this month, then, f = 13
Step-by-step explanation:
Kiri owns a coworking space that has two primary types of memberships, full time and part-time. In order to pay her bills each month (rent on the building, electricity, internet, and so on) she needs to make $5050. Full-time memberships (f) cost $225 per month, and part-time memberships (p) cost $125 per month.
If Kiri has 17 part-time members this month, how many full-time members does she need according to your equation?
Total cost = $5050
cost of full-time memberships = $225
number of full time members = f
cost of part-time memberships = $125
number of part-time members = p
Total cost = cost of full-time memberships * number of full time members + cost of part-time memberships * number of part-time members
5050 = 225f + 125p
If p = 17 this month,
5050 = 225f + 125p
5050 = 225f + 125(17)
5050 = 225f + 2,125
5050 - 2,125 = 225f
2,925 = 225f
f = 2,925/225
f = 13
number of full time members = f = 13
If p = 17 this month, then, f = 13
The angle of elevation to a nearby tree from a point on the ground is measured to be
31°. How tall is the tree if the point on the ground is 62 feet from the tree? Round
your answer to the nearest tenth of a foot if necessary.
Answer:
37.3 ft
Step-by-step explanation:
tan A = opp/adj
tan 31° = x/62
x = 62 * tan 31°
x = 37.3 ft
The height of the tree is 37.25 ft if the point on the ground is 62 feet from the tree.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Trigonometric ratios are used to demonstrate the connection between the sides and angles of a right-angled triangle.
Let h denote the tree if the point on the ground is 62 feet from the tree.
The angle of elevation = 31°. Hence:
tan 31° = h/62
h = 62 × tan 31°
h = 37.25 ft
Thus, the height of the tree is 37.25 ft if the point on the ground is 62 feet from the tree.
Learn more about the right triangle here:
https://brainly.com/question/11899922
#SPJ6
There are 120 students in class 7. It is known that
2/3
out of them like Maths, out of which 35
are girls. Also, out of total students,
3/5
are boys. (3)
(a) What is the number of girls in the class?
(b) How many students like Maths?
(c) How many boys like Maths?
Multiply total students by 2/3 to find how many like math:
Like math = 120 x 2/3 = 240/3 = 80 total students like math
Multiply total students by 3/5 to find number of boys:
120 x 3/5 = 360/5 = 72 boys
A) number of girls = total students - boys = 120 -72 = 48 girls
B) from above 80 students like math
C) number of boys that like math = number of students that like math minus girls that like math: 80- 35 = 35 boys like math
At a show, there are 19 adults, 45 teenagers, and 36 children.
What is the probability that a person chosen at random from the audience is not a teenager?
Answer:
55% or 0.55 or 11/20
Step-by-step explanation:
probability the person chosen is an adult or child out of all
so 19+36/19+36+45
55/100
The probability that the selected person is not a teenager is [tex]\frac{11}{20}[/tex].
What is probability?
Probability is a measure of happening or non happening of the outcomes of the random experiment.
Probability formulaP(E) = Total number favorable of outcomes/ Total number of outcomes
Where,
P(E) is the probability of an event.
According to the given question.
Total number of adults in the audience = 19
Total number of teenagers in the audience = 45
Total number of children in the audience = 36
Total audience = 19 + 45 + 36 = 100
Now, the probability that the selected person is teenager = [tex]\frac{45}{100} = \frac{9}{20}[/tex]
Therefore,
The probability that a selected person is not a teenager
= [tex]1 -\frac{9}{20}[/tex]
= [tex]\frac{11}{20}[/tex]
Hence, the probability that the selected person is not a teenager is [tex]\frac{11}{20}[/tex].
Find out more information about probability here:
https://brainly.com/question/11234923
#SPJ2
Which expression is equivalent to (x^4/3 x^2/3)^1/3
?
x^2/9
x^2/3
x^8/27
x^7/3
Answer:
X^2/3
Step-by-step explanation:
What is the solution of the equation x2 − 2x + 4 = 0?
Answer:
No real solution
Step-by-step explanation:
This leads to a square root of a negative number, which is not possible without imaginary numbers
A box shown below is to paint blue except the bottom. What is the area of the surface, and square inches, that will be covered with the paint?
Answer:
186
Step-by-step explanation:
Your entire surface area is
216
the area of the rectangle on the bottom is 30
substract 30 from 216
If sin θ +cosec θ = 2 then sin2θ+ cosec2θ is equal to
a) 1 b) 4
c) 2 c) 9
Answer:
C
Step-by-step explanation:
We are given that:
[tex]\sin \theta +\csc \theta = 2[/tex]
And we want to find the value of:
[tex]\sin^2\theta + \csc^2\theta[/tex]
From the first equation, we can square both sides:
[tex](\sin \theta + \csc \theta)^2=(2)^2[/tex]
Square:
[tex]\sin ^2\theta +2\sin\theta\csc\theta +\csc^2\theta =4[/tex]
Let csc(θ) = 1 / sin(θ):
[tex]\displaystyle \sin ^2\theta +2\sin\theta\left(\frac{1}{\sin \theta}\right) +\csc^2\theta =4[/tex]
Simplify:
[tex]\displaystyle \sin ^2\theta +2(1) +\csc^2\theta =4[/tex]
Therefore:
[tex]\sin ^2\theta + \csc^2\theta =2[/tex]
Our answer is C.
(HELP) A glass jar contains 5 red, 7 green, 9 blue and 11 yellow marbles. If a single marble is picked at random from the jar, what is the probability of it being a blue marble? *
1/11
5/18
9/32
5/12
Answer:
Find the volume of this prism.
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the solution set of this problem?
O (,-21)
O (--,-21]
O [-21,700)
O (21,+0)
To find the slope of the trend line below Reilly chose the points (1,80) and (2,30). explain whether the points she chose will help her write the correct equation of the line and find the equation of a trend line
Answer:
We can't see the graph
Step-by-step explanation:
What's the surface area of the pyramid?
The Answer is C 226.8 ft
I remember doing this not to long ago
Enriques bathroom measures 6 ft. Long by 5 ft. Wide His shower is 3 feet square The title he wants to buy for the floor is sold in square feet. What is the area of the floor that he has to title
Answer:
Area of the floor is 30 square ft.
Step-by-step explanation:
Length of the floor, L = 6 ft
width of the floor, W = 5 ft
The floor is in the shape of rectangle.
The area of the rectangle is
A = Length x width
So, the area of the floor is
A = L x W
A = 6 x 5
A = 30 ft^2
25 POINTS Find the slope of the line khan academy
Answer:
-8/5
Step-by-step explanation:
Using the points given ( -1,4) and (4,-4)
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -4 -4)/(4- -1)
= (-4 -4)/(4+1)
= -8/5
Helppppppp please ASAP
determine the volume of a cube with a side length of 7.5m
Answer:
V≈421.88
Step-by-step explanation:
Math help please and thank you :)
Answer:
173
Step-by-step explanation:
Area of dirt in the flower bed = area of flowerbed - area of 3 trapezoids
Area of flowerbed:
The flowerbed is in the shape of a parallelogram
The area of a parallelogram can be calculated by multiplying the base length times the height
Base length = 20ft
Height = 10ft
Area of flowerbed = 10 * 20 = 200ft^2
Area of rockbeds
The rockbeds are in the shape of trapezoids
The area of a trapezoid can be calculated using this formula
A = (a + b)/2 * h
Where a and b = bases and h = height
The rockbeds of base lengths of 2 and 4 and have heights of 3
So area of rockbeds = (4 + 2)/2 * 3
4 + 2 = 6
6 / 2 = 3
3 * 3 = 9
We then multiply that by 3 ( because there are three rockbeds )
9 * 3 = 27
Finally we subtract the areas
200 - 27 = 173
1. For each relation, state
i) the domain and the range
ii) whether or not it is a function, and justify your answer
Answer:
A and C are functions.
The domain is x and the range is y
Step-by-step explanation:
Each x - value can have only one y -value
Function= unique x-values
Y can be the same answer but the X has to be different
A line's y-intercept is 1, and its slope is -5. What is its equation in
slope-intercept form?
help please
In the system of equations , x represents .... ( please answer 12a and 12b )
Answer:
x = cost of each t-shirt
y = cost of each sweatshirt
Step-by-step explanation:
Given equation:
2x + 2y = 26 (1)
x + 3y = 33 (2)
From (2)
x = 33 - 3y
Substitute x = 33 - 3y into (1)
2x + 2y = 26 (1)
2(33 - 3y) + 2y = 26
66 - 6y + 2y = 26
- 6y + 2y = 26 - 66
-4y = -40
y = -40/-4
y = 10
Substitute y = 10 into (2)
x + 3y = 33 (2)
x + 3(10) = 33
x + 30 = 33
x = 33 - 30
x = 3
Where,
x = cost of each t-shirt = $3
y = cost of each sweatshirt = $10
Find the mean of the data.
The number of trophies won by
each team in the district.
1, 3, 1, 5, 7, 8, 10
Mean: [? ] trophies
Answer:
5
Step-by-step explanation:
the union of 2 sets is all the elements of both set's, excluding the common elements true or false
Answer:
true
Step-by-step explanation:
AUB=A+B-(A∩B)
I need help please PLEASE PLEASEEEEEEEE
Answer:
Step-by-step explanation:
I kinda need help with this
Find the mean:40,13,49,53,35
Find the Range:40,13,49,53,35
Find the median:40,13,49,53,35
Answer:
mean: 38
range: 27
median: 40
Step-by-step explanation:
mean: 40+13+49+52+35 / 5
range: 40 - 13
median : 40
Answer:
Mean = 38
Range = 40
Median = 40
Step-by-step explanation:
Arrange the terms in ascending order :
13, 35 , 40 , 49 , 53
[tex]Mean = \frac{40 + 13 + 49 + 53 + 35}{5} = 38[/tex]
[tex]Range = {53 - 13} = 40[/tex]
[tex]Median = \ the \ middle \ term = 40[/tex]
The area of a square is 81 cm squared find its perimeter
Answer:
the answer is 36
Step-by-step explanation:
?
Answer:
Step-by-step explanation:
She made the -2(6) as a positive 12. it should've been a negative 12 because a negative multiplied by a positive is a negative.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP ASAP
A triangle has a angle of x, 40 and 30 what is the angle of x
Sum of interior angles of a triangle = 180°
x+40+30= 180°
x+ 70=180
x= 180-70
x= 110°
Answer:
x = 110
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , then
x + 40° + 30° = 180°
x + 70° = 180° ( subtract 70° from both sides )
x = 110°