The number that will be next in the series will be 63 .
In the question ,
a recurrence relation is given that is 0, 3, 8, 15, 24, 35, 48, ? .
we have to find the number that will come in place of question mark .
On carefully examining the series , we can see that
3 - 0 = 3
8 - 3 = 5
15 - 8 = 7
24 - 15 = 9
35 - 24 = 11
48 - 35 = 13
we can se that increments 3,5,7,9,11,13,... form an Arithmetic Progression
with first term as 3 and common difference as 2 ,
So ,the next increment will be 13+2 = 15
let the next term be "x" .
x - 48 = 15
x = 15 + 48 = 63
the number in place of ? is 63 .
Therefore , The number that will be next in the series will be 63 .
Learn more about Arithmetic Progression here
https://brainly.com/question/25271768
#SPJ4
Melissa uses 3/5 as much water as Neil to water her plants. If Melissa uses 4 and 1/3 gallons of water, how much does Neil use?
In triangle ABC, which side is the longest if these are the measures of the angles?
mzA= 60°, mzB = (3x - 2)°, mzC = (2x + 7)°
Applying the triangle sum theorem and the angle-side relationship, the longest side of triangle ABC is: side AC.
What is the Triangle Sum Theorem?The triangle sum theorem states that if we add all three interior angles of a triangle, the sum we get would be equal to 180 degrees.
What is the Angle-Side Relationship of a Triangle?The angle-side relationship of a triangle explains that the longest side of a triangle is always opposite to its largest angle, the medium side is opposite to the medium angle, and the shortest side is to the smallest angle of the triangle.
Given that triangle ABC has the following angle measures:
m∠A = 60°
m∠B = (3x - 2)°
m∠C = (2x + 7)°
Therefore:
m∠A + m∠B + m∠C = 180
Substitute:
60° + (3x - 2)° + (2x + 7)° = 180
60 + 3x - 2 + 2x + 7 = 180
Combine like terms:
65 + 5x = 180
5x = 180 - 65
5x = 115
x = 23
Find the measure of each of the angles by plugging in the value of x:
m∠B = (3x - 2)° = 3(23) - 2 = 67°
m∠C = (2x + 7)° = 2(23) + 7 = 53°
The largest angle is m∠B = 67°.
AC is opposite to angle B, therefore, AC is the longest side of the triangle.
Learn more about the triangle sum theorem on:
https://brainly.com/question/19805547
#SPJ1
Tyrese bought 35 tickets to use at the carnival. He used some of the tickets to ride the bumper cars and play some games. Now he has 28 tickets left. What is the percentage of decrease in the number of tickets that he has?
truck travelled from Town A to Town B. A van travelled from Town B to Town A at the same time . They met 10 km from the middle of the journey. Find the distance between Town A and Town B if the truck and the van travelled at 85 km / h and 60 km / h respectively .
Answer:
58 miles
Step-by-step explanation:
One truck second truck
rate 85 60
time t t
Distance d + 10 d -10
d + 10 = 85t d - 10 = 60t
d = 85= -10 d = 60t +10
Set the two equations equal to each other and solve
85t -10 = 60t + 10 Subtract 60t from each side
25t - 10 = 10 Add 10 to each side
25 t = 20 Divide both sides by 25
t = [tex]\frac{4}{5}[/tex]
Each were driving 4/5 of an hour. Plug into the one of the equaions
d + 10 = 85t
d + 10 = 85([tex]\frac{4}{5}[/tex])
d +10 = 68 Subtract 10 from both sides
d = 58
Answer:
Step-by-step explanation:
Givens
Truck = 85 km/hr
Van = 65 km/hr
t is the time they meet
Note
Truck A is travelling faster, so the place where they meet is closest to Town B.
Solution
Let the distance travelled by the truck be
d/2 + 10
Let the distance travelled by the van be
-d/2 + 10
Let t be the time they meet
85* (d/2 + 10) /t = -60*(d/2 + 10)/t multiply both sides by t
85*(d/2 + 10)*t/t = -60*(d/2 + 10)*t/t Combine
85*(d/2 + 10) = -60(d/2 + 10) Remove the brackets.
42.5 d + 850 = -30d - 600 Add 30 d to both sides
72.5d+ 850 = - 600 Subtract 850 from both sides.
72.5d = - 600 - 850 Combine
72.5d = -1450 Divide by 72.5
d = -1450 / 72.5
d = -20
The minus means that you are looking at it from the van's point of view.
For the imaginary number, which of these is a possible value of " if n is greater than 6?
A 0
B 5
C -2
D 1
E 2
Answer:
A 0
Step-by-step explanation:
A line has a slope of 2 and passes through the point (1, 5). What
is its equation in slope-intercept form?
Answer:
Y= 2x+3
Step-by-step explanation:
Slope = (y-y1)/(x-x1)
2= (y-5)/(x-1)
Cross multiply
Y-5= 2x-2
Collect like terms
Y= 2x+3
math homework percentages help pls
Answer: 70 dollars in profit
Step-by-step explanation: 20 x 13.50 = 270 20 - 3 = 17 20 x 17 = 340 340 - 270 = 70
Fiugrie out the ratio missing table text back answer !
NO EXPLAIN HURRY THANK BYE
The ratio between the fruit and vegetable is 1:3
RatioRatio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14. The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.
We can simply say that a ratio is a fraction of one quantity over another quantity
In this case, we just have to figure the ratio between fruit and vegetables.
In the first column, we have fruit to vegetable as 2:6 = 1:3
In the second column, we have fruit missing. We can make that x.
Using the ratio between fruit and vegetable, when vegetable is 12, the fruit will be 12/3 = 4
The value of fruit in the second column will be 4.
In the third column, we have fruit as 6 and vegetable as y.
We can apply same ratio to get the vegetable which will be 6 * 3 = 18
In the third column, the vegetable is 18
Learn more on ratio here;
https://brainly.com/question/2328454
#SPJ1
Approximate negative thirteen plus square root of seventy to the nearest tenth.
−8.4
−4.6
4.6
8.4
The value of the expression -13+√70 to the nearest tenth is -4.6
What is Arithmetic operation?Arithmetic operations involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
The expression -13+√70 comprises of addition of -13 and √70
The value of √70 is 8.4(to the nearest tenth).
Therefore the value of -13+√70
=-13+8.4
= -4.6( nearest tenth)
learn more about arithmetic operations from
https://brainly.com/question/20628271
#SPJ1
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the equation.
(−4, 2); y=−1/2x+6
Answer:
y = mx + b
-2 = ½(-4) + 6
Step-by-step explanation:
formula ; y = mx + b
where y = y co-ordinate
m = slope
x = x co-ordinate
b = y intercept
Therefore; y = mx + b
-2 = ½(-4) + 6
evaluate the expression when x = 8 and y = 4 6y-x
Answer:
16
Step-by-step explanation:
=6(4)-(8)
=24-8
=16
Find the area of the circle pictured above.
Round your answer to the nearest tenth
Answer:
~201.1[tex]u^2[/tex]
Step-by-step explanation:
Formula for area of a circle:
[tex]\pi r^2[/tex]
The diameter is any straight line that passes through the circle and endpoints lie on the perimeter of the circle.
We are given the diameter: 16. The diameter is twice the radius (for all circles) Divide the diameter, 16 by 2 to get the radius. If the problem gives you the radius, which is a line from the center of the circle, do not divide by 2 and directly plug into formula.
16/2 = 8
Plug into formula.
[tex]\pi r^2[/tex]
[tex]\pi 8^2[/tex]
Using PEMDAS, the standard order of operations order for math, we firsty do 8^2 before multiplying by pi.
8^2 = 8 x 8 = 64
[tex]64*\pi[/tex] = ~201.1
I need help, The problem is in the picture
Answer: i think its a=52
and b=8 srry if its wrong tell me and ill try to fix it thx:)
Step-by-step explanation:
Solve for x
5x+7>-13
Answer:
x > - 4
Step-by-step explanation:
5x + 7 > - 13 ( subtract 7 from both sides )
5x > - 20 ( divide both sides by 5 )
x > - 4
In your own words, explain what is meant by prezygotic mechanisms of reproductive isolation. Use 1-3 sentences.
Using the theories of prezygotic, we got that in my words prezygotic mechanisms of Reproductive isolation is defined as the mechanism that keeps species from mating with others. Prezygotic isolation actually prevents the fertilization of eggs while the postzygotic isolation prevents the formation of fertile offspring.
Reproductive isolation keeps species from mating with others. Prezygotic mechanisms include the habitat isolation, mating seasons, "mechanical" isolation, gamete isolation and the behavioral isolation.
Hence, in my words, prezygotic mechanisms of reproductive isolation is defined as the mechanism that keeps species from mating with others. Prezygotic isolation actually prevents the fertilization of eggs while the postzygotic isolation prevents the formation of fertile offspring.
To know more about prezygotic, visit here:
https://brainly.com/question/11068107
#SPJ4
In quadrilateral ABCD, triangle ADC is congruent to CBA. Show
that ABCD is a parallelogram.
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97% of the people who have a disease. However, it erroneously gives a positive reaction for 5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease". What is the probability of type i error if the new blood test is used?.
The probability of a type I error in the case of the new blood test is 0.022.
Given;
It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested who do not have the condition received an incorrectly positive response. Take into account the null hypothesis that "the person does not have the disease."
A: The individual does not have the disease
B: The individual does have the disease
We know that,
Type I Error is rejecting the true null hypothesis
P (Type I Error) = P(Positive reaction to an individual who does not have the disease)
=0.022
Hence, the probability of a type I error is 0.022.
To learn more about probability click here:
brainly.com/question/11234923
#SPJ4
7) What is the value of x?
21
42°
21
Drawing not to scale
The value of x in the given figure is x = 71° , the correct option is (c) .
In the question ,
a triangle ABC is given ,
the measure of angle A = 38°
we can see that length of the sides AB and AC is 21 , and we know when the length of two sides of the triangle is equal , it is called as isosceles triangle .
In isosceles triangle , the two angles corresponding to the two equal sides are equal , that means
angle B = angle C = x
In triangle ABC ,
By Angle Sum Property , we get
angle A + angle B + angle C = 180°
38 + x + x = 180
38 + 2x = 180
subtracting 38 from both the sides , we get
2x = 180 - 38
2x = 142
Dividing both sides by 2 , we get
x = 142/2
x = 71
Therefore , The value of x in the given figure is x = 71° .
The given question is incomplete , the complete question is
What is the value of x ,in the figure given below ? Drawing not to scale
(a) 21°
(b) 42°
(c) 71°
Learn more about Triangle here
https://brainly.com/question/9358855
#SPJ1
Can anybody solve this for me?
y= -3(-1)+3[slope intercept form]
What is the product of 1/23 and −3/12?
Your team win 16 medal at a competition. The medal are gold, ilver, and bronze in a ratio of 6 : 1 : 1. How many of each medal did your team win?
In a family of 48, 24 member like caava and 36 member like potatoe. 12 member like both caava and potatoe. How many member like caava?
Using the subtraction, the number of member who only like caava is 12.
In the given question we have to find how many member like caava.
Total member of family = 48
Member who like caava=24
Member who like potato=36
Member who like both caava and potato=12
In the given number of member who like caava having a member who also like potato and some are who only like caava.
So the number of member who only like caava = Total number of member who like caava−Total number of member who like both caava and potato
The number of member who only like caava =24−12
The number of member who only like caava =12
To lear more about subtraction link is here
brainly.com/question/2346316
#SPJ4
A department store buys 400 shirts at a cost of $10,800 and sells them at a selling price of $30 each. Find the percent markup. ... The percent markup is %.
The percent markup is 11.11%.
There is a department store. The total number of shirts bought by the department store is 400. The total cost of the shirts bought by the department store is $10,800. The department store sells all the shirts for $30 each. We need to find the percent markup.
We first need to find out the cost of each shirt. The cost price of each shirt is the total cost of all the shirts divided by the total number of shirts bought by the department store.
C = $10,800/400
C = $27
Hence, each shirt was purchased for a price equal to $27. To find the markup percentage, we need to find the percentage difference between the cost price and the selling price of the shirt.
M = [(30 - 27)/27]*100%
M = (3/27)*100%
M = 100/9%
M = 11.11%
To learn more about markup, visit :
https://brainly.com/question/11999225
#SPJ1
Which of the following best describes the solution to the equation below?
9x + 5 = 9x + 5
Answer:
x is undefined
Step-by-step explanation:
Tom drove at a constant speed of 50 miles per hour for 2.5 hours.
Albert drove at a constant speed of 65 miles per hour for 2 hours.
Who drove farther? How many more total miles did he drive?
Use the equation d=r×t to solve.
Answer:
Albert drove further.
He drove 5 miles further.
Step-by-step explanation:
The formula d = r x t is used to determine distance.
D is distance. R is rate ( in this case miles per hour). T is time.
Tom: D= 50 x 2.5
50 multiplied by 2.5 hours = 125
Tom drove 125 miles.
Albert: D= 65 multiplied by 2 hours = 130
Albert drove 130 miles.
work out 2 1/4 x 3 1/5 giving in its simplest form
Answer:
36/5
Step-by-step explanation:
32.55
Step-by-step explanation:
21/4×31/5
651/20
AB= 6 cm, AC = 12 cm
Calculate the length of CD.
Give your answer to 3 significant figures.
C
D
55°
12 cm
B 6 cm
A
The length of the side CD of the triangle is 12.686 cm up to 3 significant figures.
We know from the information that
AB = 6cm AC = 12cm
Now we have to calculate the length of DC
From given figure, we have,
In Δ ACB,
CA² = BA² + BC² (By using Pythagoras theorem)
12² = CB²+ 6²
CB² = 12² - 6²
CB² = 144 - 36
CB² = 108
∴ BC = √( 108) cm.
Now consider, in Δ CBD,
as, we know that from trigonometric ratios , sin x = opposite side / hypotenuse
sin 55° = BC / DC
0.81915 = √108 / DC
DC = 10.392 / 0.81915
⇒ DC = 12.68632...
∴ DC ≈ 12.686 cm
Therefore the length of the side DC is approximately 12.686 cm up to 3 significant figures.
Disclaimer: The missing image of the triangle is attached below.
To learn more about triangle visit:
https://brainly.com/question/17307037
#SPJ1
34.7
+ 26.2
-------
um help
f(x) = 1/3x + 1; h(x)= -f(x)
Answer:
h(x) = -1/3 x - 1
Step-by-step explanation:
Solution
h(x) = - f(x) This is a given
f(x) = (1/3) x + 1 Put h(x) on the left. Use a minus sign for f(x)
h(x) =-1((1/3)x + 1) Remove the outside brackets.
h(x) = -(1/3) x - 1
The outside brackets make 1/3 x and 1 = to a minus when a minus is put in front of f(x)
The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it. The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten. Use 3.14 for pi.
The solid has an estimated volume of 1510.8 cubic yards
Volume of CylinderThe volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. Cylinder’s volume is given by the formula, πr²h , where r is the radius of the circular base and h is the height of the cylinder.
The volume of the cylinder can be calculated as
v = πr²h
v = π* 10² * 5
v = 500π yd³
Let's calculate the volume of the rectangular figure
v = l * w * h
v = 3 * 4 * 5
v = 60 yd³
We should subtract the volume of the rectangular figure from the volume of cylinder to determine the volume of the solid.
V = 500π - 60
v = 1510.8 yd³
The volume of the solid is calculated as 1510.8 yd³
Learn more on volume of a cylinder here;
https://brainly.com/question/10390389
#SPJ1
Answer:
1,510
Step-by-step explanation: