Last year Boris paid £256 for his car insurance. This year he had to pay £894 for his car insurance work out the percentage increase in the cost of his car insurance.
If you can answer this ASAP it would be really appreciated.
Answer:
349.2%
Step-by-step explanation:
£256 = 100%
£2.56 = 1%
£894 = 349.2%
9. A person stands at the window of a building so that his eyes are 12.6 m above the level ground. An
object is on the ground 58.5 m away from the building on a line directly beneath the person. Compute
the angle of depression of the person's line of sight to the object on the ground.
Answer:
[tex]\theta = 12.16^0.[/tex]
Step-by-step explanation:
Given,
Height = 12.6 m
Object distance from the person = 58.5 m
Angle of depression
[tex]tan \theta = \dfrac{P}{B}[/tex]
[tex]tan \theta = \dfrac{12.6}{58.5}[/tex]
[tex]tan \theta = 0.2154[/tex]
[tex]\theta = 12.16^0[/tex]
Hence, angle of depression is equal to [tex]\theta = 12.16^0.[/tex]
The angle of depression of the person's line of sight to the object on the ground is 12.15°.
The information forms a right angle triangle. The person eyes above the ground is the opposite side of the triangle. The object distance from the building in line of the sight is the adjacent side of the right angle triangle.
Therefore,
using trigonometric ratio,
tan Ф = opposite /adjacent
tan Ф = 12.6 / 58.5
tan Ф = 0.21538461538
Ф = tan⁻¹ 0.21538461538
Ф = 12.1549416972
Ф = 12.15°
angle of depression ≈ 12.15°
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What is the volume of the rectangular prism?
Answer:
[tex]V= \frac{15}{4}[/tex]
Step-by-step explanation:
To find find the volume of a rectangular prism you need to formula.
V = whl w is the width, h is the height, and l is the length.
It shows that the length of one box is 1/2 cm
To find the width, multiply 1/2 by 2 because there's 2 boxes
To find the height, multiply 1/2 by 3 because there's 3 boxes going up
To find the length, multiply 1/2 by 5 because there's 5 boxes going across
Now that you have the width, height, and length put them into the formula.
[tex]V = (1)(\frac{3}{2})(\frac{5}{2})[/tex] multiply everything together
[tex]V= \frac{15}{4}[/tex]
The volume of the rectangular prism is 15/4.
What is prism?In three dimensional space prism is a polyhedron where two ends are similar.
Given we have the length of one box is 1/2cm.
To find find the volume of a rectangular prism;
volume of rectangular prism = width x height x length.
To find the width,
multiply 1/2 by 2 because there's 2 boxes.
To find the height,
multiply 1/2 by 3 because there's 3 boxes in one column.
To find the length,
multiply 1/2 by 5 because there's 5 boxes in one row.
Now,
volume of rectangular prism = 2(length) x 3 (length) x 5 (length)
volume of rectangular prism = 2(1/2) x 3 (1/2) x 5 (1/2)
volume of rectangular prism = 1 x 3/2 x 5/2
volume of rectangular prism = 15/4
Therefore, the volume of the rectangular prism is 15/4.
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Need help with this ASAP. Anything is appreciated:))
So they seem to intersect around the 35 year mark, and tree B was planted at year 0, so therefore they intersected 35 years after Tree B was planted.
The x coordinate is years since B is planted. Looks like the x coordinate of the intersection is about 35 years.
Answer: 35 years
A regular hexagon is rotated about its center. Which degree measure will carry the regular hexagon onto itself ?
Final answer:
A regular hexagon will coincide with itself when rotated by angles of 60 degrees, or multiples of it like 120, 180, 240, 300, and 360 degrees, because these are the angles of rotational symmetry for a hexagon.
Explanation:
A regular hexagon has six sides of equal length and interior angles that are also equal. When a regular hexagon is rotated about its center, there are specific degree measures for which it will fit exactly onto itself, known as the angles of rotational symmetry. Since a full rotation measures 360 degrees and a hexagon has six sides, we can divide 360 degrees by the number of sides to find the smallest angle of rotation that will carry the regular hexagon onto itself.
The calculation is 360 ÷ 6 = 60 degrees. Therefore, a regular hexagon will coincide with itself every 60-degree turn. Other angles that will carry the hexagon onto itself are multiples of 60 degrees: 120 degrees, 180 degrees, 240 degrees, 300 degrees, and 360 degrees (a full rotation).
Shannon bought 5 pounds of apples. Bill bought 2 pounds of apples. Which most
closely estimates how many more pounds of apples Shannon bought than Bill?
Answer:
Shannon bought 3 more pounds of apples.
Step-by-step explanation:
5 - 2 is 3.
Answer:
3
Step-by-step explanation:
5-2=3
2. In a board game, you must roll two 6-sided number cubes. You can only start the game
if you roll a 6 on at least one of the number cubes. NOTE: This is using two cubes.
a. Make a list of all the different possible outcomes when two number cubes are
rolled (Sample Space) (2 points possible)
b. What fraction of the possible outcomes is favorable, or in other words, what is the
theoretical probability of rolling a 6 on at least one number cube when rolling
the two number cubes? (3 points possible) Hint: Highlight each pair in the
sample space that had at least one 6 in the outcome to help you identify
"favorable events
Answer:
A) Sample Space
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
B)Probability of rolling a 6
10/36
Step-by-step explanation:
Answer:
A. 1 2 3 4 5 6
1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
B. 11/36 or 0.3055555
Step-by-step explanation:
1. You can see there are 36 outcomes when rolling the dice.
2. Then you find that there are 11 possible outcomes with at least one 6. (For example 1-6 2-6 3-6.)
3. The chance of rolling at least one 6 in a pair of dice is 11/36.
4. 11 divided by 36 is 0.3055555.
(Though the calculator on Google says 0.305555556.)
The school band is selling sweatshirts and baseball caps to raise $2000 to attend a band competition. Sweatshirts cost $25 each and baseball caps cost $10 each. The equation 25x + 10y = 2000 models this situation, where x is the number of sweatshirts sold and y is the number of basebal caps sold.
Answer:
X-intercepts: (80,0)
y-intercepts: (0,200)
Step-by-step explanation:
(To find the x-intercept, substitut in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y. As shown in the pictur)
The x-intercept and y-intercept of the equation will be (8, 0) and (0, 20).
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The school band is selling sweatshirts and baseball caps to raise $2000 to attend a band competition.
Sweatshirts cost $25 each and baseball caps cost $10 each.
The equation 25x + 10y = 2000 models this situation.
Where x is the number of sweatshirts sold and y is the number of baseball caps sold.
Then the x-intercept will be
25x = 200
x = 8
The x-intercept will be (8, 0).
And the y-intercept will be
10y = 200
y = 20
The y-intercept will be (0, 20).
The x-intercept and y-intercept of the equation will be (8, 0) and (0, 20).
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HELP
Use 3.14 for π
a) What is the area of the label of a can with dimensions as shown?
cm2
b) What is the total surface area of the can?
cm2
c) What is the volume of the soup can?
cm2
Answer:
Part a) The Labeled part of the Can ⇒ 263.76 cm^2
Part b) The Surface Area of the Can is ⇒ 340.69 cm^2
Part c) The Volume of the Can is ⇒ 38.465 * 12 = 461.58 cm^2
Step-by-step explanation:
~ If the dimensions of this can is 12 centimeters by 7 centimeters... ~
Part a)
1. Now a can is in the shape of a cylinder, thus the Base would act as a circle. That being said, 7 centimeters acts as the diameter of this circle.
2. If we were to unravel the middle of the can, it would be that this circular portion turns out of be a rectangle, with dimensions of the height of the cylinder, by the circumference of the Base of the cylinder. The circumference can be calculated by πd where d is the diameter ⇒ 3.14 * 7 ⇒ 21.98 cm. Thus the dimensions of this middle part of the can is 21.98 by 12 ⇒ 21.98 * 12 ⇒ 263.76 cm^2.
The Labeled part of the Can ⇒ 263.76 cm^2
Part b)
1. We know previously, that 7 centimeters acts as the diameter of this circle, so the radius must be half of that, which is 7/2 ⇒ 3.5 cm. Now we can apply the area of a circle formula πr^2 where r ⇒ radius, such that: 3.14 * ( 3.5 )^2 ⇒ 3.14 * 12.25 ⇒ 38.465 cm^2.
2. Knowing that the Base of this can is 38.465 cm^2, multiply this value by 2 to get the surface area of the two bases, provided they are equivalent: 38.465 * 2 ⇒ 76.93 cm^2
3. We know that this labeled section of the can is ⇒ 263.76 cm^2. This means that The Surface Area of the Can is ⇒ 263.76 + 76.93 = 340.69 cm^2
Part c )
The volume of the can is calculated by Base * height. We know from the previous questions that the Base ⇒ 38.465, and the height was given to be 12 centimeters. This means that The Volume of the Can is ⇒ 38.465 * 12 = 461.58 cm^2
why does the graph of an exponentai funcation have its shape
Mr. Smith and his family came to the USA for a visit from Melbourne, Australia. After purchasing $32.00 in clothing at a department store, he was presented with a bill for $34.36. Why did the department store charge him the additional $2.36? How did the department store compute this amount? What amount should Mr. Smith pay?
explanation plss!!
Answer:
Mr. Smith should pay the department store $32.00 plus $2.36 in sales tax for a total bill of $34.36.
Step-by-step explanation:
The department store was adding sales tax to the bill. Sales tax is a tax on goods and services purchased and is normally a certain percentage added to the buyer's cost.
Solution: 2.36 ÷ $32.00 = 0.0735. Sales tax was charged by the department store at a rate of 7.375%.
Answer: Mr. Smith should pay the department store $32.00 plus $2.36 in sales tax for a total bill of $34.36.
Sales tax rates vary from state to state. Retail sales tax rates are set by the individual states in the United States and vary from 0 to 9% of the sales price. Sales tax is usually the responsibility of the merchant to collect and submit to the state, and stated separately (or implicitly added at the time of the sale) to consumers.
The additional amount Mr. Smith paid is tax.
The amount was determined by calculating 7.4% of the items bought.
Mr Smith. should pay $34.36.
Tax is an amount of money levied by the government or an agency of the government on certain goods and services. Taxes increases the price of a good or service.
In order to determine the tax paid, divide the additional amount paid by the total cost of items purchased.
(2.36 / $32) x 100 = 7.4%
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Fred has a bookcase that is 41.5 inches high. If shelves are evenly-spaced and about 8.3 inches apart, how many shelves are on Fred's bookcase?
A company logo is shaped like an equilateral triangle with 2-in.-long sides. What is the height of the logo? Round to the nearest tenth. A. 1.0 in. B. 1.7 in. C. 2.0 in. D. 1.4 in.
Answer:
B. 1.7 in
Step-by-step explanation:
Divide the triangle into 2 congruent right angle triangles
With hypotenuse: 2
Base: 2/2 = 1
Using pythagoras theorem
2² = 1² + h²
h² = 3
h = sqrt(3)
h = 1.732050808
The height of the equilateral triangle is required.
The height of the logo is option B. 1.7 in.
A perpendicular to from one of the vertices of an equilateral triangle bisects the sides into two equal halves.
a = Length of every side of the equilateral triangle = 2 in
b = Length of the bisected length = [tex]\dfrac{2}{2}=1\ \text{in}[/tex]
From the Pythagoras theorem we have
[tex]a^2=h^2+b^2\\\Rightarrow h=\sqrt{a^2-b^2}\\\Rightarrow h=\sqrt{2^2-1^2}\\\Rightarrow h=1.7\ \text{in}[/tex]
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65 centimeters = —Or—Meters
Answer:
65 cm =? m
1m =100cm
1cm=1/100m
65cm=65/100m
65cm =0.65m
Every day the teacher has her class of ten students line up for lunch. How many different ways can the students line up?
3,628,800
100
55
90
The number of different ways ten students can line up for lunch is 3,628,800, which is found by calculating the factorial of 10 (10!).
The question asks how many different ways ten students can line up for lunch. This is a problem of calculating permutations without repetition, as each student is unique and once a student takes a place in line, they cannot be in another position at the same time. The formula to calculate the number of permutations for 'n' unique items is n! (n factorial), which is defined as the product of all positive integers from 1 to n.
In this case, 'n' is 10 because there are 10 students. Therefore, the calculation is 10! = 3,628,800 different ways.
Solving systems of equations algebraically.
6x + 8y = -22
y = -5
and show work please!!!!
Step-by-step explanation:
Putting value of y
6x + 8(-5) = - 22
6x - 40 = - 22
6x = - 22 + 40
6x = 18
x = 18 / 6
x = 3
16) The cost, in dollars, of retaining the services of a computer repairman in Anchorville is given by
y = 42x + 32, where x is the number of hours worked
A) 32 signifies the hourly rate, and 42 signifies the overhead charge
B) 42 signifies the hourly rate, and 32 signifies the overhead charge
C) 74 signifies the cost for an on-site inspection
D) -42 signifies the hourly rate, and 32 signifies the travel cost
Answer:
B) 42 signifies the hourly rate, and 32 signifies the overhead charge
Step-by-step explanation:
The hourly rate is the amount of money given per hour worked. 42x basically means that for every hour, $42 are given.
As for 32, it is the overhead charge, which isn't paid every hour but rather only once. That is why it has no variable beside it.
Hope this helps!
What is the perimeter of the figure below?
Answer:
Step-by-step explanation:
To find the perimeter, you would have to add all the expressions together, so you would get 2x+x+x+y+y+1+y+y
combine like terms and you will get 4x+4y+1
Use the diagram to complete the statements. cos A = tan A = A unit circle is shown. A radius of with length of 1 goes to point (five-thirteenths, twelve-thirteenths).
Answer:
cos A= 5/13
tan A= 12/5
Step-by-step explanation:
Answer:
cos A= 5/13
tan A= 12/5
Step-by-step explanation:
Your welcome :)
The diagram shows a 5 cm x 5 cm x 5 cm cube,
Calculate the length of the diagonal AB
Give your answer correct to 1 decimal place,
5 cm
5 cm
5 cm
The required length of the diagonal AB would be 8.66 cm.
What is the formula for the length of the diagonal of a cube?The formula for the length of the diagonal of a cube follows as
d = √ (L² + W² + H² )
Where H is the height of the cube, W is the width of the cube and L is the length of the cube
We have been that the dimensions of a cube are as:
The length of the cube (L) = 5 cm
The height of the cube (H) = 5 cm
The width of the cube (W) = 5 cm
d = √ (L² + W² + H² )
d = √ (5² + 5² + 5² )
d = √ (25 + 25 + 25 )
d = √75
d = 8.66
Therefore, the required length of the diagonal AB would be 8.66 cm.
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Combine like terms to simplify the expression! Pls help me quick!!
Answer:
1/2 K-3/5
Step-by-step explanation:
2/5K simplifies to 4/10K. 4/10K+1/10K=5/10K. 5/10=1/2. 1/2K
K and 3/5 are not like terms so you can't combine them.
1/2K-3/5
Answer:
Step-by-step explanation:
add [tex]\frac{2}{5}k[/tex] with [tex]\frac{1}{10}k[/tex]
[tex]\frac{2}{5}k + \frac{1}{10}k = \frac{1}{2}k[/tex]
[tex]\frac{1}{2}k -\frac{3}{5}[/tex] and this is your answer
HELP
Which function is equivalent to y = 3(x + 2)2 + 7?
A y = 3x2 + 12x + 33
B y = 3x2 + 12x + 19
C y = 3x2 + 19
D y = 3x² + 33
Answer:
B y = 3x^2 + 12x + 19
Step-by-step explanation:
y = 3(x + 2)^2 + 7
To expand the square of the binomial,
either recall that (a + b)^2 = a^2 + 2ab + b^2, or use FOIL.
y = 3(x^2 + 4x + 4) + 7
y = 3x^2 + 12x + 12 + 7
y = 3x^2 + 12x + 19
Answer: B y = 3x^2 + 12x + 19
Final answer:
After expanding and simplifying the given function, we find that the equivalent function is y = 3x^2 + 12x + 19, which corresponds to option B.
Explanation:
The task is to find the equivalent function to y = 3(x + 2)2 + 7. We'll start by expanding the square and then distributing the 3 across the resultant terms.
First, expand the square: (x + 2)2 = x2 + 4x + 4.
Next, distribute the 3: 3(x2 + 4x + 4) = 3x2 + 12x + 12.
Finally, add the 7 to complete the expansion: 3x2 + 12x + 12 + 7 = 3x2 + 12x + 19.
Therefore, the equivalent function is B y = 3x2 + 12x + 19.
Which of the following shapes is described as having one triangular base and three lateral faces?
square pyramid
triangular prism
triangular pyramid
cone
NEXT QUESTION
ASK FOR HELP
Answer: triangular pyramid
Step-by-step explanation:
Answer:
Triangular Pyramid
Step-by-step explanation:
A triangular pyramid consists of 1 triangular base, with three lateral faces also in the shape of a triangle. Its net consists of 4 triangles, and is a solid 3-Dimensional figure. I hoped this helped.
The two triangles below are similar. What is the similarity ratio of AXYZ to AABC? (5 points)
X
10
Z
Answer:
answer is 2:3
Step-by-step explanation:
i solved it including a calculator
PLEASE HELP!!!!!!!!!!!!!!!!!! WILL MARK BRAINLIEST IF CORRECT ANSWER!!!!!!!!!!!!!!!!!!1
Kylie needs to pack her baton for a color-guard competition. The baton is 38 inches long. Will it fit in a rectangular box with a base of 13 inches by 35 inches and height of 13 inches?
Part A
Could the baton lie flat on a diagonal along the base of the box?
A. Yes, because the diagonal is 48 inches long.
B. Yes, because the diagonal is 41.4 inches long.
C. No, because the diagonal is 37.3 inches long.
D. No, because the diagonal is 18.4 inches long.
I think C. but need help, is it right? How so?
Part B
Could the baton fit along the interior diagonal of the box? Explain.
Answer:
C.; Yes
Step-by-step explanation:
A)
The longest thing that can fit along the base of the box is sqrt ( 13^2 + 35^2) = 37.3, which is less than 38, so NO, the baton can't lay flat on a diagonal along the base of the box C. No, because the diagonal is 37.3 inches long.
B) The interior diagonal of the box is sqrt(13^2 + 13^2 + 35^2) = sqrt (1563), which is 39.5, which is greater than 38, so YES, the baton can fit along the interior diagonal of the box.
The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width. Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. Write the equation that represents the volume of the storage container in terms of its width. A. V = 6w2 - 12w B. V = 6w2 + 12 C. V = 6w2 - 12 D. V = 6w2 + 12w
The answer is B.) V = 6w2 + 12w
Answer:
V = 6w² + 12w
Step-by-step explanation:
Adric owns 8 pairs of shoes. How many ways can he choose 4 pairs of shoes to pack into his luggage?
The answer is 70 but I don’t know how my teacher got that...
Answer:
70
Step-by-step explanation:
It is made with a combination. Combination of 4 taken from 8, the formula of the combination is as follows:
nCr = n! / (r! * (n-r)!)
In this case 8 is "n" and 4 is "r"
8C4 = 8! / (4! * (8-4))!
8C4 = 8! / (4! * 4!)
8C4 = 40320/576
8C4 = 70
In this way he obtained the answer that is 70
Graph the rational function. f(x )= x^2 - 7x + 10/x - 5
Answer:
x ≓ -1.425806820
Step-by-step explanation:
Answer:
Vertical Asymptotes: x=-4
Horizontal Asymptotes: y=1
a cube has a surface area of 96cm squared. what is the volume of the cube?
Answer:
v= 64cm3
Step-by-step explanation:
a cube with area of 96cm2 has a length of 4 cm
A=L squared x6
96=L2x6
96/6=16
16 square root=4cm
V=l x l xl
V=4x4x4
v=64cm3
NEED HELP WITH TRIG please show work as i am trying to learn the material i'm really puzzled. its soh cah toa but i don't remember how to do it
Answer:
see below
Step-by-step explanation:
5. sin 31 = opp/ hyp
sin 31 = 34 /x
x = 34 / sin 31
x =66.0145369
tan 31 = opp /adj
tan 31 = 34/y
y = 34/ tan 31
y= 56.5855024
6. Pythagorean theorem to find z
9^2+12^2 = z^2
81+144 = z^2
225 = z^2
z =sqrt(225) =15
sin x = opp / hyp
sin x = 9/15
take the inverse sin
x = sin^ -1 (9/15) = 36.86989765
sin y = opp / hyp
sin y = 12/15
take the inverse sin
y = sin^ -1 (12/15) = 53.13010235
Answer:
1. sin(31) = opposite/hypotenuse
sin(31) = 34/x
x = 34/sin(31) = 66.0145369
x = 66.0°
tan(31) = opposite/adjacent
tan(31) = 34/y
y = 34/tan(31) = 56.5855024
y = 56.6°
2. tan(x) = opposite/adjacent
tan(x) = 9/12
x = 36.86989765
x = 36.9°
y = 180 - 90 - x
y = 53.13010235
y = 53.1°
z² = 9² + 12²
z² = 225
z = 15