Answer:
7 years
Step-by-step explanation:
Your equation should read = 200 * e^(.08 t) = 350
solving for t = 6.99 yrs ~~ 7 years
Chords AC and DB intersect at point E. Select all pairs of angles that must be congruent.
∠ADE and ∠ACB, ∠DEA and ∠CEB, ∠CAD and ∠CBD are pairs of angles that must be congruent.
What are congruent angles?Congruent angles are said to be angles that have equal measure.
From the figure, we can see that;
∠ADE and ∠ACB are congruent because they are corresponding angles, corresponding angles are equal.
∠DEA and ∠CEB are congruent because they are corresponding angles
∠CAD and ∠CBD are also congruent because they are corresponding angles
Therefore, ∠ADE and ∠ACB, ∠DEA and ∠CEB, ∠CAD and ∠CBD are pairs of angles that must be congruent.
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Many of the amenities at a local ski hill are operated using gas generators. To transport gasoline to the top of the mountain, a special trailer has been designed. The trailer bed is in the shape of a square with a side length of 1.5 m. They wish to attach a cylindrical shaped gas tank to the trailer which is as large as possible, but cannot be taller than the trailer bed is. Determine the dimensions, volume and surface area of the gas tank.
The Dimension of the Cylinder: Height = 1.5 m and radius = 0.75 m
Volume of Cylinder = 2.649 m³
Surface Area = 10.59 m²
What is Cylinder?A cylinder is a three-dimensional solid figure which has two identical circular bases joined by a curved surface at a particular distance from the center which is the height of the cylinder.
Here, Trailer bed dimension = 1.5 m X 1.5 m
So, height of the cylindrical = 1.5 m
Radius = 1.5/2 = 0.75 m
Now, Volume of Cylinder = πr²h
= 3.14 X (0.75)²X1.5
= 2.649 m³
Surface area of cylinder = 2πrh + 2πr²
= 2πr (h + r)
= 2 X 3.14 X 0.75 ( 1.5 + 0.75)
= 10.59 m²
Thus, The Dimension of the Cylinder: Height = 1.5 m and radius = 0.75 m
Volume of Cylinder = 2.649 m³
Surface Area = 10.59 m²
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need help with this problem
Answer:
(28) 61.5, or $61,500
(29) 49.25, or $49,250
(30) the median
Step-by-step explanation:
(28) the mean can be calculated by adding together the values and then dividing by the total number of values.
(45 + 47 + 47.5 + 51 + 53.5 + 125) / 6 = 61.5
(29) the median can be calculated by crossing off the values from the outside in, alternating sides
45, 47, 47.5, 51, 53.5, 125
47, 47.5, 51, 53.5
47.5, 51
you will end with two middle values since there are six values in the set, so average these to find the median
(47.5 + 51) / 2 = 49.25
(30) The median will better reflect the value of the homes because it is not as much influenced by the outlier value, 125, as the mean is.
Carol buys a house for £234 900
She pays a 10% deposit.
Work out the amount of deposit paid by Carol.
Answer:
211410
Step-by-step explanation:
234900x.10
23490
234900-23490
211410
twice a number added to 13 is equal to 27 what is the number
The number is 7. Let's represent the number as "x." According to the given information, "Twice a number added to 13 is equal to 27," which can be expressed as an equation.
2x + 13 = 27
Now, solve the equation for "x":
Subtract 13 from both sides:
2x = 27 - 13
2x = 14
Divide both sides by 2:
x = 14 / 2
x = 7
Therefore, the number is 7.
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If f(x) = 1-x, which value is equivalent to fi)?
Answer:
[tex]\sqrt 2[/tex]
Step-by-step explanation:
[tex]f(x) = 1-x\\\\|f(i)| = |1-i| = \sqrt{1^2 +1^2 } =\sqrt 2[/tex]
which situation representd 24÷6
Answer:
= 4
Step-by-step explanation:
24÷6
= 4
Choose the words to finish the sentence. Euler’s Formula states that the of the number of faces and the number of in a polyhedron is equivalent to two more than the number of its .
Answer:
see explanation
Step-by-step explanation:
Euler's formula states that the sum of the number of faces (F) and the number of vertices (V) of a polyhedra is equivalent to two more than the number of its edges (E) , that is
F + V = E + 2
a web adminitrator is interested in the average number of visitors per day that her website receives. Match the vocab word with its corresponding example'
The correct matching of the vocabulary words and the examples given of the web administrator's process are:
Population - All the days that the website has been in existence.Statistic - The average number of visitors per day for the 42 days that the administrator tracked.Sample - The 42 randomly selected days that the administrator tracked.Variable - The number of visitors that the website receives on a given day.Data - The list of visitor counts for the 42 days that were tracked. Parameter - The average number of visitors per day that have come to the website since it was created.What metrics are used by the website administrator?The entire population being looked at would best be all the days that the website has existed and the sample will be some selected days that have been tracked.
Parameters can be created such as the average number of visitors per say and then data would be derived on this. A statistic would simple show certain information such as the average visits in the days tracked.
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Admission to a baseball game is $3.00 for general admission and $5.50 for reserved seats. The receipts were $3277.50 for 845 paid admissions. How many of each ticket were sold?
Answer:
548, 297
Step-by-step explanation:
We can set this up as a system of equations. The first equation is for how many tickets were sold, which is x+y=845. The second equation is for the cost of the tickets, which is 3x+5.5y=3277.50. The best method for this problem (other than graphing) is elimination. First, we need to multiply one equation to get the opposite of one of the variables. The easiest one to do for this problem is x. The opposite of 3 is -3, so we have to multiply ALL of the first equation by -3. If you do this, then you get -3x-3y=-2535. Now, combine the equations:
3x + 5.5y = 3277.50
-3x -3y = -2535
________________
0x+2.5y=742.5
Now, isolate y by dividing both sides by 2.5. If you do this, you get y=297. Now, plug this in for the y in the first equation. Isolate x.
x+297=845
-297 -297
__________
0 548
x=548
Hope this helps!
Which of the following values are solutions to the inequality -5 -6x > -8?
I. - 4
II. - 3
III. - 5
Answer:
I. - 4
II. - 3
III. - 5
Step-by-step explanation:
All values are the solution to the inequality
Choose the best answer. The diagonals of a square:
A. bisect each other at different angles
B. are the same length and intersect at a right angle
C. do not bisect each other and intersect at right angles
D. are the same length and intersect at different angles
Answer:
D
Step-by-step explanation:
are the same length and intersect at different angles
What are the domain and range of the function f(x)=x²-2x² -4?
Answer:
The domain is -∞, ∞
The range is -∞, -4
Step-by-step explanation:
The domain is the data in a set representing the possible real numbers for a function.
The range is the range that this function's result is likely to be in.
There is a circular pool in the backyard with an approximate area of 113 square inches. What was the diameter?
A.12 inches
B.36 inches
C.48 inches
D.144 inches
A circle is a curve sketched out by a point moving in a plane. The diameter of the circular poll is 12 inches. Thus, the correct option is A.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
The area of a circle is given as πR², where r is the radius of the circle. Since the area of the pool is 113 sq. inches, therefore, the radius of the circle will be,
Area of pool = πR²
113 sq. inches. = πR²
113/π = R²
R = √35.9690
R = 5.9974 ≈ 6 inches
Now, since the diameter of a circle is twice the radius of the circle, therefore, the diameter of the circle will be,
Diameter of the circle = 2 × 6 inches = 12 inches
Hence, the diameter of the circular poll is 12 inches. Thus, the correct option is A.
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Answer:
a. 12 inches
Step-by-step explanation:
113 ÷ 3.14 = 35.98726114649682
2√35.98726114649682 = 5.998938334947011
5.998938334947011 x 2 = 11.99787666989402
keyword approximate ;)
Which quadratic function in vertex form has a vertex at (3, 4) and passes through the point (7,-4)
Answer:
First option
Step-by-step explanation:
Given the following question:
We are being asked to find the quadratic function that has a vertex of (3, 4) and passes through the point (7, -4). Remember that the vertex of any parabola is the point on the top of the parabola, directly in the middle of the top of the function.
First option:
[tex]y=-\frac{1}{2} (x-3)^2+4[/tex]
(see photo below)
As you can see the function has a vertex of (3, 4) which means the point on the top of the parabola is (3, 4) or the vertex. It also passes through the point (7, -4) meaning the first option is your answer.
Hope this helps.
Hi i have exams coming up soon within 4 months time what can i don't to focus more and not be easily distracted?
i would recommend setting a schedule for each day. a to do list can also help. this can help you stay on track make a list of things you need to do and have set goals for every week or month. if you're studying something you dont like, i would recommend doing pomodoros. you can find videos to follow along to.
i hope this was helpful!
Connor leaves Omaha heading directly east at a rate of 32 miles per hour.
One hour later, Jason leaves from Omaha heading in the same direction at a rate of 50 miles per hour.
How long, in hours, after Jason leaves does Jason catch up with Connor?
Round your answer to the nearest hundredths place if necessary.
Answer:
1.02 miles
Step-by-step explanation:
What’s the answer to the picture I took?
Answer:
y = - x
Step-by-step explanation:
From the given table:-
( x_1,x_2): (5,-5)
( y_1,y_2): (6,-6)
1) Let's find the slope (m):-
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{ - 6( - 5)}{6 - 5} = \frac{ - 6 + 5}{1} = \frac{ - 1}{1} = - 1[/tex]
2) Substitute x_1= 5, y_1=-5 and m=-1 into y-y_1=m(x-x_1)
[tex]y - ( - 5) = - 1(x - 5)[/tex]
[tex]y + 5 = - x + 5[/tex]
[tex]y = - x + 5 - 5[/tex]
[tex]y = - x[/tex]
What is 6 months to 5 years expressed as a ratio
Answer:
6:5
Step-by-step explanation:
Find the length of the following curve. If you have a grapher, you may want to graph the curve to see what it looks like.
y=1/27((9x^2)+(6))^3/2 ,from x=3 to x=6
The length of the curve [tex]y = \frac{1}{27}(9x^2 + 6)^\frac 32[/tex] from x = 3 to x = 6 is 192 units
How to determine the length of the curve?The curve is given as:
[tex]y = \frac{1}{27}(9x^2 + 6)^\frac 32[/tex] from x = 3 to x = 6
Start by differentiating the curve function
[tex]y' = \frac 32 * \frac{1}{27}(9x^2 + 6)^\frac 12 * 18x[/tex]
Evaluate
[tex]y' = x(9x^2 + 6)^\frac 12[/tex]
The length of the curve is calculated using:
[tex]L =\int\limits^a_b {\sqrt{1 + y'^2}} \, dx[/tex]
This gives
[tex]L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx[/tex]
Expand
[tex]L =\int\limits^6_3 {\sqrt{1 + x^2(9x^2 + 6)}\ dx[/tex]
This gives
[tex]L =\int\limits^6_3 {\sqrt{9x^4 + 6x^2 + 1}\ dx[/tex]
Express as a perfect square
[tex]L =\int\limits^6_3 {\sqrt{(3x^2 + 1)^2}\ dx[/tex]
Evaluate the exponent
[tex]L =\int\limits^6_3 {3x^2 + 1} \ dx[/tex]
Differentiate
[tex]L = x^3 + x|\limits^6_3[/tex]
Expand
L = (6³ + 6) - (3³ + 3)
Evaluate
L = 192
Hence, the length of the curve is 192 units
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a)1 year into second
Answer:
31536000 seconds in a year
Step-by-step explanation:
there are 365 days in a year, 24 hours in a day, 60 minutes in an hour, and 60 seconds in each minute. you have to multiply all of them
a) The scale of a map is 1:20 000. What distance in metres does 4cm on the map represent?
Answer:
80 000
Step-by-step explanation:
1 cm : 20 000 (The question does not state the unit of the other half)
So
4 cm : 4×20 000
4 cm : 80 000
I'm not sure about units but hope this helped and brainliest please
Answer:
80 000 meters
Step-by-step explanation:
In the map:
1 cm = 20000 m
4 cm = 4(20000) = 80 000 meters
4 cm on the map represents 80 km in reality.
Hope this helps
A stright road is 1.4 long and 0.04 km wide.what area does it cover?
Step-by-step explanation:
it is a rectangle !
a straight road and its width.
so, the area is (as for any other rectangle)
length×width
in our case
1.4 km × 0.04 km = 0.056 km²
Answer:
Area formula= length x width
length of road= 1.4 km
width of road= 0.04 km
Area= 1.4 x 0.04
= 0.056 km
David has 30 sweets. He gives Sarah of his sweets and Joe 20% of his
sweets. How many sweets does David have left?
Answer:
24
Step-by-step explanation:
20 percent of 30 is 6
30-6=24
therefore david has 24 sweets left
1.
In AXYZ, |XZ| = 13 cm, XY = 12 cm and
ZXYZ = 90°. Find YZ if the area of the
triangle is 30 cm².
Step-by-step explanation:
I think you mean triangle XYZ. and angle XYZ.
so, the angle at Y is 90°.
that makes XZ the Hypotenuse (baseline opposite of the 90° angle) of the right-angled triangle.
so, we can actually use Pythagoras (we don't need the area of the triangle to solve) :
13² = 12² + YZ²
169 = 144 + YZ²
25 = YZ²
YZ = 5 cm
just to check - the area of this triangle is (remember, it is a right-angled triangle, so XY and YZ serve also as baseline and height) :
area = 12 × 5 / 2 = 60/2 = 30 cm²
correct, it fits.
A regular hexagonal prism has a height of 7 cm and base edge length of 4 cm. Identify its lateral area and surface area.
Given the base edge and the height, the lateral area and surface area of the regular hexagonal prism are 168cm² and 251.138cm² respectively.
What is lateral and surface area of the regular hexagonal prism?For a regular hexagonal prism, the Lateral surface area and the surface area is expressed as follows:
Lateral Area = 6a × h
Surface Area = 6ah + 3√3a²
Where a is base edge and h is height.
Given that;
Base edge length a = 4cmHeight h = 7cmThe Lateral Area of the regular hexagonal prism will be;
Lateral Area = 6a × h
Lateral Area = 6( 4cm ) × 7cm
Lateral Area = 24cm × 7cm
Lateral Area = 168cm²
The Surface Area of the regular hexagonal prism will be;
Surface Area = 6ah + 3(√3)a²
Surface Area = 6(4cm × 7cm) + 3(√3)(4cm)²
Surface Area = 168cm² + 3(√3)16cm²
Surface Area = 168cm² + 83.138cm²
Surface Area = 251.138cm²
Given the base edge and the height, the lateral area and surface area of the regular hexagonal prism are 168cm² and 251.138cm² respectively.
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find the product of
2a(a+b)
3xy(2x-3y)
Answer:
2a² + 2ab , 6x²y - 9xy²
Step-by-step explanation:
using the distributive property
a(b + c) = ab + ac
given
2a(a + b) ← multiply each term in the parenthesis by 2a
= 2a² + 2ab
given
3xy(2x - 3y) ← multiply each term in the parenthesis by 3xy
= 6x²y - 9xy²
Answer:
6x2-9x2
Step-by-step explanation:
because I don't know the explanation
Stephanie read 45 pages from a book of 120 pages. Which of the following equations shows the number of pages (n) Stephanie still needs to read?
The equation of the number of pages Stephanie still needs to read will be n + 45 = 120. Then the correct option is A.
The missing options are given below.
A. n + 45 = 120
B. n - 45 = 120
C. 45ⁿ = 120
D. n/45 = 120
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Stephanie read 45 pages from a book of 120 pages.
Let n be the number of remaining pages.
Then the equation, we have
n + 45 = 120
Then the correct option is A.
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Polygons: Mastery lest
?
What is the distance between C(4, 5) and
D(4,-5)?
5 units
08 units
O 10 units
Answer:
10 [units].
Step-by-step explanation:
1) the x-coordinates have the same value, then
2) the required distance can be calculated as distance between '-5' and '5':
5--5=10 [units].
How would you apply the fundamental counting principle to a bike lock combination with 5 numbers?
1. 10+ 10+ 10+ 10+10
2. 10x5
3. 10x10x10x10x10
4.none of these
Answer:
3
Step-by-step explanation: