Answer:
244 miles (nearest whole number)
Step-by-step explanation:
We can model this as a geometric series.
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common difference)
Given information:
Miles run in first week = 8Weekly increase of miles = 5%Total number of weeks in plan = 19Therefore:
[tex]a[/tex] = 8[tex]r[/tex] = 1.05[tex]n[/tex] = 19Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Therefore, sum of the first 19 terms:
[tex]\implies S_{19}=\dfrac{8(1-1.05^{19})}{1-1.05}[/tex]
[tex]\implies S_{19}=244.3120313...[/tex]
So Levi ran a total of 244 miles (to the nearest whole number)
Can someone please explain 3 and 4 to me? I don’t understand how to solve them
Answer:
see explanation
Step-by-step explanation:
3) line l and m are perpendicular so they intersect at 90 degrees
I labelled the angles that are the same measure.
2x + 23 = 90 subtract 23
2x = 67 divide by 2
x = 23.5 degrees
4) 2m + 66 = 120 subtract 66
2m = 54 divide by 2
m = 27 degrees
Express -48 by 60 as a rational number with denominator 25 pura Karen
Answer:
-20/25
Step-by-step explanation:
To change a fraction to one with a different denominator, common factors can be removed or added to numerator and denominator as required.
__
-48/60 can be reduced to lowest terms by removing the common factor of 12. It can be made to have a denominator of 25 by adding a common factor of 5.
[tex]-\dfrac{48}{60}=-\dfrac{4\cdot12}{5\cdot12}=-\dfrac{4}{5}\\\\=-\dfrac{4\cdot5}{5\cdot5}=\boxed{-\dfrac{20}{25}}[/tex]
__
Alternatively, the numerator of the desired fraction can be found by multiplying the given fraction by the desired denominator.
numerator = 25×(-48/60) = -1200/60 = -20
new fraction = -20/25
The graph and the table below show the relationship between y, the total cost, and x, the number of loads washed, at two laundromats.
2. 5 kg of potatoes cost £1. 40
workout the cost of 4. 25 kg of potatoes
What is the answer
5 3/5 - 3 14/16
Answer:
138/80
Step-by-step explanation:
5×5+3/5-3×16+14/16
28/5-62/16
28×16/5×16-62×5/16×5
448/80-310/80
448-310/80
138/80
99 like Sorbet
94 like Rocky Road and Berry
96 like Rocky Road
96 like Sorbet and Berry
99 like Berry
93 like all three
95 like Sorbet and Rocky Road
How many people prefer:
(a) none of the three?
(b) Sorbet, but not Rocky Road?
(c) Anything but Berry?
(d) only Rocky Road?
(e) Exactly two kinds of ice cream?
WILL GIVE BRAINLIEST PLLSSSS!!!!!
Answer:
b
Step-by-step explanation:
What is the axis of symmetry for y=8x² + 2x - 6?
Factor the following expression using the greatest common factor 18a+24c
Step-by-step explanation:
divide each by six
3a+4c
Answer:
6(3a+4c)
Step-by-step explanation:
GCF = 6
18a/6+24c/6
= 6(3a+4c)
In triangle ABC, m∠ A = 45˚ and a = c. Which best describes triangle ABC? *
Find the volume of the sphere, round your answer to the nearest tenth
Answer:
904.8 units^3
Step-by-step explanation:
The formula for the area of a circle is [tex]4/3 \pi r^3[/tex]
By the picture we know r = 6
Thus our answer is 4/3 * π * [tex]6^3[/tex]
This is the same as 4/3 * 216 * π = 904.778684234
Rounding to the nearest tenth yields 904.8 units^3
A standard number cube is tossed. Find P(2 or even)
Answer:
1/2
Step-by-step explanation:
there are 3 even numbers including 2. there are 6 possible outcomes. 3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
Estimate the value Square Root 49 to your best judgement and explain why
V49 = 7 because 7²=49?
.........
Find the median of the data.
24,74,61,29,38,27,68,54
Answer:
The median is 46
Step-by-step explanation:
To find the median, you must first order the numbers, from left to right, lowest to highest:
24, 27, 29, 38, 54, 61, 68, 74
Next, we have to find the number in the middle. We can do this by counting inwards one and crossing out each of the lowest and highest each time we get closer to the middle/center.
24, 27, 29, 38, 54, 61, 68, 74
, 27, 29, 38, 54, 61, 68,
, , 29, 38, 54, 61, ,
, , , 38, 54, , ,
Now, if there is no exact middle, we would add them add divide by 2. If there was an exact middle, that would be the answer. But there isn't.
38 + 54 = 92
92 / 2 = 46
The median is 46
A ladder 15 feet long leans against a house and makes an angle
of 60° with the ground. Find the distance from the house to the
foot of the ladder.
A 13 feet
)
B 7.5 feet
C 10 feet
D
8.2 feet
Answer:
B
Step-by-step explanation:
assume a right angle between the house and the ground.
then the ladder is the hypotenuse and distance from ladder to house is d
using the cosine ratio in the right triangle and the exact value
cos60° = [tex]\frac{1}{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{d}{15}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 15 ( divide both sides by 2 )
x = 7.5
distance from house to foot of ladder is 7.5 feet
Some of the dimensions of a square pyramid are shown in the diagram. The height of the square pyramid is 5.1 meters.
What is the volume of the square pyramid in cubic meters?
60 m3
40 m3
360 m3
120 m3
Answer:
27.2 m³
Step-by-step explanation:
Given:
Base edge = 4 mHeight = 5.1 metersFormula:
[tex](\text{Base edge})^{2} \times \dfrac{\text{Height}}{3}[/tex]
Replace the base edge and the height in the formula:
[tex]\implies (\text{4})^{2} \times \dfrac{\text{5.1}}{3}[/tex]
Evaluate the volume of the prism:
[tex]\implies (\text{4})(4) \times 1.7[/tex]
[tex]\implies 16 \times 1.7[/tex]
[tex]\implies 27.2 \ \text{m}^{3}[/tex]
Answer:
27.2 cm³
Step-by-step explanation:
Volume of a square pyramid
[tex]\sf V=\dfrac13a^2h[/tex]
where:
a is the base edgeh is the heightGiven:
a = 4 mh = 5.1 m[tex]\sf \implies Volume=\dfrac13\cdot 4^2\cdot5.1=27.2\;cm^3[/tex]
How do you find the measure of angle A?
Answer:
m∠A = 18
Step-by-step explanation:
Formula:
the sum of the interior angles of a triangle is 180.
____________________
According to the formula :
[tex]m\angle A\ +\ m\angle B\ +\ m\angle C=180[/tex]
⇔ x - 22 + 3x + 19 + x - 17 = 180
⇔ 5x + (19 - 17 - 22) = 180
⇔ 5x + (2 - 22) = 180
⇔ 5x - 20 = 180
⇔ 5x = 180 + 20
⇔ 5x = 200
[tex]\Leftrightarrow x = \frac{200}{5} \\\Leftrightarrow x = 40[/tex]
Conclusion:
m∠A = x - 22 = 40 - 22 = 18
Aaron was plotting the shape of his garden on grid paper. While it was an irregular shape, it was perfect for his yard. each square on the grid represents 1 square meter. What is the area of the garden?
pls, add an explanation as well as an answer, i wont open any links, thanks :)
Answer:
44 [tex]m^{2}[/tex]
Step-by-step explanation:
As the shape contain triangle ,rectangle and square so we calculate the area of all these and then add up.
As one box = 1 [tex]m^{2}[/tex]
Area of Triangle= [tex]\frac{1}{2}*b*h[/tex]
b= 8, h=2
Area of Triangle= [tex]\frac{1}{2}*8*2[/tex]
Area of Triangle= [tex]8 m^{2}[/tex]
Area of Rectangle= [tex]l*w[/tex]
l=8,w=4
Area of Rectangle= [tex]8*4\\[/tex]
Area of Rectangle= [tex]32m^{2}[/tex]
Area of Square=[tex]a^{2}[/tex]
a=2
Area of Square=[tex]2^{2}[/tex]
Area of Square=[tex]4m^{2}[/tex]
Total Area=[tex]8 m^{2}[/tex]+[tex]32m^{2}[/tex]+[tex]4m^{2}[/tex]=44[tex]m^{2}[/tex]
Using the tools from before, what is the theoretical probabilty of spinning an even number and rolling an odd number?
What life cycle adaptation allows a seahorse to make lots of babies in a short amount of time? (2 points)
a seahorse
Group of answer choices
The female hatches the eggs in the sand while the male gets rid of predators.
The female hatches the eggs in the sand while the male protects them.
The male carries the babies while the female makes more eggs.
The male makes more eggs while the female carries the babies
The seahorse make a lot of babies because the male carries the babies while the female makes more eggs.
What is mating?Mating is the process in which opposite or hermaphroditic organisms pair for reproduction.
During mating between the male and female seahorse mates, the female seahorse puts her eggs in the male pouch and the male fertilises the egg in his pouch. The eggs develop into baby seahorse in the father pouch.
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Is it possible that a packet of candies does not divide into 9 equal parts, but rather divides into 3 equal parts? Give an example with your answer.
Answer:
Yes, if there are 6 candies it can be divided equally by 3 and not 9.
Step-by-step explanation:
What is the missing term?
Answer:
-2x
filler filler filler
A carpenter has to cut four lengths of wood, each 128cm long. What is the total length of wood that he needs?
Answer:
512cm
Step-by-step explanation:
same length of 128 4 times. 512
Which statement about 6x2 7x – 10 is true? one of the factors is (x 2). one of the factors is (3x – 2). one of the factors is (2x 5). one of the factors is (x – 5).
One of the factors of the given quadratic expression is (x+2).
The given quadratic expression is:
[tex]6x^{2} +7x-10[/tex]
What is a quadratic expression?Any expression of the form [tex]ax^{2} +bx+c[/tex] is called a quadratic expression where a≠0.
Splitting the middle term of the given expression
[tex]6x^{2} +12x-5x-10[/tex]
[tex]6x(x+2)-5(x+2)[/tex]
[tex](x+2)(6x-5)[/tex]
Hence, one of the factors of the given quadratic expression is (x+2).
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What is the value of y??
Answer:
3
Step-by-step explanation:
The opposite sides are equal
2y+ 4 = 10
2y = 6
y = 3
Four more than three times a number x is 48
Look at the equation.
X-3 = 12
Which value of x makes this equation true?
4
(b9
с
15
d) 36
Answer:
c) 15
Step-by-step explanation:
Plugging in the value of x as 15 in the equation,
15-3 which is equal to 12
If the slope of a line is 0, does the line rise (from left to right), fall (from left to right), horizontal or vertical?
When the slope is 0
it is in a horizontal positionthe rise is zero, same from left to right; right to leftThis picture below shows some examples of equation with slope as 0
Answer:
horizontal
rise remains conserved
Step-by-step explanation:
Slope is 0
means
[tex]\\ \rm\dashrightarrow tan\theta=0[/tex]
[tex]\\ \rm\dashrightarrow \theta=tan^{-1}(0)[/tex]
[tex]\\ \rm\dashrightarrow \theta=0°[/tex]
Line will be parallel to x axis
A company sells cocoa powder in a cylindrical container that is 5 inches long with a circular base of diameter 4 inches. The company is planning to sell a family-size product that will use similar packaging scaled by a factor of 2.
The circumference of the original container is (62.8, 15.7, 12.57, 6.28)
inches. This is (18.84, 9.42, 37.68, 12.57)
inches less than the circumference of the new container.
The circumference of the original container is 12.57 inches.
The cirucmference of the original container is 12.57 inches less than the circumference of the new container.
What is the circumference of the cylinder?The circumference of a cylinder is the distance round the cylinder. It is the perimeter of the cylinder.
The circumference of a cylinder = πD
Where:
π = 22/7D = diameterThe circumference of the original container = 22/7 x 4 = 12.57 inches
The circumference of the family sized container 12.57 x 2 = 25.14 inches
Difference in the circumference = 25.14 - 12.57 = 12.57 inches
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Answer: 12.57 for both
Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO
6-8x=7x-9x-36 i really need help
Answer:
Simplifying
6 + -8x = 7x + -9x + -36
Reorder the terms:
6 + -8x = -36 + 7x + -9x
Combine like terms: 7x + -9x = -2x
6 + -8x = -36 + -2x
Solving
6 + -8x = -36 + -2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2x' to each side of the equation.
6 + -8x + 2x = -36 + -2x + 2x
Combine like terms: -8x + 2x = -6x
6 + -6x = -36 + -2x + 2x
Combine like terms: -2x + 2x = 0
6 + -6x = -36 + 0
6 + -6x = -36
Add '-6' to each side of the equation.
6 + -6 + -6x = -36 + -6
Combine like terms: 6 + -6 = 0
0 + -6x = -36 + -6
-6x = -36 + -6
Combine like terms: -36 + -6 = -42
-6x = -42
Divide each side by '-6'.
x = 7
Simplifying
x = 7
Answer:
x = 7
Hope This Helps! :) Please Give brainliest if you can!
Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.
4
4(1.4)
2
N(2.0)
14
-2
x
(Pl-1, -2)
M(4,0)
The perimeter is about
units.
Check the picture below, now the distance from 2,0 to 4,0 there's no need to do much calculation since that's just 2 units, as you see there.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) ~\hfill d1=\sqrt{[ 1- 2]^2 + [ 4- 0]^2} \\\\\\ d1=\sqrt{(-1)^2+4^2}\implies \boxed{d1=\sqrt{17}} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{-2}) ~\hfill d2=\sqrt{[ -1- 1]^2 + [ -2- 4]^2} \\\\\\ d2=\sqrt{(-2)^2+(-6)^2}\implies \boxed{d2=\sqrt{40}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{0}) ~\hfill d3=\sqrt{[ 4- (-1)]^2 + [ 0- (-2)]^2} \\\\\\ d3=\sqrt{(4+1)^2+(0+2)^2}\implies \boxed{d3=\sqrt{29}}[/tex]
[tex]~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{2~~ + ~~\sqrt{17}~~ + ~~\sqrt{40}~~ + ~~\sqrt{29}~~\approx~~17.83}[/tex]
The perimeter of the polygon with the vertices L = (1, 4), P = (-1, -2),
N = (2, 0) and M = (4, 0) is approximately 17.93 units.
We have,
The polygon has the following sides:
LP, PN, NM, and ML.
The coordinates for each point are:
L = (1, 4)
P = (-1, -2)
N = (2, 0)
M = (4, 0)
The perimeter of the polygons.
= LP + PN + NM + ML
Using the distance formula for the distance between two points (a, b) and (c, d):
Distance = √((c - a)² + (d - b)²)
Let's calculate the distances between the points:
LP:
Distance(LP)
= √((-1 - 1)² + (-2 - 4)²)
= √((-2)² + (-6)²)
= √(4 + 36)
= √40
= 6.32
PN:
Distance(PN)
= √((2 - (-1))² + (0 - (-2))²)
= √((2 + 1)² + (0 + 2)²)
= √(3² + 2²)
= √(9 + 4)
= √13
≈ 3.61
NM:
Distance(NM)
= √((4 - 2)² + (0 - 0)²)
= √(2² + 0²)
= √4
= 2
ML:
Distance(ML)
= √((4 - 1)² + (0 - 4)²)
= √((4 - 1)² + (-4)²)
= √(3² + 16)
= √(9 + 16)
= √25
= 5
Now,
Perimeter = LP + PN + NM + ML
Perimeter ≈ 6.32 + 3.61 + 2 + 5 ≈ 16.93
Thus,
The perimeter of the polygon is approximately 17.93 units.
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