Missing part of the question
Miguel has started training for a race. The first time he trains, he runs 0.5 mile. Each subsequent time he trains, he runs 0.2 mile farther than he did the previous time.
What is the arithmetic series that represents the total distance Miguel has run after he has trained n times?
Answer:
The least number of times Miguel must run for his total distance run during training to exceed the distance of a marathon is 17.3 miles
Step-by-step explanation:.
Given parameters
Miguel first run = 0.5 mile
Subsequent run = 0.2 mile
This question is an arithmetic progression.
We'll make use of arithmetic progression formula to solve this
Formula:.
Tn = a + (n - 1)d
Where a = first term
n = number of terms
d = common difference
In this case
a = first run = 0.5 mile
d = subsequent run = 0.2 mile
So, Tn = a + (n - 1)d become
Tn = 0.5 + (n - 1) 0.2
Tn = 0.5 + 0.2n - 0.2
Tn = 0.5 - 0.2 + 0.2n
Tn = 0.3 + 0.2n
The arithmetic series of an arithmetic progression is calculated using
Sn = ½(a + Tn) * n
By substituton, we have
Sn = ½(0.5 + 0.3 + 0.2n) * n
Sn = ½(0.8 + 0.2n) * n
Sn = 0.4n + 0.1n²
b.
Since the race is 26.2 miles then the least number of times is given as
Sn ≥ 26
0.4n + 0.1n² ≥ 26.2
0.1n² + 0.4n - 26.2 ≥ 0
Using quadratic formula
n = (-b ± √(b² - 4ac))/2a
Where b = 0.4 a = 0.1 and C = -26.2
So,
n = -0.4 ± √(0.4² - 4 * 0.1 * ,26.2)/2 * 0.1
n = (-0.4 ± √10.64)/0.2
n = (0.4 ± 3.26)/0.2
n = (0.4 + 3.26)/0.2 or (0.4 - 3.26)/0.2
n = 3.46/0.2 or -2.86/0.2
n = 17.3 or -14.3
Since n can't be negative
n = 17.3 miles
The least number of times Miguel must run for his total distance run during training to exceed the distance of a marathon is 17.3 miles
Answer:
15 times
Step-by-step explanation:
Please help!
Will mark as brainliest for answering questions 10-16!
Please and thank you guys so much, hope you guys are protected from Coronavirus!
Answer:
10. Perimeter = 56 ft ; Area = 195 sq. ft.
11. If my math is correct, Perimeter = 76 km ; Area = 706 sq. km
12. Circumference = 100[tex]\pi[/tex] cm ; Area = 2500[tex]\pi[/tex] sq. cm
13. Circumference = 24[tex]\pi[/tex] ft. ; Area = 144[tex]\pi[/tex] sq. ft.
14. Perimeter = 62 ft. ; Area = 238 sq. ft.
15. Circumference = 22[tex]\pi[/tex] yd. ; Area = 121[tex]\pi[/tex] sq. yd.
16. Perimeter = 40 mm ; Area = 100 sq mm
Step-by-step explanation:
The function F(x) = logo.75^x is decreasing.
O
A. True
O
B. False
Answer:
true
Step-by-step explanation:
We assume you intend your function to be ...
A logarithm with a base less than 1 is a decreasing curve. Here, the base appears to be 0.5, a value less than 1. Hence the curve is decreasing.
Yes, The function F (x) = log (0.75)ˣ is a decreasing function.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ F (x) = log (0.75)ˣ
Now, We know that;
If derivative of logarithmic function is less than 1 then, it is decreasing.
Here, The function is,
⇒ F (x) = log (0.75)ˣ
After differentiation,
⇒ F ' (x) = log 3 - log 4 < 1
Hence, The function F (x) = log (0.75)ˣ is a decreasing function.
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What is the definition of area of a kite
Answer:
The diagonal * the other diagonal, all divided by two.
Step-by-step explanation:
A kite in other words is a rhombus. To find the area of a rhombus we need to multiply 1/2 * p * q
Where p is one diagonal and q is the other.
Step-by-step explanation:
[tex] \sf \:a = \dfrac{pq}{2}[/tex]
The area of a kite is half the product of the lengths of its diagonals.
please help in the question it should be if t=-6 when r =-2 its an error
Answer:
r = - [tex]\frac{12}{7}[/tex]
Step-by-step explanation:
Given that r varies inversely as t , then the equation relating them is
r = [tex]\frac{k}{t}[/tex] ← k is the constant of variation
To find k use the condition t = - 6 when r = - 2, then
- 2 = [tex]\frac{k}{-6}[/tex] ( multiply both sides by - 6 )
12 = k, thus
r = [tex]\frac{12}{t}[/tex] ← equation of variation
when t = - 7, then
r = [tex]\frac{12}{-7}[/tex] = - [tex]\frac{12}{7}[/tex]
Which relationship describes angle 1 and 2
Answer:A
Step-by-step explanation:
A circular plot of land has a diameter of 14 yards. What is the area of the land? Use 3.14 for π.
Answer:
A =153.86 yd^2
Step-by-step explanation:
The area of a circle is given by
A = pir^2
We need to get the radius. We are given the diameter
r = d/2 = 14/2 =7
A = pi (7)^2
A =49pi
Using 3.14 for pi
A = 49 (3.14)
A =153.86 yd^2
Use the distributive property to fill in the blanks below.
(5 x 8) + (5 x 7) = 5 x (blank+blank)
Fill in the blanks please and respond quickly.
will give extra points for correct and fastest responder
Please help What are the coordinates of -2 , -3 of you move 6 units to the right
Answer:
(4,-3)
Step-by-step explanation:
Answer:
(4,-3)
Step-by-step explanation:
Moving 6 units to the right would only affect the x coordinate. Sinceinc we are moving to the right, there is a positive increase in the x coordinate.
-2+6=4
So our new point is (4,-3)
A can contains 40 chips: 10 each of read and blue, 12 pink, and the remaining black.If Susan were to remove 3 black and 2 red chips, what is the probability that next one she removes is black? Please Help!
Answer:
1:7
Step-by-step explanation:
R = RED | B = BLUE | P = PINK | BL = BLACK | c = chips
10R + 10B + 12P = 32 chips
40c - 32c = 8 black chips
8BL - 3BL = 5 black chips
10R - 2R = 8 red chips
2R + 3BL = 5 chips
40c - 5c = 35 chips
5BL : 35c = 1:7
The probability that next one Susan removes is black chips is 1/7.
What is probability?
The probability is defined as the possibility of an event is equal to the ratio of the number of outcomes and the total number of outcomes.
Total no. of chips = 40
No. of red chips = 10
No. of blue chips = 10
No. of pink chips = 12
No. of black chips = 8
If Susan were to remove 3 black and 2 red chips
So, No. of available black chips = 8 -3 = 5
No. of available red chips = 10 - 2 = 8
Total removed chips = 5
Total no. available of chips = 35
The probability that next one Susan removes is black chips = 5/35 = 1/7
Hence, the probability that next one Susan removes is black chips is 1/7.
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A smaller rectangle is inside of a larger rectangle. The smaller rectangle has sides lengths of 9 x and 6 x. The distance to the larger rectangle on all sides is x. The space between the smaller rectangle and the larger rectangle is shaded.
The figure shows two rectangles. Which expression represents the area of the shaded region?
16x2
34x2
54x2
88x2
Answer:
im sorry if this is late but the answer is 34x2. goodluck :D
Step-by-step explanation:
I took the test
34x² represents the area of the shaded region. Option b is correct.
Two concurrent rectangle are given dimension of smaller rectangle is 9x and 6x. larger rectangle has offset of x with smaller rectangle. So the dimension of the larger rectangle is 9x+2x and 6x+2x . space between the rectangle is shaded and area of the shaded portion to be determine.
What is rectangle?rectangle is four sided polygon whose opposites sides are equal and has angle of 90° between its sides.
Now the area of the shaded portion,
= area of larger rectangle - area of smaller rectangle
= 11x*8x - 9x*6x
= 88x - 54x
= 34x
Thus, 34x² represents the area of the shaded region.
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for the given function f(x)=2x+4,find f(12)
Answer:
f(12) = 28
Step-by-step explanation:
All you have to do is plug in 12 as x.
f(12) = 2(12) + 4
= 24 +4
= 28
And you're done! :)
Answer:
f(12)=28
Step-by-step explanation:
We want to find what y or f(x) is when x equals 12
To find f(12), substitute 12 in for x
f(x)=2x+4
f(12)=2(12)+4
Multiply
f(12)=24+4
Add
f(12)=28
1.
Carmen tosses two coins and records the outcomes. Her results are recorded in the table
below. She intends to toss two coins an additional 250 times. Based on the data in the table,
how many times will both coins land on tails or both coins land on heads?
Toss phone : 1 2 3 4 .5 | 6 7 | 8 | 9 | 10
| First coin, IHI HITITITIHITEHIHTT.
Second coin | TTT HITTA HITH
eco
im
The expected number of times that both coins will land on the same result in 250 throws is given as follows:
100 tosses.
How to obtain the expected number?The expected number is obtained applying the proportions in the context of the problem.
In the 10 tosses, 4 resulted in the same result for both coins, hence the proportion of the same result is given as follows:
4/10 = 0.4.
Hence, out of 250 tosses, the expected amount is given as follows:
0.4 x 250 = 100 tosses.
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On Saturday, Bob's bakery sold 80 cupcakes for $5 each. His profit margin on the cupcakes was 50%. Which calculation yields the amount of profit he made on the cupcakes? A) 50 × 5, then 250 ÷ 2 B) 80 × 5, then 400 ÷ 2 C) 80 × 5, then 400 ÷ 50 D) 80 × 50, then 4,000 ÷ 5
Answer:
B) 80 × 5, then 400 ÷ 2
brainliest?
This equation shows how the total number of novels Brad has in his collection is related to the amount of money he spends on additional novels.
n = d
The variable d represents the amount of money he spends on additional novels, and the variable n represents the total number of novels in his collection. How much money does Brad need to spend on new novels in order to have a total of 69 novels in his collection?
Which of the following shows the Identity Property for Addition?
A. 9 + (-9)=0
B. 9 + 0 = 9
C. 9 = 9
D. 9 x 1 = 9
The rectangle below has an area of x^2+8x+15x
2
+8x+15x, squared, plus, 8, x, plus, 15 square meters and a width of x+3x+3x, plus, 3 meters.
What expression represents the length of the rectangle?
Answer:
The length of the rectangle is x+5.
Step-by-step explanation:
Given : The rectangle below has an area of [tex]x^2+8x+15[/tex] square meter and a width of [tex]x+3[/tex] meter.
To find : What expression represents the length of the rectangle?
Solution :
The area of the rectangle is given by,
[tex]\text{Area}=\text{Length}\times \text{Breadth}[/tex]
[tex]\text{Area}=x^2+8x+15[/tex]
[tex]\text{Breadth}=x+3[/tex]
[tex]x^2+8x+15=\text{Length}\times(x+3)[/tex]
[tex]\text{Length}=\frac{x^2+8x+15}{x+3}[/tex]
[tex]\text{Length}=\frac{(x+5)(x+3)}{x+3}[/tex]
[tex]\text{Length}=x+5[/tex]
Therefore, the length of the rectangle is x+5.
Final answer:
The length of the rectangle is found by dividing the area (x² + 8x + 15) by the width (x + 3), which simplifies to x + 5 meters, as the (x + 3) factor cancels out.
Explanation:
To find the length of the rectangle, we can use the area formula for rectangles, which is area = length × width.
According to the question, the area of the rectangle is given by the quadratic expression x² + 8x + 15, and the width is given by x + 3. To find the length, we divide the area by the width:
length = ²/(x + 3)
² + 8x + 15 is factorable, and its factors are (x + 5)(x + 3), which simplifies to:
length = (x + 5)(x + 3)/(x + 3)
When the polynomial is factored, we can see that the (x + 3) terms cancel each other out:
length = x + 5
So, the expression representing the length of the rectangle is x + 5 meters. It is important to note that when dealing with units, one must ensure they are consistent. However, there is no need for conversion here since the area and width are already in terms of meters and square meters respectively.
What is 150% of 3? Round to the nearest hundredth (if necessary).
Answer:
4.5
Step-by-step explanation:
Answer:
4.5
Step-by-step explanation:
150% = 1.5
so 150% of 3 = 1.5 × 3 = 4.5
Help!!! 30 points and brainliest
[tex]2x^{2} +6x - 5 = 0[/tex]
Answer:
Should be in the pic below
Step-by-step explanation:
Answer:
x = [tex]\frac{-3+\sqrt{19} }{2}[/tex] or x = [tex]\frac{-3-\sqrt{19} }{2}[/tex]
Step-by-step explanation:
We want to factor this. In order to factor it, we need to use the quadratic formula:
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] or [tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
Here, a = 2, b = 6, and c = -5, so plug these in:
[tex]x=\frac{-6+\sqrt{6^2-4*2*(-5)} }{2*2}=\frac{-6+\sqrt{76} }{4} =\frac{-6+2\sqrt{19} }{4} =\frac{-3+\sqrt{19} }{2}[/tex]
AND
[tex]x=\frac{-6-\sqrt{6^2-4*2*(-5)} }{2*2}=\frac{-6-\sqrt{76} }{4} =\frac{-6-2\sqrt{19} }{4} =\frac{-3-\sqrt{19} }{2}[/tex]
Thus, the answers are x = [tex]\frac{-3+\sqrt{19} }{2}[/tex] or x = [tex]\frac{-3-\sqrt{19} }{2}[/tex].
Hope this helps!
which expressions represents a quadratic expression in factored form
Answer:
( x + 3 )( x - 7 ) and ( x + 1 )( x - 2 )
Step-by-step explanation:
Both of these represent 2 terms x 2 terms, so that means they are both in factored form.
Example:
Which is an example of phototropism?
A.roots of seedling growing away from light.
B.tendrils of plant attaching to a nearby stem
C.roots of seedling growing down toward the pull of gravity.
D.stems and leaves of plant growing up away from the pull of gravity
Answer:
i think it is A
Step-by-step explanation:
sorry if i am wrong...hope this helped, also can i have brainliest pls?
Answer:
I believe the answer is A
Step-by-step explanation:
3. Your expenses that change month to month are called?
Answer:
Variable expenses
Step-by-step explanation:
There are 4 types of expenses
-Variable Expenses: Expenses that vary from month to month.
-Fixed Expenses: Expenses that remain the same from month to month.
-Intermittent Expenses: Expenses that occur at various times throughout the year and tend to be in large amounts.
Discretionary Expenses: Expenses for things we don't need
A new golf bag has a compartment that is roughly a rectangular prism that has dimensions of 6 inches by 8 inches by 9 inches. How many golf balls will
fit in the compartment if a golf ball has a diameter of 1.7 inches? (Reminder: You can assume that for random packing space 190% of the volume of the
sphere is needed to pack the spheres and Volume of Sphere = 4/3 pim3)
21 balls
88 balls
63 balls
57 balls
To find the number of golf balls that can fit in the compartment, we calculate the volume of the compartment and then divide by the volume required to pack a golf ball. We can fit around 88 golf balls in the bag.
Explanation:We first need to find the volume of the rectangular prism. The volume of a rectangular prism can be found by multiplying the length, width, and height. So, volume = 6 * 8 * 9 = 432 cubic inches.
Next, we can find the volume of a golf ball which is a sphere using the formula 4/3 * π * r³ where r is the radius of the sphere. The diameter of the golf ball is given as 1.7 inches, which means the radius is 1.7/2 = 0.85 inches. So, the volume of the golf ball = 4/3 * π * (0.85)^3 = 2.57 cubic inches (approx).
As per the question, in a random packing of spheres, 190% of the volume of the sphere is needed. Therefore, the required volume for each ball = 2.57 * 190/100 = 4.87 cubic inches. The total number of balls that will fit = volume of rectangle/volume of each ball = 432/4.87 = 88 (rounded down to a whole number). So, the answer is 88 balls.
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Someone please give me the answers...And thank you
Answer:
Step-by-step explanation:
1) 4x + 3 <= 3x - 5
Subtract 3 from both sides
4x + 3-3 <= 3x - 5 -3
4x <= 3x - 8
Subtract 3x form both sides
4x - 3x <= 3x -3x - 8
x <= -8
Answer:
CHALLENGE ACCEPTED!!
Step-by-step explanation:
4x + 3 ≤ 3x - 5
4x - 3x ≤ -5 -3
x ≤ -8
sorry, cant draw the number line but hope the solution helps.
-2x > 6
-2x ÷ -2 > 6 ÷- 2
x > -3
1/8(3x - 16) < 4
3/8x - 2 < 4
3/8x < 4 + 2
3/8x < 6
x = 16
x - 3/2 ≥ -5
x - 3 ≥ -5 × 2
x - 3 ≥ -10
x ≥ -10 + 3
x ≥ 7
Graph m > −5 on a number line.
Graphing an inequality involves drawing a number line, marking the critical value, here -5, with an open circle because it's not included in the solution, and indicate with an arrow every number greater than -5, as these are the solutions to the inequality.
Explanation:To graph m > -5 on a number line, you first need to draw a straight line, representing the number line. Mark -5 on the line. Since the inequality is 'greater than' (-5), you will have an open circle at -5. The open circle indicates that -5 is not included in the solution. The solutions for the inequality are all values to the right of -5, so you would draw an arrow pointing towards the right from the open circle. This demonstrates that all numbers greater than -5 are the solution to the inequality.
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ERGENT I NEED HELP ON ATH PROBLEM
Answer:
Kite, Parallelogram, and Rectangle.
Step-by-step explanation:
BTW, you spelled Urgent wrong.
The answers are, Kite, Parallelogram, and Rectangle.
Answer:
Kite, Parallelogram, and Rectangle.
Step-by-step explanation:
BTW, you spelled Urgent wrong.
The answers are, Kite, Parallelogram, and Rectangl
A 9-pound bag of potatoes costs $4.14. What is the unit price per pound? 2 points
$0.46
$2.17
$0.046
O
$0.22
Answer:
Step-by-step explanation:
Unit price = Total price
number of items
= 4.14/9
= $0.46
The box plots show the average gas mileage, in miles per gallon, of cars and minivans tested by a certain company.
Cars
+
+
+
+
+
14
16
18
20
22
24
26
28
30
32
34
Minivans
Which correctly compares the interquartile ranges?
The interquartile range for cars is about 12 mpg, and the interquartile range for minivans is about 12 mpg.
The interquartile range for cars is about 7 mpg, and the interquartile range for minivans is about 3 mpg.
The interquartile range for cars is about 24 mpg, and the interquartile range for minivans is about 19 mpg.
The interquartile range for cars is about 8 mpg, and the interquartile range for minivans is about 7 mpg.
Answer:
b.The interquartile range for cars is about 7 mpg, and the interquartile range for minivans is about 3 mpg.
Step-by-step explanation:
i got it right
Answer:
The answer is B
Step-by-step explanation:
Use the net to find the surface area of the square pyramid.
A) 152 in2
B) 264 in2
C) 336 in2
D) 448 in2
Answer:
b
Step-by-step explanation:
Answer:
C) 336 in2
Step-by-step explanation:
336 in 2
Area of base → 82 = 64
Area of each triangle →
1
2
· 8 · 17 → 68
64 + 68 + 68 + 68 + 68 = 336 in2
I understood the last one but now I have one that makes me solve for a short side
n^2 + 10^2 = 26^2
n^2 + 100 = 676
n^2 = 576
n = 24
A marker is almost 14 centimeters long. This length ends between
which two centimeter-marks on a ruler? Enter the smaller centimeter-
mark first.
centimeter-mark and the
The length ends between the
centimeter-mark.
Answer:
It ends between 13cm and 14cm mark.
Step-by-step explanation:
Since this marker in question is almost 14 centimeters long and definitely ends between two centimeter marks, the two centimeters that the length of this marker ends between on a ruler should be the 13cm and 14cm marks on the ruler.
Final answer:
The length of a marker almost 14 centimeters long ends between the 13 centimeter-mark and the 14 centimeter-mark on a ruler.
Explanation:
When measuring a marker that is almost 14 centimeters long, we look at the ruler and identify the two consecutive centimeter marks between which the length of the marker falls. If the marker is almost 14 centimeters long, this means it is greater than 13 centimeters but less than 14 centimeters.
Therefore, we can confidently say that the marker's length lies between the 13 centimeter-mark and the 14 centimeter-mark on the ruler. The smaller centimeter-mark would be 13, as it is the immediately preceding whole centimeter before the marker ends.