Answer: 2.5 miles
We are given that
Total length of path=10 mile
Han runs at a pace=12 minutes per mile
Tyler runs at a pace=15 minutes per mile
We have to find the distance run by Han after a half hour.
Half hour=30 minutes
Using unitary method
Han runs distance in 12 minutes=1 mile
Han runs distance in 1 minute= mile
Han runs distance in 30 minutes= miles
Hence, Han runs 2.5 miles after half hour.
Step-by-step explanation:
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days: f(d) = 11(1.01)°
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm.
What is a reasonable domain tc plot the growth function?
(4 points)
Part B: What does the y-intercept of the graph of the function f(c) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)
Answer:
Step-by-step explanation:
a.
f(d)=11(1.01^d
d=6.97 days
b.
t
f(c) represents the size of algae after c days
c.
f(2)=11(1.01)^2
f(7)=11(1.01)^7
[tex]rate=\frac{f(7)-f(2)}{7-2} \\=\frac{11(1.01)^7-11(1.01)^2}{5} \\=\frac{11[(1.01)^7-(1.01)^2]}{5} \\\approx 0.0104 ~mm[/tex]
explain how the value of a digit changes if the digit moves one place to the right or left.
When talking about a number line, the farther right the digit moves, the large the number. The farther left it goes, the smaller the number.
For example, 81 would be to the right of 80. And 79 would be on the left. The larger the negative number, the smaller it is. So -70 is smaller than -20.
I hope this helps!
NO LINKS!! Please help me with this problem. Find all points on the x-axis that are a distance 5 from P(-8,4)
Answer:
[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
The points that are a distance of 5 units from P(-8, 4) will be all the points on the circumference of a circle with center (-8, 4) and radius 5.
Substitute the center and radius into the formula to create an equation of the circle:
[tex]\implies (x+8)^2+(y-4)^2=25[/tex]
The y-value of any point on the x-axis is zero.
Therefore, to find the points on the x-axis that are 5 units from point P, substitute y = 0 into the equation of the circle and solve for x:
[tex]\implies (x+8)^2+(0-4)^2=25[/tex]
[tex]\implies (x+8)^2+(-4)^2=25[/tex]
[tex]\implies (x+8)^2+16=25[/tex]
[tex]\implies (x+8)^2+16-16=25-16[/tex]
[tex]\implies (x+8)^2=9[/tex]
[tex]\implies \sqrt{(x+8)^2}=\sqrt{9}[/tex]
[tex]\implies x+8=\pm3[/tex]
[tex]\implies x+8-8=\pm3-8[/tex]
[tex]\implies x=-8\pm3[/tex]
[tex]\implies x=-11, x=-5[/tex]
Therefore:
[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]
Which statement about the ordered pairs (-9, 3) and (2, 4) is true for the equation 6x = 14?
(-9, 3) is a solution to the equation. O Both ordered pairs are solutions.
O Neither ordered pair is a solution.
(2, 4) is a solution to the equation.
The correct statement will be "Neither ordered pair is a solution".
What are ordered pairs?
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.In order to understand a point visually, it can be helpful to position it on the Cartesian plane.An ordered pair's numerical values may be fractions or integers.Ordered Pair is equal to (x,y), where x is the distance between a point and the principal axis (x).Additionally, y = ordinate measures how far a point is from the secondary axis "y."Given equation is: 6x = 14
For ordered pair (-9, 3) , the values of x=-9 and y=3
Plugging these values into the given equation
6(-9) = 14
-54 = 14 (False)
Now for ordered pair (2, -4) , the values of x=2 and y=-4
Plugging these values into the given equation
6(2) = 14
12 = 14 (False)
The correct statement will be "Neither ordered pair is a solution".
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Your round trip drive to work is 4 3/10 miles. How many miles do you drive to and from work in 3 days?
Answer:
Below
Step-by-step explanation:
4 3/10 * 3 = 43/10 * 3 = 129 / 10 = 12 9/10 miles
The graph below represents the paths of a squirrel traveling up and down a tree over time. The position of the squirrel can be calculated using the function p(t)=at^2+bt+c. What is the value of a? What is the value of b? What is the value of c?
The values of the variables a, b and c are; a = 5/19, b = -160/19, c = 960/19
How to interpret Quadratic graphs?
We are given the quadratic function formula as;
p(t) = at² + bt + c
Thus, the equation is now;
p(t) = at² + bt + 0
p(t) = at² + bt
From the graph, we see that when x = 8, y = 0. Thus;
p(8) = a(8²) + 8b + c = 0
64a + 8b + c = 0 ------(1)
From the graph, we know that the axis of symmetry is;
x = -b/2a
Thus;
16 = -b/2a
b = -32a -----(2)
From the graph, we see that when x = 5, y = 15. Thus;
p(8) = a(5²) + 5b + c = 0
25a + 5b + c = 15 ------(3)
Put -32a for b in eq 1 and 3 to get;
64a + 8(-32a) + c = 0
-192a + c = 0 ------(4)
25a + 5(-32a) + c = 15
-135a + c = 15 ------(5)
Subtract eq 4 from eq 5 to get;
192a - 135a = 15
57a = 15
a = 15/57
a = 5/19
Thus;
b = -32(5/19) = -160/19
-135(5/19) + c = 15
15 + (675/19) = c
c = 960/19
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Simplify x^2-4/x^2+2
Answer:x^4+6
Step-by-step explanation:
you must combined both x squared to get x^4 and then add the opposite of -4 Which is +4 and what you do to one side you must do to the other therefore you add the 2 to it as well. in conclusion you get x^4+6. hope this helps:)
what is the value of tan 30?
The value of tan 30° after using trigonometric ratio is [tex]\frac{1}{\sqrt{3} }[/tex] .
What is trigonometric ratio?
There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.
Here the given
=> tan30°
Now ,Tan 30 degrees in radians is written as
=>tan (30° × π/180°)
=> [tex]\frac{1}{\sqrt{3} }[/tex]
Therefore the value of tan30° is [tex]\frac{1}{\sqrt{3} }[/tex] .
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what expression is equivalent to 3x+3(x+y)
Answer:
6x + 3y
Step-by-step explanation:
Distribute:
=3x + (3)(x) + (3)(y)
=3x + 3x + 3y
Combine Like Terms:=3x + 3x +3y
=(3x + 3x) + (3y)
=6x + 3y
Answer:
I do not see the choices. There could be more than one right answer
6x + 3y
Step-by-step explanation:
3x + 3(x+y)
3x + 3x + 3y
6x + 3y
simplify - (y+2) +2y
Answer:
y-2
Step-by-step explanation:
Which of the following expressions contains only 1 constant? Select TWO that apply.
A 18+5r³
B
C.
90(h - 4)
766
D. 41y-8y + 7y
The expressions which have only one constant are:
A. 18+5r³
B. 90(h-4)
Given: we have a set of equations.
an equation is a combination of variables and constants.
In the given set of equations we have a single variable with a single constant.
those are:
→ 18+5r³
→ 90(h-4)
In the other equations we don't have constants.
A constant is defined as an object whose value is fixed regardless of changes in its usage.
Even after the expression is changed, these values stay the same.
Natural numbers, whole numbers, real numbers, integers, and decimal numbers are examples of constants in mathematics.
A variable is a thing whose value changes depending on how it's used and isn't fixed.
Hence we get the required answer.
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Please help with this equation question?
Select the true statement about the following linear equation.
y= -2x + 4
The graph is a curve
The y-intercept is -2
The slope is -2
The slope is 2
The general form of a linear equation is slope m and y-intercept c is given as y = mx + c thus the slope of the line y = -2x + 4 is -2 so option (C) is correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given line,
y = -2x + 4
The general form of a linear equation is the slope(m) and y-intercept (c) is given as
y = mx + c
Compare,
m = -2 and c = 4
Slope = -2 and y-intercept = 4
Hence "The slope of the line y = -2x + 4 is -2 and y-intercept is 4".
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Solve the equation by using the square root property. Express all radicals in simplest form.
k²=17
The simplest form of radicals is [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]
What is a radical expression?
An nth root of a number x is a number r that, when multiplied by n, equals x, where n is a positive integer, also known as the degree of the root. Degree 3 roots are referred to as cube roots, while degree 2 roots are known as square roots.
We have,
k² = 17
The variable in this non-linear equation needs to be separated. This is achieved by exponentiating both sides by the reciprocal of the exponent of the variable, which in our example is equal to 1/2.
[tex](k^{2} )^{\frac{1}{2} } = 17^{\frac{1}{2} }[/tex]
[tex](k^{2} )^{\frac{1}{2} } = -17^{\frac{1}{2} }[/tex]
[tex]k= 17^{\frac{1}{2} }[/tex]
[tex]k = -17^{\frac{1}{2} }[/tex]
Hence, the simplest form of radicals is [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]
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1) 3x(x-3)+x(x-1)=50
2) 4x^2-10x=50
3) 2x^2-5x-25=0
How do you get from steps 1 to 2 to 3?
Step-by-step explanation:
okok
3x(x-3)+x(x-1)=50multiply inside the brackets then3x^2-9x+x^2-x=50then arrange then according to power and add or subtract 4x^2-10x=50 here is your step 2take 2 common form LHS as2(2x^2-5x)=50then you will get your step 3 as2x^2-5x=25.....25 comes from 50/2 and 2 is from LHS. You lean a 16 foot ladder against the wall. If the base is 4 feet from the wall, what angle does
the ladder make with the ground? Round your answer to the nearest tenth.
Check the picture below.
[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{16}}\implies cos(\theta )=\cfrac{1}{4}\implies \theta =cos^{-1}\left( \cfrac{1}{4} \right)\implies \theta \approx 75.5^o[/tex]
Make sure your calculator is in Degree mode.
A 40-foot rope is cut into 2 pieces. Seven less than four times the length of the longer rope piece x is five times the length of the shorter piece, which is (40 − x) ft. Find the length of the longer rope piece x (in ft). (Enter an exact number.)
If a 40-foot rope is cut into 2 pieces. the length of the longer rope piece x is 23ft.
How to find the length?Seven less than 4 times = 4x-7
4x-7=5(40-x)
4x-7=200-5x
Collect like terms
9x=207
Divide both side by 9x
x = 207 /9
x=23 ft (longer part of the rope)
Shorter part of the rope
40-x where x is 23
40 -23
= 17ft
Therefore the longer part is 23ft.
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Out of 5,000 students 1,000 preferred diet drinks over sugared sodas. What percent preferred non diet drinks?
A toaster oven usually sells for $60. If the toaster oven is 20% off, and sales tax is 7%, what is the total price of the toaster oven, including tax?
Find
(Round your answer to the nearest hundredth)
The value of the unknown angle x would be 43 degrees.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We have been given a right-angle triangle with a perpendicular side of 6 units and a hypotenuse of 10 units.
The unknown angle is x which needs to find.
Therefore, applying trigonometry;
Sin x = perpendicular/hypotenuse
Sin x = 6/10
Sin x = 3/5
Sin x = 0.6
x = Sin inverse (0.6)
x = 43 degrees.
Hence, the value of the unknown angle x would be 43 degrees.
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A rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. Another agency charges a fee of $70.00 plus $54.00 per day to rent the same car.
using a graphing calculator, find the number of days fpr which the costs are the same. round your answer the the nearest whole day
A. 9
B.3
C. 5
D. 8
Answer: The answer to this question would be: 5 days
In this question, there are two kinds of rent pricing and you are asked to find the number of days when both of them will charge the same price.
From the description, you can get an equation of each price which would look like this(x=number of day rent):
cost1= 110 + 46x
cost2= 70 + 54x
Then, the days when the price same would be:
cost1 = cost2
110 + 46x= 70+54x
110-70= 54x - 46x
40= 8x
x=5
Step-by-step explanation:
12²+6² ÷2 =
please help me
Answer:
162
Step-by-step explanation:
12²+6² ÷ 2
= 144 + 36 ÷ 2
= 144 + 18
= 162
In 1965, the population of a certain town was 2010. In 1995, the population was 3620. If the population during this time period grew according to an exponential model, what will the population be in 2050?
According to the growth function, the population be in 2050 will be 10,635
Growth function:
The growth function refers the pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Given,
In 1965, the population of a certain town was 2010. In 1995, the population was 3620.
Here we need to find the population in 2050.
While we looking into the given problem, let us consider,
P refers the final population
A refers the the starting population, and
x refers the time passed
Now, we need to determine the value of the growth factor n and it can be calculated using the information for the years 1965 and 2010.
Here we know that, in 1965, the population of a certain town was 2010. In 1995, the population was 3620.
And the value of x is 30
So, it can be written as,
=> 3620 = 2010eⁿˣ³⁰
=> 3620/2010 = e³⁰ⁿ
=> 362/201 = e³⁰ⁿ
Here by applying ln to both sides of the equation:
⇒ln(362/201) = ln(e³⁰ⁿ)
By, using the laws of logarithms:
=> 30n = ln(362) - ln(201)
=> n = [ln(362) - ln(201)] / 30
=> n = 0.0196
Here we have to use this information to determine P in 2050.
Here the value of A will still be 2010, but x will be 85 years.
Here we have to apply these values then we get,
=> P = 2010e⁰°⁰¹⁹⁶ˣ⁸⁵
=> P = 2010e¹°⁶⁶⁶
=> P = 2010 x 5.2909
=> P = 10635
Therefore, there are 10635 in 2050.
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I need help fast please!
The time it takes to cover the distance between two cities by car varies inversely with the speed of the car.
The trip takes 7 hours for a car moving at 36 mph.
What is the speed of a car that makes the trip in 9 hours?
Answer:
28 mph
Step-by-step explanation:
Given that a car moving 36 mph takes 7 hours for a trip, you want to know the speed if the trip takes 9 hours.
Time and SpeedThe speed and time vary inversely for the same distance. If the time goes up by a factor of 9/7, the speed will go down by the inverse factor: 7/9.
7/9 × 36 mph = 28 mph
The speed of the car is 28 mph for the 9-hour trip.
<95141404393>
Calculate the standard score (z-score) of the given sample mean. Round your answer to two decimal places.
μ = 35 and o = 9; n = 60; x = 32
The standard score (z-score) of the given sample is -20.
Given,
[tex]u[/tex] = 35
[tex]o[/tex] = 9
n = 60
x = 32
To calculate standard score (z-score) use formula,
[tex]z=\frac{x-u}{\frac{o}{n} }\\\\z=\frac{32-35}{\frac{9}{60} }\\\\z=\frac{-3}{0.15}\\ \\z=-20[/tex]
Thus, the standard score(z-score) of given sample mean is -20.
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Determine whether (-9,-5) is a solution of 9x + 4y = 10.
...
Answer:
It is not a solution
Step-by-step explanation:
put in (-9,-5) in for x and y
9(-9)+4(-5)=10
-81-20=10
-101=10
This is false so (-9,-5) is not a solution to the equation 9x+4y=10
If sin(x)=5/6 , and x is in quadrant I, determine the exact value of each of the following. Use fractions and radicals only, no decimals. You do not need to rationalize the denominator.
sin(x/2) =
cos(x/2)=
Tan(x/2)=
please help
The value of sin(x/2)= √(1-√11/6)/2
The value of cos(x/2)=√(1+√11/6)/2
The value of tan(x/2) = 5/6/(√(1+√11/6)
What trigonometry of half angles?In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45 and so on. If θ is an angle, then the half angle is represented by θ/2.
In trigonometry, sin( x/2)= √(1-cosx)/2
cos( x/2)= √(1+cosx)/2
tan( x/2)=sinx/1+cosx
if sin (x) = 5/6
this means that 5 is the opposite and 6 is the hypotenuse, then the adjascent is
a= √(6^2-5^2)
a= √36-25
a= √11
therefore if cos x= √11/6
sin(x/2)= √(1-√11/6)/2
cos(x/2)= √(1+√11/6)/2
tan(x/2)=5/6/(√(1+√11/6)
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Work out M and C for the line:
Y=2x+5
M= C=
In the given equation we get the following values:
M = 2
C = 5
Given, we have the equation:
Y = 2x + 5
we are asked to determine the following values of m and c.
The given equation is in the form of slope intercept form.
slope intercept form is given as:
y = mx+c
hence :
M = 2 and
C = 5
One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).
The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. This relationship will be the equation of a straight line:
the line must satisfy the coordinates of every point along it.Any location that is not on the line will not satisfyhence we get the required values.
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Eve is going to buy 30 pens from either shop A or shop B.
Shop A: pack of 10 pens for £2
Shop B: pack of 5 for £1.10 buy 1 pack and get 1 half price.
What is the difference in cost for all 30 pens between the two shops?
PLSS HELPPPP
The difference in the cost of all 30 pens between two shops is,
£1.05
Given, Eve is going to buy 30 pens from either shop A or shop B.
Shop A: pack of 10 pens for £2
Shop B: pack of 5 for £1.10 buy 1 pack and get 1 half price.
So, the cost of 30 pens from the shop A is,
as, a pack of 10 pens is of £2
1 pen = 2/10
30 pens = £6
Now, the cost of 30 pens from the shop B is,
as, a pack of 5 for £1.10
1 pen = 1.10/5 = £0.22
also buy 1 and get 1 at half price.
So, 2 pens = 0.22 + 0.11 = £0.33
Therefore, 30 pens = £4.95
So, the cost of 30 pens from shop A is £6 and from shop B is £4.95.
Hence, the difference in the cost of all 30 pens between two shops is,
£1.05
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Logic
Consider the following statements:
Alex's bag is heavier than Hisham's bag
Hisham's bag is lighter than both Aya's bag
and Irene's bag
Aya's bag is heavier than Alex's bag and
Irene's bag
Whose bag is the heaviest?
Aya
In given order puzzle Aya's bag is the heaviest bag .
What is order puzzle?
A puzzle is a thing that is difficult to understand or explain. The term also refers to a game, toy, or problem designed to test ingenuity or knowledge. Math puzzles are problems that require mathematical logic and calculation. These types of puzzles carry recreational as well as educational value for the pupils.
Here the given statements ,
=> Alex bag > Hisham bag
And Hisham bag < Aya bag and Irene bag
Now ,
=> Aya bag > Alex bag and Irene bag
Then combine the given ,
=> Aya bag> Alex bag>Irene bag>Hisham bag.
Therefore Aya's bag is the heaviest bag.
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