Karen runs 6 miles in 50 minutes. at the same rate, how many miles would she run in 35 minutes?
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Related Questions
Find the area under the standard normal curve between z = -1.5 and z = 2.5
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To area under the standard normal curve between z = -1.5 and z = 2.5 is 0.927
Explanation:A standard normal curve, also known as the standard normal distribution, is a bell-shaped, symmetrical probability distribution with a mean of 0 and a standard deviation of 1. It serves as a reference for many statistical analyses and is often denoted as the Z-distribution.
To find the area under the standard normal curve between z = -1.5 and z = 2.5, we need to use the z-table. The z-score of -1.5 corresponds to an area of 0.0668 and the z-score of 2.5 corresponds to an area of 0.9938. To find the area between these two z-scores, we subtract the smaller area from the larger area:
= 0.9938 - 0.0668
= 0.927
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The area between these z-scores is 0.9270.
The area under the standard normal curve between z = -1.5 and z = 2.5 can be found using the z-table.
First, find the area to the left of
z = -1.5, which is 0.0668.
Next, find the area to the left of
z = 2.5, which is 0.9938.
Subtract these two values to get the area between z = -1.5 and z = 2.5 :
0.9938 - 0.0668
= 0.9270.
Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
-3x^5 + 9x^4 + 5x^3 + 3
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In this case because the highest order term is -3x^5, as x approaches -oo, y approaches +oo. And as x approaches +oo, y approaches -oo.
The cosine of the angle is 4/5
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The cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]
In triangle ABC, where angle ABC is a right angle (90 degrees) and sides AB, BC, and AC are given as 6, 8, and 10 units respectively, we can use the cosine and cotangent functions to find the cotangent of angle ABC.
The cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse.
In this case,[tex]\(\cos(\angle ABC) = \frac{BC}{AC} = \frac{8}{10} = \frac{4}{5}\).[/tex]
The cotangent [tex](\(\cot\))[/tex] of an angle is the reciprocal of the tangent (tan).
The tangent is the ratio of the opposite side to the adjacent side.
Therefore,[tex]\(\cot(\angle ABC) = \frac{1}{\tan(\angle ABC)}\).[/tex]
Since [tex]\(\tan(\angle ABC) = \frac{AB}{BC} = \frac{6}{8} = \frac{3}{4}\)[/tex], we can find the cotangent:
[tex]\[ \cot(\angle ABC) = \frac{1}{\tan(\angle ABC)} = \frac{1}{\frac{3}{4}} = \frac{4}{3} \][/tex]
Therefore, the cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]
The probable question may be:
The cosine of a certain angle is 4/5. What is the cotangent of the angle?
In triangle ABC , Angle ABC=90 degree, AB=6, BC=8 AC=10
Final answer:
The cosine of an angle being 4/5 means that the ratio of the adjacent side to the hypotenuse in a right triangle is 4/5.
Explanation:
The given question states that the cosine of an angle is 4/5. In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. So, if we have a right triangle with an angle A, and the cosine of A is 4/5, it means that the ratio of the length of the adjacent side to the hypotenuse is 4/5.
Thus, we can say that if the length of the adjacent side is 4 units, then the length of the hypotenuse would be 5 units, assuming the units are consistent. This relationship holds true for any right triangle with an angle whose cosine is 4/5.
For example, if we have a right triangle with an adjacent side of 8 units, then the hypotenuse would be 10 units.
Which translation will change figure ABCD to figure A'B'C'D'?
A. 7 units left and 6 units up
B. 6 units left and 7 units up
C. 7 units left and 5 units up
D. 5 units left and 7 units up
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In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -x2 -6. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
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g(x)=-x^2-6
g(x)=-(x^2+6) so g(x) will have no x-intercepts as its maximum value will be -6.
g(x) is f(x) reflected about the x axis and shifted downwards by 6 units.
The vertical ______ of the function secant are determined by the points that are not in the domain.
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Divide 35b^5 +20ab^3 +20a^2b^2 by 5b^2
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So 35b^5 / b^2 = 35b^3, 30ab^3 / b^2 = 30ab, and 20a^2b^2 / b^2 = 20a^2.
So your final answer is 35b^3 + 30ab + 20a^2.
Point r is located at (3,0). point s is located at (0,-4). what is the equation of the line through these two points
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slope = (-4 - 0) / (0 - 3) = -4/-3 = 4/3
y = mx + b
slope(m) = 4/3
(0,-4)....x = 0 and y = -4
now we sub and find b, the y int
-4 = 4/3(0) + b
-4 = b
so ur equation is : y = 4/3x - 4....or 4x - 3y = 12 <==
what is larger 0.0013 or 0.02
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The population of a type of local frog can be found using an infinite geometric series where a one equals 84 and the common ratio is one over five find the sum of the infinite series that will be the upper limit of this population. 87,105,425, or this series is divergent
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Since r, the common ratio squared is less than one, the sum will converge to a limit. Rule: if r^2<1 infinite series converges, otherwise it diverges.
Since the sum of any geometric sequence is:
s(n)=a(1-r^n)/(1-r)
And if r^2<1, (1-r^n) becomes 1-0=1 as n approaches infinity.
So whenever r^2<1 the sum of the infinite series is just:
s(n)=a/(1-r)
Since a=84 and r=1/5 this infinite series has a sum of:
s(n)=84/(1-1/5)
s(n)=84/(4/5)
s(n)=5(84)/4
s(n)=105
If BC = 5 and CD = 26, find AC.
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Answer:
[tex]AC=\sqrt{130}[/tex]
Step-by-step explanation:
AC is the geometric mean. Solve it using this proportion:
[tex]\frac{BC}{AC}=\frac{AC}{CD}[/tex]
Now fill in the values we know:
[tex]\frac{5}{AC}=\frac{AC}{26}[/tex]
Cross multiply to get
[tex](AC)^2=130[/tex]
That means that
AC = [tex]\sqrt{130}[/tex], which, in decimal form is
AC = 11.40175425
Peter bought an antique piece of furniture in 2000 for $10,000. Experts estimate that its value will increase by 12.12% each year. Identify the function that represents its value. Does the function represent growth or decay?
A) V(t) = 10000(1.1212)t; growth
B) V(t) = 10000(0.8788)t; decay
C) V(t) = 10000(1.1212)t; decay
D) V(t) = 10000(0.8788)t; growth
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the exponent will be 1.1212
3!3! = 362,880 81 36
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3!3! = 3*2*1*3*2*1 = 6*6 = 36
3! ----) 3 . 2 . 1 ----------) 3!3! = 36
if you subtract 23.47 km from 560.589 km, how many significant digits would your answer have?
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alrite... looks good, however, when it comes to dealing with significant digits, for addition/subtraction, we go with the lowest significant amount for decimals, in this case,
560.589 <--- has 6 significant digits, accurate to the 1000th place
23.47 <--- has 4 significant digits, and is accurate to the 100th place
thus, our answer will have to be rounded up in 2 significant decimals, or 537.12
and that only has 5 significant digits, since is rounded up to the 100th place.
if the trapezoid below is reflected across the x axis what are the coordinates of B
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answer is B. (5,-9)
If the coordinate B is reflected over x-axis, the resulting coordinate will be (5, -9)
Reflection of imageIf an image is reflected over the x-axis, the resulting coordinate will be (x, -y). The reflections shows the mirror image of a figure.
Given the coordinate B before reflection as (5, 9)> If the coordinate is reflected over x-axis, the resulting coordinate will be (5, -9)
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4n-3<12 solve and please don't give me the answer just the equation
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So first bring -3 to the right hand side:
4n-3<12 => 4n < 12+3 => 4n < 15
Then divide by 4
4n/4 < 15/4 => n < 15/4
You can't simplify it beyond that.
How many cans of paint are needed to cover an area of 2,200 square units if one can of paint covers an area of 400 square units? 4 5 6 8?
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Then you just need to divide 2,200 square units with 400 square units.
The equation will be : (2,200 square units / 400 square units) x 1 can= 4.5 cans
After you round up the result it would be 5 cans.
Answer: 5 cans
When 332 college students are randomly selected and surveyed, it is found that 113 own a car. find a 99% confidence interval for the true proportion of all college students who own a car?
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n = 332, sample size
p = 113/332 = 0.3404, sample proportion
99% confidence interval
The confidence interval for the population is calculated from
[tex]p \pm z^{*} \sqrt{ \frac{p(1-p)}{n} } [/tex]
where z* = 2.58 for the 99% confidence level (from tables)..
[tex]2.58 \sqrt{ \frac{0.3404(1-0.3404)}{332} } =0.0671[/tex]
Therefore the 99% confidence interval is
(0.3404 - 0.0671, 0.3404 + 0.0671) = (0.2733, 0.4075)
Answer:
The 99% confidence interval is (0.273, 0.408) or (27%, 41%).
That is, between 27% and 41% of the students own cars.
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -(x-4)2. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answers
g(x) is f(x) reflected about the about the x-axis and shifted to the right by 4 units.
Since -x^2-5 = 0 implies x = +-sqrt(5)i, there are no x-intercepts
Transformations:
Reflect f(x) in the x-axis,
then vertically shift the result down by 5 units,
to get g(x).
A particular metal alloy a has 20% iron and another alloy b contains 60% iron. how many kilograms of each alloy should be combined to create 80 kg of a 52% iron alloy?
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t+s=80, s=80-t
(0.2t+0.6s)/80=0.52 multiply both sides by 80
0.2t+0.6s=41.6, now using s=80-t in this equation gives us:
0.2t+0.6(80-t)=41.6 perform indicated multiplication on left side
0.2t+48-0.6t=41.6 combine like terms on left side
-0.4t+48=41.6 subtract 48 from both sides
-0.4t=-6.4 divide both sides by -0.4
t=16, since s=80-t
s=64
So 16kg of 20% alloy is mixed with 64kg of 60% allow to make 80kg of a 52% alloy.
Smallville’s town council has records of the town’s budget over a 10-year period. Create a best fit and model for the data. What does the model predict the town’s budget will be in the year 2011?
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If these were the missing choices:
A)$391,000
B)$417,000
C)$404,000
D)$411,000
My answer is D) $411,000 in 2011.
There is an average increase of 4% from the previous budget to arrive at the amount of the current year.
2009 budget $381,700
381,700 * (1.04)² = 381,700 * 1.0816 = 412,846.72 only Choice D. is nearest to the amount
2000 budget $265,100
265,100 * (1.04)¹¹ = 265,100 * 1.540 = 408,254 only Choice D. is nearest to the amount.
HOW DO YOU MOVE A VARIABLE FROM ONE SIDE OF AN EQUATION TO ANOTHER? I need to know as I'm reviewing module 7 algebra and i want to know please
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For example in the equation 5+a=7, subtract a from both sides to get 5=7-a.
If the initial equation was 5-a=7, add from both sides (5=a+7).
Basically, if the initial value is negative, add its value to cancel to zero.
Do the opposite if the initial value is positive.
enter an equation in slope-intercept form that describes a line that contains the points (4,1) and (4,2)
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so... the slope is undefined, the graph of it is just a vertical line, check the picture below, and that's the equation.
now... you can't quite put it in y = mx + b, or slope-intercept form, since it has no defined slope and it doesn't have an y-intercept either.
Which of the following relations represent a function? {(1,-3),(-2,0),(1,4)} {(-2,0),(3,0),(-2,1)} {(3,-8),(-2,0),(4,1)} {(4,12),(4,13),(-4,14)}
Answers
example
(1,2) and (1,4) would not be a function
but (1,2) and (3,2) is
no firs tnumber repeats
first one, 1 repeats with -3 and 4
2nd one, -2 repeatts with 0 and 1
3rd one, no repeats
4th one, 4 repeats with 12, 13, 14
answer is 3rd one or
{(3,-8),(-2,0),(4,1)}
To determine if a relation is a function, check for repeated x-values. The relations that represent a function are {(1,-3),(-2,0),(1,4)} and {(3,-8),(-2,0),(4,1)}.
Explanation:In order for a relation to represent a function, each input (x-value) must correspond to exactly one output (y-value). We can determine if a relation is a function by checking for any repeated x-values. If there are no repeated x-values, then the relation is a function. Let's apply this to the given relations:
The relation {(1,-3),(-2,0),(1,4)} represents a function because each x-value is unique.
The relation {(-2,0),(3,0),(-2,1)} does not represent a function because there is a repeated x-value (-2).
The relation {(3,-8),(-2,0),(4,1)} represents a function because each x-value is unique.
The relation {(4,12),(4,13),(-4,14)} does not represent a function because there is a repeated x-value (4).
So, the relations that represent a function are {(1,-3),(-2,0),(1,4)} and {(3,-8),(-2,0),(4,1)}.
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Match the perfect square trinomials with their factors 4a2 + 4a + 1 (2 + a)(2 + a) 4a2 − 4a + 1 (2a + 1)(2a + 1) 4 − 4a + a2 (2a − 1)(2a − 1) 4 − 4a − a2 (2 − a)(2 − a) 4 + 4a + a2
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4 − 4a + a2 = (2 - a)^2 = (2 − a)(2 − a)
4a2 − 4a + 1 = (2a -1)^2 = (2a − 1)(2a − 1)
4 + 4a + a2 = (2 + a)^2 = (2 + a)(2 + a)
Yana is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below: A triangle ABC is shown. D is a point on side AB and E is a point on side AC. Points D and E are joined using a straight line. The length of AD is equal to 4, the length of DB is equal to 5, the length of AE is equal to 6 and the length of EC is equal to 7. She starts with the assumption that segment DE is parallel to segment BC. Which inequality will she use to contradict the assumption? 4:9 ≠ 6:13 4:9 ≠ 6:7 4:13 ≠ 6:9 4:5 ≠ 6:13
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Please see attached file for the triangle’s figure:
Going with the image attached, if DE is parallel to BC
then
4: (4 + 5) = 6 : (6 + 7).
Therefore, the inequality that she will use to contradict the assumption
is 4:9 ≠ 6:13.
To add, a relation that holds
between two values when they are different in mathematics is called an inequality. A is not equal to b also means the notation a ≠ b.
Inequalities are governed by the following properties:
Transitivity
Converse
Addition and subtraction
Multiplication and division
Additive inverse
Multiplicative inverse
Applying a function to both sides
Answer:
4:9 ≠ 6:13.
Step-by-step explanation:
Write a possible function rule for the following sequence.
11, 15, 19, 23, 27, ...
a(n)=?
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a(n)=a+d(n-1), a=initial term, d=common difference, n=term number
In this case we know a=11 and d=4 so
a(n)=11+4(n-1) which can be simplified...
a(n)=11+4n-4
a(n)=4n+7
PLEASE HELP!! IMAGE ATTACHED find the measure of angle 2
Answers
the figure is an equilateral triangle, which all angles are 60 degrees
angle 3 divides a 60 degree angle in half so angle 3 = 30 degrees
the base is a right triangle which is 90 degrees
90+30 = 120
180-120 = 60
Angle 2 is 60 degrees
How do I set up this equation and solve ?
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angles in a triangle need to equal 180 degrees
so x = 180 - 47 - 58
x = 180-105
x= 75 degrees
A carnival ride is in the shape of a wheel with a radius of 20 feet. The wheel has 16 cars attached to the center of the wheel. What is the central angle, arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable. You must show all work and calculations to receive credit.
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The total central angle around the wheel is 2π.
Therefore the central angle between two cars is
(2π)/16 = π/8 = 0.39 radians (nearest hundredth)
The arc length between two cars is
s = (20 ft)*(π/8 radians) = 2.5π = 7.85 ft (nearest hundredth)
The area of a sector formed by two cars is
(1/16)*(π*20²) = 78.54 ft² (nearest hundredth)
Answers: (to the nearest hundredth)
Between two cars,
Central angle = 0.39 radians (or 71.4°)
Arc length = 7.85 ft
Area of a sector = 78.54 ft²
Refer to the diagram shown below, which shows two of 16 equally-spaced cars attached to the center of the wheel.
The total central angle around the wheel is 2π.
Therefore the central angle between two cars is
(2π)/16 = π/8 = 0.39 radians (nearest hundredth)
The arc length between two cars is
s = (20 ft)*(π/8 radians) = 2.5π = 7.85 ft (nearest hundredth)
The area of a sector formed by two cars is
(1/16)*(π*20²) = 78.54 ft² (nearest hundredth)
Answers: (to the nearest hundredth)
Between two cars,
Central angle = 0.39 radians (or 71.4°)
Arc length = 7.85 ft
Area of a sector = 78.54 ft²