17. it is recommended that hikers' backpacks weigh no more than 20% of their body weight on overnight bikes and no more than 10% of their body weight on day hikes there are restrictions a hiker who weighs 160 pounds is planning an overnight hike. the weight of her backpack when packed with essential equipment is 15 pounds. write an inequality to show how many pounds, p, the hiker can still add to her backpack and stay within the recommended weight a hiker who weighs 180 pounds is planning a day hike. the weight of his backpack when packed with part a part b
Expressions can be represented as equations or inequalities
(a) The hiker's backpack weighs 15 lb.
(b) the hiker can add additional 19.5 pounds
The inequality that represents the additional weight is:
The hiker can add additional 19.5 pounds
(a) Long hike
The hiker's weight is given as:
, the recommended weight (x) of the backpack is calculated as:
The hiker's backpack weighs 15 lb.
So now what weare supposed to do is
Subtract 15 from both sides
(b) Day hike
The hiker's weight is given as:
The hiker is embarking on a day hike (i.e. short hike), the recommended weight (x) is calculated as:
The hiker's backpack weighs 7.5 lb.
So, the additional weight the hiker can add is represented as:
Subtract 7.5 from both sides
Hence, the hiker can add additional 19.5 pounds
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Anyone help this is 1 grade homework
Answer:
(What's a number story?) Sam had 10 coins. Then, he gave 3 to his sister. How much money does he have left?
Addition fact: I think it's that you have to take the amount of money he has left (Which is 7), and add it to 3 to make 10.
Hope this helps!
For i = √-1, (1 + 2i)² = ?
The value of given expression is F(x) = (-3 +4√-1)
What is the expression?An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
Given i = √-1
F(x) = ( 1 + 2i)²
F(x) = ( 1 + 4i² + 4i)
F(x) = ( 1 - 4 + 4√-1)
F(x) = ( -3 + 4√-1)
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Can someone help me with this, please? I really need help!
Strontium-90 (Sr-90) has a half-life of approximately 29 years. Let the initial amount of Sr-90 in a sample be 100g. If the decay function s(y)=100*0.5^y/29 expresses the amount of Sr-90 that remains in the sample after y years, in how many years will 1g of Sr-90 be left? Round up your answer to the nearest number of years
Answer: Approximately 193 years
=======================================================
Work Shown:
y = number of years
s(y) = amount of Strontium-90 (Sr-90) in grams
We plug in s(y) = 1 and solve for y to determine how long it takes for the initial 100 gram sample to decay to 1 gram.
s(y)=100*0.5^(y/29)
1=100*0.5^(y/29)
1/100 = 0.5^(y/29)
0.01 = 0.5^(y/29)
Log[ 0.01 ] = Log[ 0.5^(y/29) ] .... see note1 below
Log[ 0.01 ] = (y/29)*Log[ 0.5 ] .... see note2
(y/29)*Log[ 0.5 ] = Log[ 0.01 ]
y/29 = Log[ 0.01 ]/Log[ 0.5 ]
y = 29*Log[ 0.01 ]/Log[ 0.5 ]
y = 192.671829503468
y = 193
Footnotes
note1: if the variable is in the trees, aka exponent, then log it down. In other words, we use logs to isolate the exponent.note2: use the log rule that Log(A^B) = B*Log(A) which is the actual act of pulling down the exponent and it helps us isolate it.Which of the following correctly shows clustering for the problem 24 x 14?
24 x 12 + 24 x 2
24 x 10 + 24 x 4
24 x 10 + 24 x 14
20 x 10 + 4 x 4
HELP PLEASEE ASAP HELP HELP!!
Which equations represent exponential growth?
Which equations represent exponential decay?
Place each equation with its correct group (decay or growth)
Exponential Growth Exponential Decay
V = 18,000(0.78)^t
P = 4500(1.04)^t
A = 7000(1.0575)^t
P = 50(1/2)^t
P = 45(2)^t
A = 9000(0.9)^t
The equation are
1. V = 18,000(0.78)^t is exponential decay.
2. P = 4500(1.04)^t is exponential growth.
3.A = 7000(1.0575)^t is exponential growth.
4.P = 50(1/2)^t is exponential decay.
5.P = 45(2)^t is exponential growth.
6.A = 9000(0.9)^t is exponential decay.
Given that,
We have to find which equation is exponential growth and exponential decay.
Knowing that an exponential function takes the form where a represents the function's y=a.bˣ initial value a and b represents its exponential growth or exponential decay, B should be more than 1 for exponential growth and less than 1 for exponential decay.
b>1= exponential growth.
b<1= exponential decay.
Let's now examine each equation in turn to see which one represents exponential growth and which exponential decay.
1. [tex]V=18000(0.78)^{t}[/tex]
The initial values a and b in this option are 18000 and 0.78 respectively. Since 0.78 is smaller than 1, this equation describes exponential decay.
2.[tex]P=44500(1.04)^{t}[/tex]
Since 1.04 is obviously more than 1, and we can see that a = 4,500 and b equals 1, we may conclude that this equation represents exponential growth.
3.[tex]A=7000(1.0575)^{t}[/tex]
Since 1.0575 is clearly more than 1 and since a equals 7000 and b equals 1.0575, this equation clearly represents exponential growth.
4.[tex]P=50(1/2)^{t}[/tex]
Given that a = 50 and b equals 1, and that 0.5 is unmistakably less than 1, it is evident that this equation describes exponential decay.
5. [tex]P=45(2)^{t}[/tex]
Since a and b are equal to 45 and 2, respectively, and 2 is obviously greater than 1, this equation represents exponential growth.
6.[tex]A=9000(0.9)^{t}[/tex]
Since 0.9 is obviously less than 1 and that an equals 9000 and b equals 0.9, this equation represents exponential decay.
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HELPME PLEASE
Find the slope if exist of the line containing the pair of points
(7,0) and (0,-1)
The slope m=
Answer:
m = 1/7
Step-by-step explanation:
Given:
(x1 = 7, y1 = 0) and (x2 = 0, y2= -1)
We know:
slope m = vertical change in y / horizontal change in x
m= (y2-y1)/(x2-x1)
Calculate slope:
m= (y2-y1)/(x2-x1) = (-1-0)/(0-7) = -1/ -7 = 1/7
NEED HELP!!! TIMED!!!
An exponential function and a quadratic function are graphed below. Which of the following is true of the growth rate of the functions over the interval 0 <= x <= 1?
The exponential grows at half the rate of the quadratic.
The exponential grows at the same rate as the quadratic.
The exponential grows at twice the rate of the quadratic.
The exponential grows at four times the rate of the quadratic.
The statement which is true of the growth rate of the functions over the interval 0 ≤ x ≤ 1 is that: B. The exponential grows at the same rate as the quadratic.
What is the rate of change?The rate of change can be defined as a type of function that describes the average rate at which a quantity increases or decreases with respect to another quantity.
Mathematically, the rate of change can be calculated by using this formula;
[tex]Rate = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Rate = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
From the given interval and graph (see attachment), the data point for the exponential function would be as follows:
Point (x₁, x₂) = (0, 1)Point (y₁, y₂) = (1, 2)Next, we would calculate the rate of change of the exponential function over the given interval:
Rate of change = (2 - 1)/(1 - 0)
Rate of change = 1/1
Rate of change = 1.
From the given interval and graph (see attachment), the data point for the quadratic function would be as follows:
Point (x₁, x₂) = (0, 1)Point (y₁, y₂) = (0, 1)Next, we would calculate the rate of change of the quadratic function over the given interval:
Rate of change = (1 - 0)/(1 - 0)
Rate of change = 1/1
Rate of change = 1.
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the delivery times for a distributing site are normally distributed with an unknown population mean and standard deviation. if a random sample of 25 deliveries is taken to estimate the mean delivery time, what t-score should be used to find a 98% confidence interval estimate for the population mean?
The t-statistic is the t-value at the intersection of the row for DF = 25 and the 0.025 (one-tail) column is 2.06
How to calculate confidence interval for population mean for small sample?If the sample size is given to be n < 30, then for finding the confidence interval for mean of population from this small sample, we use t-statistic.
The number of degrees of freedom will be n - k
The confidence level in the confidence interval
The parameters given in the question is;
The number of pizza orders in the sample is n
The sample size = 26
The number of samples used in the estimate, k = 1 group of 26 randomly sampled.
The level of confidence that the interval contains the population mean = 95%
Therefore, the significance level;
α = 1 - 95% = 1 - 95/100
= 0.05
Here α-level for the upper and lower limit of the interval are;
α/2 = 0.05/2 = 0.025 long
The degrees of freedom, DF = n - k
DF = 26 - 1 = 25
The t-statistic is the t-value at the intersection of the row for DF = 25 and the 0.025 (one-tail) column (0.025 two-tail column);
[tex]t_{\alpha/2, DF} = 2.06[/tex]
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please help me with this!!!!
Answer:
x int = (5,0)
y int = (0,-2)
Step-by-step explanation:
To solve for x int set y as zero
4x - 10(0) = 20
4x - 0 = 20
4x = 20 divide by 4 to get x alone
x = 5
To solve for y set x as zero
4(0) - 10y = 20
0 - 10y = 20
- 10y = 20 divide by -10 to get y alone
y = -2
Is this right? I really need to know
Yes, this is right. theta is angle C.
What are angles?In Euclidean geometry, an angle is made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles can be formed by two rays in the plane where they are placed. Additionally, when two planes overlap, angles are created. Dihedral angles are what they are called. When two straight lines or rays intersect at a single point, an angle is created. The vertex of an angle is the location where two points converge.
Here, angle is formed at C, A and B, but here B is 90 and the angle sign is given at C.
So, theta is angle C.
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Conrad has 6 more marbles than Rory has. Let r represent the number of marbles that Rory has. Select the expression that represents the number of marbles that Conrad has.
Answer:
Conrad = r + 6
Step-by-step explanation:
Mr.peters has 80 sheets of colored paper.Seven of his students need the paper for a project.how many sheets does each student get? How many sheets are leftover?
Answer:
each student gets 1 sheet. There are 73 sheets left.
Step-by-step explanation:
Each student only needs 1 sheet and so you just do 80-7 and you get 73
VAT is set at 15%, how do you calculate the amount of VAT if the price of an article is R345
51.75 is the amount of VAT.
How does the VAT work?
VAT, or value-added tax, is a tax that must be paid on purchases made within the borders of EU member states. The end consumer of the commodity or service is always responsible for paying the tax.In the United States, there is no VAT. However, even though the US doesn't have a VAT, consumers are still required to pay federal excise taxes when buying goods like cigarettes, alcohol, and fuel. Several states and towns also levy sales taxes.= 15% of VAT on Rs 345
= 345 * 15%
= 345 * 15/100
= 51.75
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pleaseeeee answer Separatrix Separation
The separatrix, which marks the transition from one type of motion to another, can typically be determined under straight forward circumstances.
We have to explain the separatrix separation.
When in motion, a pendulum can either swing from side to side or rotate continuously. The separatrix, which marks the transition from one type of motion to another, can typically be determined under straight forward circumstances. But when the pendulum is pushed at a nearly constant rate, the math breaks down.
A pendulum in motion has two possible motions: a continuous circle or a side-to-side swing. The separatrix—the point at which it switches from one kind of motion to another—can be estimated in the majority of straight forward circumstances. However, the mathematics breaks down when the pendulum is pushed at a nearly constant velocity.
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x² + 16x + c = 0
What is the value of “c”
The equation can be solved as below
What is an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definitions of the word equation and its cognates in various languages might vary slightly. For instance, in French, an equation is defined as having one or more variables, but in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations.
The equation can be solved as
x² + 16x + c = 0
or, c = - x² - 16x
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the research and rescue center currently has 9 snow geese. Each goose eats 16 ounces of seeds each day. There are 1,656 ounces of seeds. how many days of food is available for all snow geese before the center runs out?
PLEASE I WILL GIVE BRAINIES
The food is available for all snow geese for 11.5 days before the research and rescue center runs out.
According to the question,
We have the following details:
Number of snow geese in the research and rescue center = 9
Number of ounces of seeds eaten by each goose = 16 ounces
So, number of ounces of seeds eaten by 9 snow geese = (16*9) ounces
Number of ounces of seeds eaten by 9 snow geese = 144 ounces
Now, there are 1,656 ounces of seeds.
So, the number of days before the center runs out of the food = Total number of ounces of seeds/Number of ounces of seeds eaten by 9 snow geese
Number of days before the center runs out of the food = 1656/144
Number of days before the center runs out of the food = 11.5 days
Hence, the number of days for which food is available for all snow geese before the center runs out is 11.5 days.
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Answer:
The food is available for all snow geese for 11.5 days before the research and rescue center runs out.
Step-by-step explanation:
a loading dock is 5 feet high. if a ramp makes an angle of 25 d with the ground and is attached to the loading dock, how long is the ramp?
The length of the ramp is 10.7 feet high.
What is ratio of triangle ?
The definition of the tangent (tan) of the angle is the ratio of the opposing to the neighbouring in any right triangle. The tangent's value for the red triangle is given by: tan(c) = 1 / 2 =.5. We maintain the same angle c for the blue triangle, but we have doubled the sizes of the adjacent and opposite sides.
It always helps to draw a diagram and find the right triangle.
In this case, the triangle has the loading dock as one leg, the ramp as the hypotenuse, and the distance of the ramp from the loading dock as the other leg.
Call that distance x. Use the tangent of 25° to find x.
=> tan(25°) = [tex]\frac{opposite }{adjacent}[/tex]
=> tan(25°) = [tex]\frac{5}{x}[/tex]
=> x = 5/ tan(25°)≈ 10.7 feet.
Hence the length of ramp is 10.7 ft.
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Which would be the result if we divide the sum of 275 and 325 by 25?
A.
25
B.
24
C.
20
D.
30
E.
40
Answer: B. 24
Step-by-step explanation:
275+325= 600
600/25 = 24
Hence, 24 is the outcome
B. 24 is your answer
Write equation trough (-2,-4) and parallel line 2x+4y=8
Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.
Detailed explanation:The slope of parallel lines is the same. By converting the line 2x -4y = 8 to slope intercept form, first determine its slope.
4y = 8-2x y = 1/2x - 4 2x + 4y = 8
Here, the slope is 1/4
Fill in the point slope form with (-2, -4) and m = 1/4 After that, simplify to obtain the standard form and slope intercept form.
The slope intercept form is y = 1/4x + 6, while the point slope form is y - (-4) = 1/4(x+4).
Now, by rearranging the terms into the formula Ax + By = C, the standard form may be discovered.
6 becomes -1/4x + y = 6 when y= 1/4x + 6. Since fractions for A or B cannot be expressed in standard form, the equation is multiplied by 4 to get x + 4 y = 24.
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Select the equation of the line that goes through the point (6,-10) and is
parallel to the equation below.
6x + 2y = 12
Answer:
3x+y = 8
yes, its parallel
Step-by-step explanation:
Choices:
a. 3x+y=18
b. 3x+y=-8
c. 3x+y=8
d. 3x+y=-10
1. if we plug in (6, -10) to 3x+y=8 we get:
3(6) + (-10) = 8
18 - 10 = 8
8 = 8, this is true
2. if we simplify 6x+2y=12 we get:
2y = -6x + 12
y = -3x + 6
if we simplify 3x+y = 8 we get
y = -3x + 8
the slopes of the equations are the same, therefore they are parallel.
how did you get the answer for 1.13-0.46
help me....
Answer: 0.67 Just subtract
Step-by-step explanation:
I'm confused about what you are asking But ill assume you want to subtract?
1.13 minus 0.46 is 0.67
Answer:
0.67
Step-by-step explanation:
just get the answer taking out
a/ Find a polynomial U with integer coefficientsthat satisfies the given conditions: degree 5, theleading coefficient 63, and zeros are 1/3, whichhas multiplicity 2, -4, and i
Since the zeroes are 1/3 which has multiplicity 2, -4 and i, then
The factors of the polynomial are
[tex]x=\frac{1}{3}\rightarrow3x=1\rightarrow(3x-1)\rightarrow(3x-1)^2[/tex][tex]x=-4\rightarrow(x+4)[/tex][tex]x=i\rightarrow(x-i)(x+i)\rightarrow x^2-i^2\rightarrow(x^2+1)[/tex]Multiply the 3 factors
[tex]\begin{gathered} (3x-1)^2=(9x^2-6x+1) \\ U=(9x^2-6x+1)(x+4)(x^2+1) \end{gathered}[/tex]Multiply The first 2 brackets
[tex]U=(9x^3+36x^2-6x^2-24x+x+4)(x^2+1)[/tex]Add the like terms in the 1st bracket
[tex]U=(9x^3+30x^2-23x+4)(x^2+1)[/tex]Multiply the 2 brackets
[tex]U=9x^5+30x^4-23x^3+4x^2+9x^3+30x^2-23x+4[/tex]Add the like terms
[tex]U=9x^5+30x^4-14x^3+34x^2-23x+4[/tex]Since the leading coefficient is 63, multiply all terms by 7
[tex]U=63x^5+210x^4-98x^3+238x^2-161x+28[/tex]4(x−3)−7x≥6 Responses
Answer:
x ≤ -6
Step-by-step explanation:
4(x-3) -7x ≥ 6 Distribute the 4
4x - 12 -7x ≥ 6 Combine like terms
-3x - 12 ≥ 6 Add 12 to both sides
-3x ≥ 18 Divide both sides by -3 Remember to flip the inequality sign
x ≤ -6
Under her cell phone plan, Nora pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill at $42 per month. Write and solve an equation which can be used to determine g, the number of gigabytes of data Nora can use while staying within her budget.
Answer:
Step-by-step explanation:
the answer is 1.3 gigabytes
Answer:the equation which can be used to determine the number of gigabytes is 35.5 + 5x = 42 and the solution is x = 1.3
Step-by-step explanation:
Solving Inequalities with One Variable
Show work
4+1+2≥5
Answer: The statement is true
4+1+2≥5
4+1+2 can be simplified to 7
7≥5, 7 is indeed greater than 5
write an equation for the line, in point slope form that passes through the following points
(3,4)
(6,10)
The linear equation in the slope-point form is:
(y - 4) = 2*(x - 3)
How to get the equation for the line?
For a line with a slope M that passes through a point (a, b), the point-slope form is:
(y - b) = M*(x - a)
And if the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
M = (y₂ - y₁)/(x₂ - x₁)
In this case the line passes through (3,4) and (6,10) is:
M = (10 - 4)/(6 - 3) = 6/3 = 2
And using the point (3, 4), we can write:
(y - 4) = 2*(x - 3)
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can someone explain how to solve this?
The cost of a family membership at a local gym is $20 for a parking permit plus $15 for each member of the family. express this cost as a function of the number of people in a family, x, using one car.
(A) f(x) = 20x + 15
(B) f(x) = 35x
(C) f(x) = 15x + 20
(D) f(x) = 20x + 1
(E) f(x) = 15x + 1
PLEASE ANSWER ASAP! I WILL GIVE YOU BRAINLIEST IF CORRECT!
Answer:
its C cause when it said permit plus $15 for each member in the family they mention by C
please help!! I really need help please help
Answer:
Step-by-step explanation:
Second answer: Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.
Third answer: The transitive property of equality formula is given as follows: If x = y and y = z, then x = z. Where x, y and z belongs to the same category elements. For example, if “x” represents the measurement of a line segment, then y and z should represent the measurement of the line segment.
Fourth answer: Congruent segments are segments that have the same length. ≅ Points that lie on the same line are called collinear.
