ANSWER
B' has coordinates (16,14).
EXPLANATION
The given coordinates of square ABCD are :
A (2,7) , C (8,1),D (2,1)
In order to form a square, the coordinates of B should be: (8,7)
The mapping for dilation with a scale factor 2, about the origin is
[tex](x,y)\to (2x,2y)[/tex]
This implies that:
[tex]B(8,7)\to B'(2 \times 8,2 \times 7)[/tex]
When we simplify we get:
[tex]B(8,7)\to B'(16,14)[/tex]
Hence B' has coordinates (16,14).
Suzi starts her hike at 230 feet below sea level. When she reaches the end of the hike, she is still below sea level at ?138 feet. What was the change in elevation from the beginning of Suzi's hike to the end of the hike?
Answer:
92 feet.
Step-by-step explanation:
1. Suzi started at 230 feet
2. Suiz ended at 138 feet
3. Subtract the starting and end numbers 4. 23 - 138= 92
Answer:
whats the answer
Suppose f⃗ (x,y)=xyi⃗ +(x−y)j⃗ and c is the triangle from (4,0) to (−4,0) to (0,4) to (4,0). (a) find the line integral of f⃗ along each segment of the triangle
Parameterize each leg by
[tex]\vec r_1(t)=(1-t)(4\,\vec\imath)+t(-4\,\vec\imath)=(4-8t)\,\vec\imath[/tex]
[tex]\vec r_2(t)=(1-t)(-4\,\vec\imath)+t(4\,\vec\jmath)=(-4+4t)\,\vec\imath+4t\,\vec\jmath[/tex]
[tex]\vec r_3(t)=(1-t)(4\,\vec\jmath)+t(4\,\vec\imath)=4t\,\vec\imath+(4-4t)\,\vec\jmath[/tex]
each with [tex]0\le t\le1[/tex].
The line integrals along each leg (in the same order as above) are
[tex]\displaystyle\int_0^1((4-8t)\,\vec\jmath)\cdot(-8\,\vec\imath)\,\mathrm dt=0[/tex]
[tex]\displaystyle\int_0^1(16t(t-1)\,\vec\imath-4\,\vec\jmath)\cdot(4\,\vec\imath+4\,\vec\jmath)\,\mathrm dt=\int_0^1(64t(t-1)-16)\,\mathrm dt=-\frac{80}3[/tex]
[tex]\displaystyle\int_0^1(16t(1-t)\,\vec\imath+(8t-4)\,\vec\jmath)\cdot(4\,\vec\imath-4\,\vec\jmath)\,\mathrm dt=\int_0^1(64t(1-t)-4(8t-4))\,\mathrm dt=\frac{32}3[/tex]
###
The total line integral then has a value of -16. We can confirm this by checking with Green's theorem. Notice that [tex]C[/tex] as given as clockwise orientation, while Green's theorem assumes counterclockwise. So we must multiply by -1:
[tex]\displaystyle\int_{-C}\vec f\cdot\mathrm d\vec r=-\iint_D\left(\frac{\partial(x-y)}{\partial x}-\frac{\partial(xy)}{\partial y}\right)\,\mathrm dA=-\int_0^4\int_{y-4}^{4-y}(1-x)\,\mathrm dx\,\mathrm dy=-16[/tex]
as required.
To calculate a line integral over a curve in a vector field, parametrize each segment of the curve, substitute these parametrizations into the integral and evaluate the resulting integral over the range of the parameters. Without knowing the paths between the points in question, a specific solution can't be given. However, basic calculus techniques would be used to evaluate these integrals.
Explanation:The objective here is to find the line integral of the given vector field f⃗=xyi⃗ + (x−y)j⃗ along each segment of the triangle defined by the points (4,0), (-4,0) and (0,4). The vector field involves two variables, x and y. A line integral is a type of integral where a function is integrated along a curve. In this vector field, the function is defined in two variables x and y. Our first step in calculating the line integral is to parametrize each path between these points. Then, we substitute these parametrizations into the integral, which is then evaluated with respect to the parameter. Let's evaluate the line integral over the three segments of the triangle.
Unfortunately, without further information on the specific functional forms of the paths between these points, a concrete solution can't be provided. However, usually, this process involves applying the formula for a line integral over a vector field and using fundamental calculus techniques to simplify and evaluate these integrals. If the paths between points were straight lines, for example, the path parametrizations would be simple linear functions.
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Cindy is designing a rectangular fountain in the middle of a courtyard the rest of the courtyard will be covered in stone. The part of the courtyard that will be covered in stone has an area of 246 square feet. What is the width of the fountain
Answer:
Step-by-step explanation:the answer is 3 ft
The width of the fountain is 9 feet.
The area of the fountain is 0, it means the width of the fountain doesn't affect the total area of the courtyard. Therefore, the width of the fountain can be any value, including 9 feet.
To find the width of the fountain, we first need to determine the area of the entire courtyard, including the fountain and the stone-covered area. Since the courtyard is rectangular, we can assume the width of the fountain is the same as the width of the courtyard.
Let's denote the width of the fountain as \( w \) feet and the length of the courtyard as \( l \) feet.
Given that the area covered by stone is 246 square feet, we can write the equation:
[tex]\[ w \times l - 246 = \text{area of the fountain} \][/tex]
Since the entire courtyard area is the sum of the area covered by stone and the area of the fountain, we have:
[tex]\[ w \times l = 246 + \text{area of the fountain} \][/tex]
We know the total area of the courtyard, but we still need to find the length [tex](\( l \))[/tex] of the courtyard to solve for the width of the fountain.
To find the length, we can use the fact that the entire courtyard area is the product of its length and width:
[tex]\[ l \times w = \text{total area of the courtyard} \][/tex]
Since the total area of the courtyard is given as 246 square feet, we have:
[tex]\[ l \times w = 246 \][/tex]
Now, we have two equations:
[tex]\[ w \times l = 246 + \text{area of the fountain} \][/tex]
[tex]\[ l \times w = 246 \][/tex]
Substituting [tex]\( l \times w = 246 \)[/tex] into the first equation, we get:
[tex]\[ 246 = 246 + \text{area of the fountain} \][/tex]
[tex]\[ \text{area of the fountain} = 246 - 246 = 0 \][/tex]
Since the area of the fountain is 0, it means the width of the fountain doesn't affect the total area of the courtyard. Therefore, the width of the fountain can be any value, including 9 feet.
Complete question:
Cindy is designing a rectangular fountain in the middle of a courtyard the rest of the courtyard will be covered in stone. The part of the courtyard that will be covered in stone has an area of 246 square feet. What is the width of the fountain
Given that U is the centroid of triangle OPQ find PS.
Answer:
PS=5.4
Step-by-step explanation:
The centroid divides each median in the ratio 2:1
If U is the centroid, then
[tex]3.6:x+0.8=2:1[/tex]
We use ratio to obtain;
[tex]\frac{3.6}{x+0.8}=\frac{2}{1}[/tex]
Cross multiply;
[tex]3.6=2(x+0.8)[/tex]
Expand;
[tex]3.6=2x+1.6[/tex]
Group similar terms;
[tex]3.6-1.6=2x[/tex]
[tex]2=2x[/tex]
x=1
PS=PU+US
PS=3.6+1+0.8
PS=3.6+1+0.8
PS=5.4
The equation of a parabola is (y−1)2=16(x+3) .
What is the equation of the directrix of the parabola?
Enter your answer in the box.
Answer:
x = -7
Step-by-step explanation:
Since the equation for a directrix of a parabola that opens horizontally is x = h-p, we can plug it in. So h = -3 and p = 4. So x = -3-4 or x = -7.
Answer:
x=-7
Step-by-step explanation:
Find the value for 4x if x = 5
Answer:
20
Step-by-step explanation:
4 multiplied by 5 is equal to 20. You substitute 5 for x.
Answer:
20
Step-by-step explanation:
You are to multiply 5 by 4: the outcome is 20. That's all.
Please help me ..........
Answer:
242.4 ft
Step-by-step explanation:
The angle immediately adjacent to the 29° angle is (90° - 29°) , or 61°.
The cosine function relates this 61° angle to the 500 ft hypotenuse and the unknown adjacent side y:
y
cos 61° = -----------
500 ft
so that y = (500 ft)(cos 61°) = (500 ft)(cos 61°) = (500 ft)(0.485) = 242.4 ft
Please help me ...............
Answer:
b= 7 times the square root of 2
Step-by-step explanation: In a 45-45-90 degree triangle the base and the height both equal x and the hypotenuse is equal to x times the square root of 2.
Hope this helps
Answer:
a = 7
b = 7√2
Step-by-step explanation:
45 45 90 right triangle and it's also isosceles right triangle
a = 7
Ratio of leg : hypotenuse = x : x√2
leg a = 7
hypotenuse b = 7√2
please help it would be much appreciated!
Answer:
Part a) Option d
Part b) Option a
Step-by-step explanation:
Part a
if we look at the options given and the data available
Option a) x^4+9
Putting x= 2 we get (2^4) + 9 =25
Putting x= 3 we get (3^4) + 9 =90 but f(x) =125 so not correct option
Option b) (4^x)+9
Putting x= 2 we get (4^2) + 9 =25
Putting x= 3 we get (4^3) + 9 =73 but f(x) =125 so not correct option
Option c) x^5
Putting x= 2 we get (2^5) =32 but f(x) =25 so not correct option
Option d) 5^x
Putting x= 2 we get (5^2) =25
Putting x= 3 we get (5^3) =125
Putting x= 4 we get (5^4) =625
So Option d is correct.
Part (b)
3(2)^3x
can be solved as:
=3(2^3)^x
=3(8)^x
So, correct option is a
Para medir la altura de una torre, juan se situa en un punto del suelo horizontal y observa el punto mas alto de la torre bajo un angulo de 62°. Se acerca 6 metros a la torre en linea recta y el angulo es de 79° haya la altura de la torre
Answer:
The height of the tower is 17.79 m
Step-by-step explanation:
The question in English is
To measure the height of a tower, Juan stands at a point on the horizontal ground and observes the highest point of the tower under an angle of 62°. He approaches the tower 6 meters in a straight line and the angle is 79° Find the height of the tower
see the attached figure to better understand the problem
In the right triangle ABC
tan(62°)=h/x
h=(x)tan(62°) ------> equation A
In the right triangle DBC
tan(79°)=h/(x-6)
h=(x-6)tan(79°) ------> equation B
Equate equation A and equation B and solve for x
(x)tan(62°)=(x-6)tan(79°)
(x)tan(62°)-(x)tan(79°)=-(6)tan(79°)
x=-(6)tan(79°)/[tan(62°)-tan(79°)]
x=9.46 m
Find the value of h
h=(9.46)tan(62°)=17.79 m
Answer:
son las dos en punto
Step-by-step explanation:
What is the correlation coefficient r for the data set?
Enter your answer to the nearest hundredth in the box.
X Y
0 8
1 7.5
2 6
2 5.5
3 5.5
3 4
4 3
5 3
6 2.5
Answer:
-0.95
Step-by-step explanation:
The value of R is -0.9538.
What is correlation coefficient?A correlation coefficient is a metric that expresses a correlation, or a statistical link between two variables, in numerical terms. Two columns of a specific data set of observations, sometimes referred to as a sample, or two parts of a multivariate random variable with a known distribution may serve as the variables.
Given
X Values
∑ = 26
Mean = 2.889
∑(X - Mx)² = S[tex]S_{x}[/tex] = 28.889
Y Values
∑ = 45
Mean = 5
∑(Y - My)²= S[tex]S_{y}[/tex] = 32
X and Y Combined
N = 9
∑(X - Mx)(Y - My) = -29
R Calculation
r = ∑((X - My)(Y - Mx)) / √((S[tex]S_{x}[/tex])(S[tex]S_{y}[/tex]))
r = -29 / √((28.889)(32)) = -0.9538
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11.
♡
What is the standard form of the equation of a circle with center (3,-2) and radius 4?
AO (X - 3)2 + (y + 2)2 = 16
BO (x – 3)2 + (y + 2)2 = 4
C. (x + 3)2 + (y – 2)2 = 16
D. (x – 3)2 + ( – 2)2 = 16
Answer:
(x-3)^2+(y+2)^2=16
Step-by-step explanation:
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where h and k are the coordinates of the center and r is the radius, which is squared. From our information, h is 3--> (x-3) and k is -2--> (y-(-2))--> (y+2) and 4 squared is 16. Your choice is A.
Answer:
(x-3)^2+(y+2)^2=16
Step-by-step explanation:
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where h and k are the coordinates of the center and r is the radius, which is squared. From our information, h is 3--> (x-3) and k is -2--> (y-(-2))--> (y+2) and 4 squared is 16. Your choice is A.
The sum of the polynomials 6x3 + 8x2 – 2x + 4 and 10x3 + x2 + 11x + 9 is . Adding 3x – 2 to this sum gives a sum of .
Answer:
The sum of polynomials [tex](6x^{3} +8x^{2} +2x+4)[/tex] and [tex](10x^{3} +x^{2} +11x+9)[/tex] is [tex]16x^{3} +9x^{2} +13x+13[/tex].
Adding [tex](3x-2)[/tex] to the sum above gives a sum of [tex]6x^{3} +9x^{2} +16x+11[/tex]
Step-by-step explanation:
To add two polynomials, the coefficients of the terms of the same degree must be added together. The result of adding two terms of the same degree is another term of the same degree. If any term is missing from any of the grades, it can be completed with 0.
[tex](6x^{3} +8x^{2} +2x+4)+(10x^{3} +x^{2} +11x+9)= 16x^{3} +9x^{2} +13x+13[/tex]
If we adding [tex](3x-2)[/tex] to the sum above, we get:
[tex](16x^{3} +9x^{2} +13x+13)+(0x^{3} +0x^{2} +3x-2)= 16x^{3} +9x^{2} +16x+11[/tex]
What is the most appropriate unit you would use to measure the weight of a house?
Answer:
tons
Step-by-step explanation:
Velma must make five bottles of lemonade for the kids playing outside. Each bottle requires 3?4 cup of sugar. How much sugar does she need?
5×3/4=3.75
she needs 3.75 cups of sugar
While on vacation, a student visits the area around a volcano that has recently erupted. the student can expect to find samples of -?
Answer:
Volcanic Ash
Step-by-step explanation:
choose the single logarithm expression that is equivalent to the one shown 1 / 3 log 3x + 2 / 3 log 3x
To choose the single logarithm expression that is equivalent to the given expression, we need to combine the two logarithms into one logarithm using the properties of logarithms. The single logarithm expression that is equivalent to the given expression is log (3x).
Explanation:To choose the single logarithm expression that is equivalent to the given expression, we need to combine the two logarithms into one logarithm using the properties of logarithms.
Using the property that the logarithm of a product is the sum of the logarithms, we can rewrite the given expression as:
1/3 log (3x) + 2/3 log (3x) = log((3x)^(1/3) * (3x)^(2/3))
Simplifying the expression inside the logarithm gives:
log((3x)^(1/3 + 2/3)) = log((3x)^1) = log (3x)
Therefore, the single logarithm expression that is equivalent to the given expression is log (3x).
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Thirteen poker chips are numbered consecutively 1 through 10, with three of them labeled with a 5 and placed in a jar. A chip is drawn at random. Find the probability of drawing a 5.
Answer:
3/13
Step-by-step explanation:
There are 3 5's in the jar and thirteen chips total. You have a probability of pulling 1 of the three 5's out so there is a 3/13 chance of pulling a 5.
Answer:
sample space is 13
3/13
Step-by-step explanation:
A quadrilateral has two right angles. The measure of the third angle is 99°. What is the measure of the fourth angle?
Answer:
The measure of the fourth angle is 81°
Step-by-step explanation:
we know that
The sum of the internal angles of a quadrilateral must be equal to 360 degrees
Let
x----> the measure of the fourth angle
we have
90°+90°+99°+x=360°
Solve for x
279°+x=360°
x=360°-279°=81°
Please help me out!!!!
Answer:
3√10
Step-by-step explanation:
27² + y² = x²
⇒⇒⇒ y² = x² - 27² ----------------- [ 1 ]
3² + y² = z²
⇒⇒⇒ y² = z² - 3² ----------------- [ 2 ]
Equate [ 1 ] and [ 2 ] :
x² - 27² = z² - 3²
x² - z² = 27² - 3²
x² - z² = 720 ----------------- [ 3 ]
x² + z² = 30²
x² + z² = 900 ----------------- [ 4 ]
[ 3 ] - [ 4 ] :
-2z² = -180
z² = 90
z = √90
z = 3√10
Use the given graph to determine the limit, if it exists. Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..
By the confront theorem we know that the limit only exists if both lateral limits are equal
In this case they aren't so we don't have limit for x approaching 2, but we can find their laterals.
Approaching 2 by the left we have it on the 5 line so this limit is 5
Approaching 2 by the right we have it on the -3 line so this limit is -3
Think: it's approaching x = 2 BUT IT'S NOT 2, and we only have a different value for x = 2 which is 1, but when it's approach by the left we have the values in the 5 line and by the right in the -3 line.
ANSWER
The limit does not exist.
EXPLANATION
From the graph the left hand limit is the value the graph is approaching as x-values approaches 2.
[tex] \lim_{x \to {2}^{ - } }(f(x)) = 5[/tex]
Also the right hand limit is the value that the graph approaches, as x-values approach 2 from the right.
[tex]\lim_{x \to {2}^{ + } }(f(x)) = - 3[/tex]
Since the left hand limit is not equal to the right hand limit, the limit as x approaches 2 does not exist
Using the Distributive Property to factorize the equation 3x2 + 24x = 0, you get . The solution of the equation is .
Answer:
0, -8
Step-by-step explanation:
3x² + 24x = 0
Taking out common factor 3x.
3x(x + 8) = 0
Apply zero product property.
3x = 0 or x + 8 = 0
Evaluate.
x = 0 or x = -8
Answer:
First is 3x (x + 8) =0. The second is x = 0, x = -8.
Step-by-step explanation:
These are the correct answers on Plato, I got it correct.
There are 8 marbles in a bag. Each marble is a different color. The colors are: red, orange, yellow, green, blue, purple, black, and white. Two marbles are randomly drawn from the bag without replacement.
What is the probability that the red marble is drawn first and the white marble is drawn second?
A. 1/64
B. 1/56
C. 1/28
D. 1/4
Answer:
B. 1/56
Explanation:
There are 8 different marbles. In the first draw, you have a one out of 8 chance of getting the red. In the second draw, there are 7 marbles remaining, so a one out of 7 chance of drawing a white marble. To find the total probability of drawing the red and then white marble, we multiply the probabilities if each draw.
(1/8)*(1/7)=1/56
This question is based on the probability. Therefore, the correct option is B, [tex]\dfrac{1}{56}[/tex] is the probability that the red marble is drawn first and the white marble is drawn second.
Given:
There are 8 marbles in a bag. Each marble is a different color. The colors are: red, orange, yellow, green, blue, purple, black, and white. Two marbles are randomly drawn from the bag without replacement.
We need to determined the probability that the red marble is drawn first and the white marble is drawn second.
According to the question,
It is given that, there are 8 different marbles. In the first draw, you have a one out of 8 chance of getting the red is [tex]\dfrac{1}{8}[/tex].
In the second draw, there are 7 marbles remaining, so a one out of 7 chance of drawing a white marble i.e. [tex]\dfrac{1}{7}[/tex].
Now, calculating the total probability of drawing the red and then white marble, we multiply the probabilities if each draw.
⇒ [tex]\dfrac{1}{8} \times \dfrac{1}{7} = \dfrac{1}{56}[/tex]
Therefore, the correct option is B, [tex]\dfrac{1}{56}[/tex] is the probability that the red marble is drawn first and the white marble is drawn second.
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An apple farmer is deciding how to use each day's harvest. She can use the harvest to produce apple cider or apple juice for the apple festival in two weeks. The information she uses to make the decision is listed below.
- 1 bushel of apples will make 20 quarts of apple cider
- 1 bushel of apples will make 15 quarts of apple juice
- The apple farmer collected 18 bushels of apples
- Today the apple farmer needs to produce a total of 330 quarts
The information given can be modeled with a system of equations. Define your x and y variables
x- variable ________
y- variable ________
Write two different equations that can be used to model the situation. (explain what each equation represents)
Equation 1: ___________
Explanation:
Equation 2_____________
Explanation:
Answer:For this item, we let x and y be the number of bushels of apple that will be used to produce apple cider and apple juice, respectively. The situation above is best represented by the following equations,
x + y = 18
20x + 15y = 330
The values of x and y from the equations above are 12 and 6, respectively. Therefore, 12 bushels will be used to make apple cider and 6 bushels will be used to make apple juice.
Step-by-step explanation:
Answer:
For this item, we let x and y be the number of bushels of apple that will be used to produce apple cider and apple juice, respectively. The situation above is best represented by the following equations, x + y = 18 20x + 15y = 330The values of x and y from the equations above are 12 and 6, respectively. Therefore, 12 bushels will be used to make apple cider and 6 bushels will be used to make apple juice.
Step-by-step explanation:
A county in Alabama has a population of 90,000 people. It has an area of 800 mi2. How many people are there per square mile? A) about 72 B) about 88 C) about 113 D) about 720
Answer:
C) about 113
Step-by-step explanation:
"How many people are there per square mile?" means that we want a ratio with miles as denominator. In other words, to find the population density, we just need to divide the population by the land area (miles squared):
[tex]population-density=\frac{people}{land-area}[/tex]
We know that the population of Alabama is 90,000 people and its land area is 800 miles squared, so [tex]people=90000[/tex] and [tex]land-area=800mi^{2}[/tex].
Replacing values:
[tex]population-density=\frac{people}{land-area}[/tex]
[tex]population-density=\frac{90000}{800mi^{2}}[/tex]
[tex]population-density=112.5[/tex]
Which rounds to:
[tex]population-density=113[/tex]
We can conclude that there are approximately 113 people per square mile in Alabama.
Answer:
About 113
Step-by-step explanation:
Hope this help
Help PLZZZ!!!
Select the correct answer from the drop-down menu.
The roots of the quadratic equation_________ are x = 2 ± i.
options
a. x^2-4x-5=0
b. x^2+4x+5=0
c. x^2-4x+5=0
d. x^2+4x-5=0
Answer:
Option C
Step-by-step explanation: I think this is right because when you substitute the 2 for x you get the answer. Hope this helps darling!!
A quadratic equation is in the form of ax²+bx+c. The roots of the quadratic equation x² - 4x + 5 = 0 are x = 2 ± i. Thus, the correct option is C.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
Given the roots of the quadratic equation are x = 2 ± i. Therefore, we can write the roots as,
α = 2+i
β = 2-i
Now, we know that a quadratic equation can also be written in the form,
x² - (α+β)x + αβ = 0
Therefore, we need to find the value of (α+β) and αβ,
α+β = 2 + i + 2 - i
α+β = 4
αβ = (2+i)(2-i)
αβ = 2²-i²
αβ = 4 + 1
αβ = 5
Thus, the quadratic equation is x² - 4x + 5 = 0.
Hence, The roots of the quadratic equation x² - 4x + 5 = 0 are x = 2 ± i. Thus, the correct option is C.
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(Writing Expressions) John charges $20.00 to mow each lawn and $5.00 to cut each bush. He mows x number of lawns and cuts y number of bushes. Which expression shows how much money John will earn? A) (20+5)xy B) 20y + 5x C) 20x + 5y D) (20 + 5) + (x + y)
Answer:
D
Step-by-step explanation:
Let E(x,y) represent the total earnings.
Then E(x,y) = ($20/lawn)x + ($5/bush)y (Answer D)
Lorenz needs to run 13 1/2 miles this week to meet his goal for his training plan. So far this week he has run 3 1/2 miles on Monday and 4 1/4 Tuesday. How many moremiles does he needs to run this week in order to meet his goal
Answer:
The Answer is 5 (3/4) more miles.
Step-by-step explanation:
For this we just need to add and subtract fractions.
We we want to get to 13 (1/2) miles...however we have already ran
3 (1/2) + 4 (1/4) ... this is the same as 3.5 plus 4.25. When we add those up we get...
3.5+4.25 = 7.75 then we subtract ... 13.5 - 7.75 = 5.75 = 5 (3/4) our answer.
Final answer:
Lorenz needs to run 5 3/4 more miles to meet his goal for his training plan this week.
Explanation:
To find out how many more miles Lorenz needs to run this week to meet his goal, we need to add up the miles he has already run and subtract that from his goal. Lorenz has already run 3 1/2 miles on Monday and 4 1/4 miles on Tuesday, so we can add these two amounts to get 3 1/2 + 4 1/4 = 7 3/4 miles. Next, we subtract this amount from his goal of 13 1/2 miles: 13 1/2 - 7 3/4 = 5 3/4 miles. Therefore, Lorenz needs to run 5 3/4 more miles to meet his goal for his training plan this week.
A bee keeper estimates that his bee population will triple each year. Currently he has 150 bees. Write a function to represent the growth of the keepers bee population over time. Use x to represent the number of bees
The function that would represent the growth of the keepers bee population over time would [tex]\( x = 150 \times 3^n \)[/tex]
How to find the function ?
To model the growth of the bee population in the beekeeper's hive, we can use an exponential growth function. The key information here is that the population triples each year. This means the growth factor is 3.
The function would therefore be:
[tex]\( x = 150 \times 3^n \)[/tex]
The equation is an exponential growth model where:
150 is the initial number of bees.
3 is the growth factor (since the population triples each year).
n is the number of years passed.
For example, to find the bee population after 2 years, you would calculate:
[tex]\( 150 \times 3^2 = 150 \times 9 \\= 1350 \) bees[/tex]
A store pays $29.99 for a pair of jeans. The percent of markup is 20%. What is the selling price, including markup, for 5 pairs of jeans?
Answer:
$179.94 for 5 pairs of jeans
Step-by-step explanation: