Answer:
Complete the square on x by adding 49 to both sides.
Complete the square on y by adding 81 to both sides.
Step-by-step explanation:
We have been given an equation [tex](x^2+14x)+(y^2+18y)=5[/tex]. We are asked to complete the squares for both x and y.
We know to complete a square, we add the half the square of coefficient of x or y term.
Upon looking at our given equation, we can see that coefficient of x is 14 and coefficient of y is 18.
[tex](\frac{14}{2})^2=7^2=49[/tex]
[tex](\frac{18}{2})^2=9^2=81[/tex]
Now, we will add 49 to complete the x term square and 81 to complete y term square on both sides of our given equation as:
[tex](x^2+14x+49)+(y^2+18y+81)=5+49+81[/tex]
Applying the perfect square formula [tex]a^2+2ab+b^2=(a+b)^2[/tex], we will get:
[tex](x+7)^2+(y+9)^2=135[/tex]
Therefore, We can complete the square on x by adding 49 to both sides and the square on y by adding 81 to both sides.
Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?
Answer:
You require 10 helpers
Step-by-step explanation:
The problem could be solved in many ways ( like using an optimization software) but I propose you this.
Start with production of large cakes. In the time kitchen is available one helper could make, if only works in large cakes:
(2 large cakes / 1 hour) * (3 hours ) = 6 large cakes
So with 3 helpers using all their 3 hours we would have
3 helpers *6 large cakes /helper = 18 large cakes.
We need 2 more large cakes so we can use one more helper and in his first hour he can produce
(2 large cakes / 1 hour) * (1 hour ) = 2 large cakes
The 4th helper has two hours of work left so he can produce small cakes.
(35 small cakes/hour* 2 hours = 70 small cakes.
With 4 helpers we have the 20 large cakes and 70 small ones. We still have to makes
700 - 70 = 630 small cakes left
In the 3 hour period a helper can make
(35 small cakes / 1 hour) * (3 hours ) = 105 large cakes
So if 1 helper does 105 large cakes we would need to finish production with
630 / 105 = 6 helpers
So in total we have 3 helpers in only large cakes 6 in only small cakes and one helper doing both - total 10 helpers
On three consecutive hands of draw poker a gambler wins $9, loses $20, and then loses another $16. Write an expression using positive and negative numbers to describe this situation and then simplify.
The simplified result is $_____
9 + -20 + -16= 2of course it’s going to be a negative 27 because wen u had a positive u lost 20 and then lost another 16 now u owe 27 which is -27 in your pockets
The simplified result is -$27.
To describe the gambler's situation using positive and negative numbers, we use the following expression:
$9 - $20 - $16
We can simplify this step-by-step:
First, add the positive and negative amounts: $9 - $20 = -$11
Then, subtract the next amount: -$11 - $16 = -$27
Therefore, the simplified result is -$27.
A seed company sells two grades of seed. A 100-pound bag of a mixture of rye and Kentucky bluegrass sells for $235, and a 100-pound bag of bluegrass sells for $341. How many bags of each are sold in a week when the receipts for 17 bags are $4,949?
Answer:
The company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrass
Step-by-step explanation:
This is a classical problem that can be solved using a system of equations:
Let us first define our variables:
[tex]x[/tex] as the number of 100-pound bags which contain a mixture of rye and Kentucky bluegrass and,
[tex]y[/tex] as the number of 100-pound bags of bluegrass.
The problem tells us that in a week a total of 17 bags were sold, therefore, we can say that this number must be equal to the number of bags containing the mixture of rye and Kentucky bluegrass plus the number of bags containing bluegrass. Then, according to our variable names:
[tex]x+y=17[/tex] (1)
The problem also says that the company got a receipt for $4,949 in total. Hence, this number has to be equal to the total number of bags that contain rye and Kentucky bluegrass seeds times its price plus the number of bags containing bluegrass multiplied by its price. Then,
[tex]235x+341y=4949[/tex] (2)
Now we have the system of equations:
[tex]x+y=17[/tex] (1)
[tex]235x+341y=4949[/tex] (2)
Solving for [tex]x[/tex] in equation (1)
[tex]x+y=17\\x=17-y[/tex] (3)
And substituting [tex]x[/tex] in equation (2)
[tex]235x+341y=4949\\235(17-y)+341y =4949\\3995 - 235y +341y=4949\\-235y+341y = 4949-3995\\106y=954\\y=\frac{954}{106}\\ y=9[/tex]
Then, substituting [tex]y=9[/tex] in equation (1):
[tex]x+y=17\\x+9=17\\x=17-9\\x=8[/tex]
Thus, the company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrass.
8 bags of the 100-pound mixture are sold, and 9 bags of the 100-pound bag of bluegrass are sold in a week.
Explanation:Let's assume that:
x = number of bags of the 100-pound mixture of rye and Kentucky bluegrass sold
y = number of bags of the 100-pound bag of bluegrass sold
We can set up a system of equations based on the given information:
x + y = 17 (The total number of bags sold is 17) 235x + 341y = 4949 (The total cost of the receipts is $4949)
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:
Multiply equation (1) by 235 to eliminate x: 235x + 235y = 3955 Subtract equation (2) from the result of step 1: (235x + 235y) - (235x + 341y) = 3955 - 4949
Simplifying the equation in step 2 gives us -106y = -994. Solving for y, we get y = 9.
Substituting the value of y back into equation (1), we get x + 9 = 17. Solving for x, we get x = 8.
Therefore, 8 bags of the 100-pound mixture are sold, and 9 bags of the 100-pound bag of bluegrass are sold in a week.
A street light is at the top of a 25 ft pole. A 4 ft tall girl walks along a straight path away from the pole with a speed of 6 ft/sec. At what rate is the tip of her shadow moving away from the light (ie. away from the top of the pole) when the girl is 45 ft away from the pole?
When the girl is 45 ft away from the pole, the tip of her shadow is moving away from the light at a rate of approximately 4.8 ft/sec.
Given:
Height of the pole (h): 25 ft
Height of the girl (4 ft)
Rate of the girl walking away from the pole (dx/dt = 6 ft/sec)
Distance from the pole to the girl (x = 45 ft, when the girl is 45 ft away from the pole)
Objective:
Find the rate at which the tip of her shadow is moving away from the light (ds/dt) when the girl is 45 ft away from the pole.
Step 1: Set up the Similar Triangles Equation
s/x = h/(x + s)
Step 2: Differentiate both sides with respect to time t:
(1/x) * ds/dt - (s/x^2) * dx/dt = (h/(x + s)^2) * (dx/dt + ds/dt)
Step 3: Substitute Known Values:
Substitute x = 45, dx/dt = 6, and h = 25 into the equation.
(1/45) * ds/dt - (s/45^2) * 6 = (25/(45 + s)^2) * (6 + ds/dt)
Step 4: Solve for ds/dt:
Combine like terms and isolate ds/dt.
(1/45) * ds/dt - (s/45^2) * 6 = (25/(45 + s)^2) * (6 + ds/dt)
Step 5: Substitute x = 45 into the equation:
(1/45) * ds/dt - (4/2025) = (25/(90 + s)^2) * (6 + ds/dt)
Step 6: Solve for ds/dt:
ds/dt ≈ 4.8 ft/sec
This table represents a quadratic function with a vertex at (1,0). What is the
average rate of change for the interval from x = 5 to x = 6
Answer:
9 (option D)
Step-by-step explanation:
Hi Dlynjen! How are you?
Well, as maybe you know a quadratic function is a polynomial of degree 2, that is, the highest exponent in the variable is 2 (formula: y = ax^2 + bx + c). The graph of a quadratic function is a parabola (it has a U-shape).
The vertex of a parabola is the highest or lowest point of the curve (depending on whether the U opens up or down). In this case the parabola opens up because the exercise mentions the vertex is the point (x = 0, y = 1) and then for the other values of “x” (1, 2, 3, etc.) the values of “y” are higher (1, 4, 9, etc.), that's why the vertex is the lowest point in this case.
The exercise asks you to calculate the slope (or average rate of change) of the curve between x = 5 and x = 6, all you know so far is that as the curve opens up it is assumed that the slope will be positive but to calculate the slope must apply the following formula:
M = (y2 - y1) / (x2 -x1)
But we only know x1 = 5, x2 = 6, y1 = 16 (value of the table that corresponds to x1 = 5) and we must first know how much y2 is worth (for x2 = 6). For this we must know what is the quadratic function (formula) that gives rise to our parable.
If we analyze the table, we see that for each value of “x”, the value of “y” is equal to the square of (x-1), that is, if we take x = 3 as an example, the value of Y = (3 -1) ^ 2 = (2) ^ 2 = 4. And so with all the values. Having obtained this formula we can now calculate the value of “y” for x2 = 6:
Y2 = (6-1) ^ 2 = (5) ^ 2 = 25
Finally, we calculate the average exchange rate with the previous formula, knowing x1 = 5, x2 = 6, y1 = 16 and y2 = 25:
m = (y2 - y1) / (x2 -x1)
m = (25-16) / (6-1)
m = (9) / (1)
m = 9
I hope I've been helpful!
Regards!
On a coordinate plane, a circle has a center at (negative 2, 1). Which is the general form of the equation of the circle shown? x2 + y2 + 4x – 2y – 4 = 0 x2 + y2 + 4x – 2y + 2 = 0 x2 + y² – 4x + 2y – 4 = 0 x2 + y² – 4x + 2y + 2 = 0
Final answer:
The correct general form of the equation of a circle with a center at (-2, 1) is x² + y² - 4x + 2y - 4 = 0, as it aligns with the pattern of the standard circle equation upon completion of the square.
Explanation:
The general form of the equation of a circle on a coordinate plane with a center at (-2, 1) can be found using the standard equation of a circle (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Since we do not have the radius given, our primary goal is to expand and arrange the given options to match this standard form and check which one relocates the center to (-2, 1).
The equation that matches this pattern would be x² + y² - 4x + 2y - 4 = 0. Here's why: when you complete the square to revert it back to the standard equation, you'll add 4 to both sides to get (x - (-2))² + (y - 1)² = 4, which indicates a center at (-2, 1) when you compare with the standard equation.
Solve by Substitution
Show Steps
−2x + 3y + 5z = −21
−4z = 20
6x − 3y = 0
−2x + 3y + 5z = −21
−4z = 20
6x − 3y = 0
do -4z=20 first
divide both sides by -4 to get z by itself
-4z/-4=20/-4
z=-5
Use z=-5 into −2x + 3y + 5z = −21
-2x+3y+5(-5)=-21
-2x+3y-25=-21
move -25 to the other side
sign changes from -25 to +25
-2x+3y-25+25=-21+25
-2x+3y=4
6x-3y=0
find x by eliminating y
Add the equations together
-2x+6x+3y+(-3y)=4+0
-2x+6x+3y-3y=4
4x=4
Divide by 4 for both sides
4x/4=4/4
x=1
Use x=1 into 6x − 3y = 0
6(1)-3y=0
6-3y=0
Move 6 to the other side
6-6-3y=0-6
-3y=-6
Divide both sides by -3
-3y/-3=-6/-3
y=2
Answer:
(1, 2, -5)
A gecko is in a room that is 12 feet long, 10 feet wide and 8 feet tall. The gecko is currently on a side wall ($10^{\prime}$ by $8^{\prime}$), one foot from the ceiling and one foot from the back wall ($12^{\prime}$ by $8^{\prime}$). The gecko spots a fly on the opposite side wall, one foot from the floor and one foot from the front wall. What is the length of the shortest path the gecko can take to reach the fly assuming that it does not jump and can only walk across the ceiling and the walls?
The shortest path the gecko can take is 20 feet long, consisting of 8 feet along the ceiling and 12 feet along the opposite side wall.
Explanation:Distances:
Gecko to ceiling edge: 1 foot
Ceiling edge to opposite wall edge: 10 feet (room width)
Opposite wall edge to fly: 1 foot
Path calculation:
Ceiling path: 1 foot (to edge) + 8 feet (along edge) = 9 feet
Side wall path: 1 foot (to edge) + 11 feet (remaining wall) = 12 feet
Shortest path:
Add ceiling and wall paths: 9 feet + 12 feet = 20 feet
Therefore, the shortest path for the gecko is 20 feet long.
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates, and 1 unit of fat. Every package must provide at least 7 units of protein, at least 11 units of carbohydrates, and no more than 10 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.
a. Write a system of inequalities to express the conditions of the problem.
b. Graph the feasible region of the system.
a. Fill in the chart.
Fruit
Nuts
Requirements per package
Protein
nothing unit(s) per ounce
nothing unit(s) per ounce
At least
nothing unit(s)
Carbohydrates
nothing unit(s) per ounce
nothing unit(s) per ounce
At least
nothing unit(s)
Fat
nothing unit(s) per ounce
nothing unit(s) per ounce
No more than
nothing unit(s)
Answer:
See explanation
Step-by-step explanation:
Each ounce of fruit will supply
1 unit of protein, 2 units of carbohydrates, 1 unit of fat.Each ounce of nuts will supply
1 unit of protein, 1 unit of carbohydrates, 1 unit of fat.Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.
Then x ounces of fruit will supply
x units of protein, 2x units of carbohydrates, x units of fatand y ounces of nuts will supply
y units of protein, y units of carbohydrates, y units of fat.Every package must provide
at least 7 units of protein, then x+y≥7,at least 11 units of carbohydrates, then 2x+y≥11,and no more than 10 units of fat, then x+y≤10.A. You get the system of three inequalities
[tex]\left\{\begin{array}{l}x+y\ge 7\\ 2x+y\ge 11\\x+y\le 10\end{array}\right.[/tex]
B. See attached diagram
[tex]\begin{array}{cccc}&\text{Protein}&\text{Carbohydrates}&\text{Fat}\\\text{Fruit}&x&2x&x\\\text{Nuts}&y&y&y\\&\text{at least 7}&\text{at least 11}&\text{no more than 10}\end{array}[/tex]
Three inequalities were formulated: 1x + 1y ≥ 7 for protein, 2x + y ≥ 11 for carbohydrates and x + y ≤ 10 for fat, with x being fruit and y being nuts. These needs to be graphed to find a feasible region that meets all conditions. A table summarizing the needed unit amount per ounce for protein, carbohydrates, and fats for both fruits and nuts was also provided.
Explanation:To solve your question, first, let's express the given conditions as inequalities:
For Protein: The amount of protein per ounce for the fruit is 1 and for the nuts is 1. So we will have 1x + 1y ≥ 7 units of protein. For Carbohydrates: The units of carbohydrates per ounce for fruit is 2 and for nuts is 1. Therefore, the inequality will be 2x + y ≥ 11 units of carbohydrates.For Fat: Each fruit and each nut both contains one unit of fat per ounce. The inequality for total fat units will be x + y ≤ 10 units of fat.Graphing
these inequalities would result in a feasible region that should fulfill all conditions.
The following table summarizes this:
Fruit
Nuts
Requirements per package
Protein1 unit per ounce1 unit per ounceAt least 7 unitsCarbohydrates2 units per ounce1 unit per ounceAt least 11 unitsFat1 unit per ounce1 unit per ounceNo more than 10 units
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Determine the resulting polynomial:
f(x)=10x−5
g(x)=2x2+4x−4
Find: f(x)⋅g(x)
I don’t know how to do this help :(
Help Me ASAP!!!!! PLS
Luca bought his home for $115,000 in 2007. Property values have increased 5% every year since she has owned the home. Which of the following equations can be used to represent the price of the home x years after 2010?
y = 115,000(1.5)x
y = 115,000(0.95)x
y = 115,000(1.05)x
y = 115,000(0.05)x
Answer:
C. y = 115 000(1.05)^x
Step-by-step explanation:
The formula for the amount accrued on an investment earning compound interest is
[tex]A = P(1 + r)^{t}[/tex]
where
P = the amount of money invested (the principal)
r = the interest rate per period expressed as a decimal fraction
t = the number of periods
In this problem,
P = $115 000
r = 5 % = 0.05
By 2010, Luca's house will have increased in value for three years. Its value will be
[tex]A = 115000(1 + 0.05)^{3}\\\text{The correct formula for the value of his home x years after 2010 is}\\ y = 115000(1.05)^{x}[/tex]
Answer:
C: y = 115,000(1.05)x
Step-by-step explanation:
(havn’t actually did any math, but this is just process of elemination.)
{I’m just looking at the end of these, because the start is all the same}
if the number with the (perenthese) is below 1, it is a decreas, and the problem says it’s increasing by 5%. (1.5) Is equal to 50% increase so that means your answer would be (1.05) Because anything times 1 is the larger number, but when u add that 0.5, it’s raising the number up by 5%.
Police plan to enforce speed limits by using radar traps at four different locations within the city limits. The radar traps at each of the locations L1, L2, L3, and L4 will be operated 40%, 30%, 20%, and 30% of the time. If a person who is speeding on her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that she will receive a speeding ticket?
Answer:
The probability that the person gets a speeding ticket is 0.27
Step-by-step explanation:
The probability that the person receives a speeding ticket is the probability that the person passes through any of the speed limits and the radar is operating at that time.
Let [tex]P(L_1)[/tex] is the probability that the person passes through radar [tex]L_{1}[/tex] and it is operating at that time is
[tex]P(L_{1})=P(1)\times P(2)[/tex]
Where
P(1) is the probability of person passes through [tex]L_{1}[/tex]
P(2) is probability that the radar is operating
[tex]P(L_1)=0.2\times 0.4=0.08[/tex]
Similarly the probabilities are calculated for other radars in the similar manner as
[tex]P(L_2)=0.1\times 0.3=0.03[/tex]
[tex]P(L_3)=0.5\times 0.2=0.1[/tex]
[tex]P(L_4)=0.2\times 0.3=0.06[/tex]
Thus the reuired probability of the reuired event is
[tex]P(E)=P(L_1)+P(L_2)+P(L_3)+P(L_4)\\\\P(E)=0.08+0.03+0.1+0.06=0.27[/tex]
Quieres?
jsjsjsjjsjsjsjisiiajajjsjsjs
Answer:
si
Step-by-step explanation:
por el telefono
HELP PLEASE!!! :( ONLY TWO QUESTIONS
1.)The ratio of the angle measures in a quadrilateral is 4: 5 :8 :7 . What is the measure of each angle? ** Must show ALL work and steps for credit!
2.)JKLM~QRST with a scale factor of 4:7 MJ. = 58M. What is the value of TQ ?
Answer:
1) 60°, 75°, 120°, 105°
2) 101.5 m
Step-by-step explanation:
1) The sum of ratio units is 4+5+8+7 = 24, which corresponds to the sum of angles, 360°. Then each ratio unit must stand for 360°/24 = 15°. Multiplying the given ratio units by 15° gives the angle measures:
4×15° = 60°5×15° = 75°8×15° = 120°7×15° = 105°__
2) The similarity statement and the scale factor mean ...
MJ : TQ = 4 : 7
7·MJ = 4·TQ . . . . . . . . . "cross multiply"
TQ = 7/4×MJ = 7/4(58 m) . . . . . divide by 4, substitute the value of MJ
TQ = 101.5 m
Please help justify these steps. First one to solve gets brainliest, hearts, and 5 stars. This question is worth 50 points!!!!!!!!
What is the justification for each step in solving the inequality?
2x+1≤3(x+1/)2
Select from the drop-down menus to correctly justify each step.
Answer:
Step-by-step explanation:
2x+1 ≤ 3(x+1)/2
2x+1 ≤ 3x+3/2
Multiply by 2 on both sides
4x+2 ≤ 3x + 3
Subtract 2 on both sides
4x ≤ 3x + 1
Subtract 3x from both sides
x ≤ 1
I think this is what you were asking?
What is the value of A?
Answer:
a = 14
Step-by-step explanation:
Since QR = QP then the triangle is isosceles and
QS is a perpendicular bisector, thus
RS = SP ← substitute values
3a = a + 28 ( subtract a from both sides )
2a = 28 ( divide both sides by 2 )
a = 14
Solve
An airplane went 20 miles an hour faster than twice the speed of a car that ran x miles an hour
Answer: B
Because you can eliminate the ones that don’t have an inequality symbol so that leaves you with B and D and the 20 should be on the right by itself since that is the constant we are given and it’s not altered in the question
The algebraic expression for the given problem is:
Speed of airplane = 2x + 20
What is Expression?In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, −, ×, ÷, ^) used to represent a quantity or a mathematical relationship between quantities.
" An airplane went 20 miles an hour faster than twice the speed of a car that ran x miles an hour"
The algebraic expression for the given problem is:
Speed of airplane = 2x + 20
Where x is the speed of the car in miles per hour.
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17. How would you find x and solve for it?
The formula for secant lines is the outside x the overall length is equal to the outside times the overall length of the second line.
A) 5*(x+5) = 6*10
SImplify:
5x +25 = 60
Subtract 25 from both sides:
5x = 35
Divide both sides by 5:
x = 35/5
x = 7
B) 3*8 = 4*(x+4)
Simplify:
24 = 4x +16
Subtract 16 from both sides:
4x = 8
Divide both sides by 4:
x = 8/4
X = 2
A function follows the rule y = -75 - 5x. When the function's output is 25, the equation is 25 = -75 - 5x. What is the function input when the output is 25?
Answer:
The function input is -20 when the output is 25
Step-by-step explanation:
we have
[tex]y=-75-5x[/tex]
where
y is the dependent variable or output
x is the independent variable or input
If the output is 25
then
y=25
substitute
[tex]25=-75-5x[/tex]
Solve for the function input is the same that solve for x
Isolate the variable x
Adds 5x both sides
[tex]25+5x=-75-5x+5x[/tex]
[tex]25+5x=-75[/tex]
subtract 25 both sides
[tex]25+5x-25=-75-25[/tex]
[tex]5x=-100[/tex]
Divide by 5 both sides
[tex]x=-20[/tex]
therefore
The function input is -20 when the output is 25
Final answer:
To find the function input when the output is 25, solve the given equation 25 = -75 - 5x to find x = -20.
Explanation:
When the function's output is 25, the equation is 25 = -75 - 5x. To find the function input when the output is 25, solve for x:
25 = -75 - 5x
100 = -5x
x = -20
Therefore, the function input when the output is 25 is -20.
gx+mp=c
Solve for X please
Answer:
x = (c -mp)/g
Step-by-step explanation:
Subtract the term not containing x, then divide by the coefficient of x.
gx +mp = c . . . . . given
gx = c - mp . . . . . subtract mp
x = (c -mp)/g . . . . divide by g
_____
Comment on the process
This process can be described various ways. A usual description is "get the x term by itself on one side of the equal sign, then divide by the x-coefficient."
I like a more general description of the solution to "solve for" problems: undo what is done to the variable, in reverse order.
Here, the variable x is multiplied by g, then added to mp. To undo those operations (in reverse order), first we undo the addition of mp. We accomplish that by subtracting mp, or by adding the opposite of mp, as you wish.
Having done that, we undo the multiplication by g by dividing by g.
(gx)/g = (c -mp)/g
x = (c -mp)/g
The steps we actually perform here are identical to the steps in "get the x-term by itself, ...". However, the process we have described can be applied to any sort of equation, not just a 2-step linear equation.
Latanya leaves her house at 12:30 p.M. And bikes at 12 mi/h to Marta's house. She stays at Marta's house for 90 minute. Both girls walk back to latanya's house at 2.5 mi/h. They arrive at latanya's house at 3:30 p.M. How far is Marta's house from latanya's house?
Answer:
Marta's house is 3.10 miles from Latanya's house
Step-by-step explanation:
Marta's house is at 3.1 miles fron Latanya's house.
How far is Marta's house from latanya's house?From 12:30pM to 3:30pM there are a total of 3 hours, remember that.
Let's say that the distance between the two houses is D, then we can write the equations:
12mi/h*t₁ = D
2.5mi/h*t₂ = D
These are equations of the form:
speed*time = distance
Where t₁ is the time that Latanya takes to arrive to Marta's house, and t₂ is the time that they take to arrive to Latanya's house.
We know that the total time of this is 3 hours, and they spent 90 minutes = 1.5 hours in Marta's house, then:
t₁ + t₂ + 1.5 = 3
t₁ + t₂ = 3 - 1.5 = 1.5
Now we have a system of equations:
12*t₁ = D
2.5*t₂ = D
t₁ + t₂ = = 1.5
We can write:
D/12 = t₁
D/2.5 = t₂
And replace that in the last equation:
D/12 + D/2.5 = 1.5
2.5*D + 12D = 1.5*2.5*12
14.5D = 45
D = 45/14.5
D = 3.10 miles
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True or false?
An even function is one in which f(x) = f(-x) for all x's and odd function is one where g(x) = -g(-x) for all x's.
Answer:
True
Step-by-step explanation:
f is odd if the graph of f is symmetric with respect to the origin.
f is even if and only if f(-x) = f(x) for all x in the domain of f.
I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.
A single microvillus is a rod-like structure that is 1.0 μm in height. It has a hemispherical top approximately 0.1 μm in diameter. Calculate the surface area of the cylinder that forms the "sides" of the microvillus rod. Use 3.14 for π.
Answer:
so, the figure here is a cylinder with a semi sphere on the top, we know the height of whole structure, and the radius of the semi sphere, which is the same as the radius of the cylinder (you can see it because the radius of the semisphere is constant, and you can thin on it as half a sphere over a cylinder).
First, the cylinder will be the structure without the semi sphere, so his height will be te total height minus the radius of the semi sphere, which is 0.9μm.
so now we know the height and the radius of the cylinder, the surface or the sides of it is 2*3.14*r*h = 2*3.14*0.9μm*0.1μm = 0.5662[tex]μm^{2}[/tex].
The surface area of the cylindrical part of the microvillus is calculated by multiplying pi (3.14) with the diameter (0.1μm) and height (1.0μm) to yield a result of 0.314μm².
Explanation:To calculate the surface area of the cylindrical 'sides' of the microvillus, which we can consider to be a cylinder without its top and bottom parts, the formula used is: π * diameter * height. In this case, the diameter of the microvillus is 0.1μm (which is the diameter of the hemispherical top) and the height is 1.0μm.
Substitute these values into the formula:
Surface area = π * diameter * height = 3.14 * 0.1μm * 1.0μm = 0.314μm².
Thus, the surface area of the cylindrical part of the microvillus is 0.314 micrometers squared.
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Anyone know how to solve this
Hey!
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Solution:
5 1/5% = 0.052
325 x 0.052 = 16.9
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Answer:
D. 16.899...
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Hope This Helped! Good Luck!
Answer:
16,9
Step-by-step explanation:
To convert from a percentage to a decimal, move the decimal point twice to the left:
5,2% = 5⅕%
5,2% → 0,052
[tex](0,052)(325) = 16,9[/tex]
I am joyous to assist you anytime.
Norma Jean makes $25 per hour. She works 35 hours per week. She gets a commission of 15% on her total sales. How much should Norma sell to make $4,500 in a single week?
Norma needs to make sales worth $ _____ to make $4,500.
Answer:
$24,166.67
Step-by-step explanation:
Let carry out the breakdown:
So Norman Jean makes a flat rate of $25 per hour, also she works 35 hours per week.
From the above statement Jean will make => 25 × 35 = $875 in a single week without commission.
For Jean to make $4500 in a week, we derive an equation for this:
875 + x = 4500;
x is the amount of commission Jean has to get in a week to make up to $4500 in that week => x = 4500-875; x = $3625.
Let y be the amount of sales Jean has to make to get a commission of x, we derive the following equation: 0.15 × y = x.
y = x ÷ 0.15 => 3625 ÷ 0.15
y = 24166.67.
So for Jean to meet her target of $4500 in a single week, Jean needs to make a sale worth $24,166.67.
The amount of sales that Norma needs to make in a week in order to earn $4500 in a week is; 24167
How to solve algebra word problems?
We are told that;
Norma Jean makes $25 per hour
Total time worked per week = 35 hours
Commision on total sales = 15%
Basic amount earned for the 35 hours in a week = 25 * 35 = $875
Now, if the amount of sales she makes that earns her commision is x, then it means for her to earn $4500 in a single week;
875 + 0.15x = 4500
0.15x = 4500 - 875
x = (4500 - 875)/0.15
x = 24166.67
Approximating to a whole number is;
x = 24167 sales
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Jill had $125 to spend at the mall. She spent 27% of that money on a pair of shoes. Jill spent $___ on the shoes. (Make sure to enter the answer as a decimal number only. Do not enter special characters such as the dollar symbol.)
Answer:
%33.75
Step-by-step explanation:
I put the answer that the other person answered and I got it wrong so here is the right answer!
Answer:
33.75
Step-by-step explanation:
A recipe calls for cup of applesauce, cup of nuts, cup of flour, and cup of raisins. Which statement about the amount of apple sauce, nuts, flour, and raisins in the recipe is true? The recipe contains more raisins than flour. The recipe contains more nuts than raisins. The same amount of applesauce and flour is used. The same amount of applesauce, nuts, flour, and raisins is used.
Answer:
The same amount of applesauce, nuts, flour, and raisins is used.
Step-by-step explanation:
Have you ever heard of the question, "which weighs more, a pound of steel, or a pound of feathers?" And then everyone is shocked when they weigh the same, even though they both were said to weigh a pound?
This question is like that.
One cup of each is used, so they are all a cup, which means an equal amount of all of them were used.
Two cars leave an intersection, one traveling west and the other south. After some time, the slower car is 7 mi nearer to the intersection than the faster car. At that time, the two cars are 13 mi apart. How far did each car travel?
Answer:
Step-by-step explanation:
let x and y be the distances of each car from the intersection after sometime.
let x<y
then y-x=7
and y+x=13
add 2y=20
y=10
x=13-10=3
slower car travels 3 miles and faster car travels 10 miles
Ms. Bergen is a loan officer at Coast Bank and Trust. From her years of experience, she estimates that the probability is .025 that an applicant will not be able to repay his or her installment loan. Last month she made 40 loans. Use the poisson approximation to the binomial.
a. What is the probability that three loans will be defaulted?
b. What is the probability that at least 3 loans will be defaulted?
Answer:
a) 0.0613 b)0.0803
Step-by-step explanation:
Ms. Bergen estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan.
p = 0.025
Let's consider that an applicant is not be able to repay his or her installment loan as a ''success''
p (success) = 0.025
Last month she made 40 loans ⇒ n = 40
For the poisson approximation to the binomial we need to calculate n.p that will be the λ parameter in our poisson approximation
[tex]n.p=40.(0.025)=1[/tex]
λ=n.p=1
Let's rename λ = j
In our poisson approximation :
[tex]f(k,j)=\frac{e^{-j} .j^{k} }{k!}[/tex]
f(k,j) is the probability function for our poisson variable where we calculated j,e is the euler number and k is the number of success :
[tex]f(k,1)=\frac{e^{-1} .1^{k} }{k!}[/tex]
For a) We are looking the probability of 3 success :
[tex]f(3,1)=\frac{e^{-1} .1^{3} }{3!}=0.0613[/tex]
For b) We are looking for the probability of at least 3 success
If ''L'' is the number of success
[tex]P(L\geq 3)=1-P(L\leq 2)[/tex]
[tex]P(L\leq 2)=P(L=0)+P(L=1)+P(L=2)[/tex]
[tex]P(L\leq 2)=f(0,1)+f(1,1)+f(2,1)[/tex]
[tex]P(L\leq 2)=e^{-1} +e^{-1}+\frac{e^{-1}}{2} =e^{-1}(1+1+\frac{1}{2} )[/tex]
[tex]P(L\geq 3)=1-P(L\leq 2)=1-e^{-1}(1+1+\frac{1}{2} )=0.0803[/tex]
The probability that three loans will default is 0.0613
The probability that at least 3 loans will default is 0.0803
Calculations and Parameters:Ms. Bergen estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan.
p = 0.025
Hence, we consider that an applicant is not able to repay his or her installment loan as a ''success''
p (success) = 0.025
Last month she made 40 loans ⇒
n = 40
For the Poisson approximation to the binomial, we need to calculate n.p which will be the λ parameter in our Poisson approximation
n.p= 40.(0.025) =1
λ=n.p=1
Let's rename λ = j
In our Poisson approximation :
f(k,1) = e^-j.j^k/k!
Hence, the probability of 3 success is:
f(3,1)= e^-1.1^3/3!
=0.0613.
The probability of at least 3 successes is:
If ''L'' is the number of successes.
P(L≥ 3) = 1- P(L≤ 2)
P(L≥ 3)= 0.0803.
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