Answer:
-9
Step-by-step explanation:
Recall the following relationships about the sum of cubes and a square binomial:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex](a+b)^2=a^2+2ab+b^2[/tex]
The second factor on the right hand side of equation 1 looks similar to the right hand side of equation 2, but differs slightly.
Carefully choosing to subtract 3ab from both sides of the equation 2, and Combining like terms yields...
[tex](a+b)^2-3ab=a^2-ab+b^2[/tex]
This now matches the second factor on the right hand side of the first equation. So, with substitution, the first equation becomes:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex]a^3+b^3=(a+b)((a+b)^2-3ab)[/tex]
Note that all of the parts on the right hand side of the equation are given in the question:
a+b=3 and ab=4
With some substitution and simplification
[tex]a^3+b^3=(a+b)((a+b)^2-3ab)[/tex]
[tex]=(3)((3)^2-3(4))[/tex]
[tex]=(3)(9-3(4))[/tex]
[tex]=(3)(9-12)[/tex]
[tex]=(3)(-3)[/tex]
[tex]=-9[/tex]
Asap!!!! Solve the equation for v. v over 8 minus 4 equals negative 12 (18 points)
v = -128
v = -64
v = 16
v = 92
Answer:
v = -64
Step-by-step explanation:
First, you add 4 to both sides to isolate the variable term:
v/8 = -8
Next, you multiply both sides by 8 to isolate the variable on one side:
v = -64
So, the solution to the equation v/8 - 4 = -12 is v = -64.
El 91 no es un número primo porque tiene más divisores que el 1 y el 91 verdadero o falso
The statement''El 91 no es un número primo porque tiene más divisores que el 1 y el 91'' is true because 91 is not a prime number.
A prime number is a positive integer that has only two divisors, 1 and itself. To check if 91 is a prime number, we need to find its divisors. We can start by dividing 91 by 2, but we find that 2 is not a divisor of 91. Next, we can try dividing it by 3, and we get 30 with a remainder of 1. This means that 3 is not a divisor of 91 either.
We continue dividing by 4, 5, 6, and so on until we reach 13, which gives us 7 as a quotient and 0 as a remainder. Therefore, the divisors of 91 are 1, 7, 13, and 91, which means that 91 is not a prime number because it has more than two divisors. Hence, the statement is true.
91 ÷ 2 = 45 r 1
91 ÷ 3 = 30 r 1
91 ÷ 4 = 22 r 3
91 ÷ 5 = 18 r 1
91 ÷ 6 = 15 r 1
91 ÷ 7 = 13 r 0
Since 91 has more than two divisors, it is not a prime number.
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The Anderson family went on a trip to see the Paul Bunyan and Blue Ox statue near Lake Bemidji. It took the family 6 hours to travel 330 miles to the statue. What was the Anderson family's average miles per hour (mph)?
btw I don't know how to mark people brainiest so if you tell me how I will to if you help me.
Determine the unique solution, y(x), to the differential equation that satisfies the given initial condition. dy/dx = 8x⁷/y⁴, y(0) = 4
y(x) = ...
The unique solution, y(x), to the given differential equation with initial condition y(0) = 4 is
:
y(x) = [-(6x⁸ - 64)]¹/³
Determine the unique solution?
To determine the unique solution, y(x), to the given differential equation with initial condition y(0) = 4, we first need to separate the variables and integrate both sides with respect to x and y, respectively.
dy/y⁴ = 8x⁷ dx
Integrating both sides, we get:
-1/3y³ = 2x⁸ + C
where C is the constant of integration.
Now we can use the initial condition y(0) = 4 to solve for C:
-1/3(4)³ = 2(0)⁸ + C
C = -64/3
Substituting C back into the previous equation, we get:
-1/3y³ = 2x⁸ - 64/3
Multiplying both sides by -3 and taking the cube root, we get:
y(x) = [-(6x⁸ - 64)]¹/³
Therefore, the unique solution, y(x), to the given differential equation with initial condition y(0) = 4 is:
y(x) = [-(6x⁸ - 64)]¹/³
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A corporation earned a profit of $ 2.5 × 1 0 4 $2.5×10 4 for 200 days in a row. What was the corporation’s total profit during this time period? Express your answer in scientific notation.
Answer: hopefully the image helps
Step-by-step explanation:
Can someone help me asap? It’s due today
Step-by-step explanation:
the answer will be "15" according to the question.
Can someone help me fast!?!?
Trying to get better at doing these kinds of problems.
Graph the line -3x + 5y = 15
Which one would it be? This will help a lot :D
According to the question the graph the line -3x + 5y = 15, we can start by solving for y:
-3x + 5y = 15
5y = 3x + 15
y = (3/5)x + 3
Define graph.As an algebraic framework that depicts a specific function by joining a collection of points, a graph is defined. It establishes a pairwise connection among the items. The graph is made up of nodes (vertices) linked by edges. (lines).
Briefing :
Now we have the equation in slope-intercept form (y = mx + b) where the slope is 3/5 and the y-intercept is 3.
To graph the line, we can start at the y-intercept (the point (0, 3)) and then use the slope to find additional points. Since the slope is 3/5, we can move up 3 units to the right 5 units to get to the point (5, 6), and down 3 units to the left 5 units to get to the point (-5, 0). Connect these points to get the line.
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A baseballâ player's batting average is 0. 343â, which can be interpreted as the probability that he got a hit each time at bat. â Thus, the probability that he did not get a hit is 1â0. 343=0. 657. Assume that the occurrence of a hit in any givenâ at-bat has no effect on the probability of a hit in otherâ at-bats. In oneâ game, the player had 5 âat-bats. What is the probability that he had 3 âhits? What expression can be used to calculate theâ probability?
0.135 or 13.5% is the probability that he had 3 âhits
The probability that the player had 3 hits in 5 at-bats can be calculated using the binomial probability formula, which is:
P(x) = (nCx) * p^x * (1-p)^(n-x)
where:
- P(x) is the probability of getting x hits
- n is the number of at-bats (in this case, 5)
- x is the number of hits we want to find the probability for (in this case, 3)
- p is the probability of getting a hit in one at-bat (in this case, 0.343)
- (1-p) is the probability of not getting a hit in one at-bat (in this case, 0.657)
Plugging in the values, we get:
P(3) = (5C3) * 0.343^3 * 0.657^(5-3)
P(3) = (10) * 0.039304527 * 0.4305961
P(3) = 0.134912947
Therefore, the probability that the player had 3 hits in 5 at-bats is approximately 0.135 or 13.5%.
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2 A model of (CH₂O)4 was created using colored beads. Carbon atoms were
represented by black beads, hydrogen atoms by red beads, and oxygen atoms
by blue beads. Which of the following combinations of beads shows an accurate
model of (CH₂O)4?
A 4 black, 8 red, and 4 blue
B 1 black, 2 red, and 1 blue
C 4 black, 6 red, and 4 blue
D
1 black, 8 red, and blue
The correct number of beads is; 4 black, 8 red, and 4 blue. Option A
What is a molecular model?A molecular model is a depiction of molecules or chemical compounds made physically, visually, or mathematically in order to comprehend their behavior and characteristics. These models can range from real models made of plastic or metal to computer-generated graphics or mathematical formulae, and they can be straightforward or sophisticated.
There are four carbon atoms, eight hydrogen atoms and four oxygen atoms.
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WILL MARK BRAINLIEST!!
The amount that Benjamin must save every month to pay off the discounted premium is $ 40. 80
The total premium for the year would be $ 637. 20
How to find the amount saved ?The amount that Benjamin's discounted premium would come to for the year is:
= 1, 080 x ( 1 - 66 %)
= $ 367. 20
The amount he would need to save every month on deployment is :
= 367. 20 / 9
= $ 40. 80
His total premium would be :
= 367. 20 + ( 1, 080 / 12 x 3 months when he comes back )
= $ 637. 20
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Integrate fover the given curve. f(x,y) = x+ y, C: x^2 + y^2 = 4 in the first quadrant from
(2,0) to (0,2)
The integral of f(x, y) = x + y over the given curve is 8.
To integrate the function f(x, y) = x + y over the curve C: x² + y² = 4 in the first quadrant from (2, 0) to (0, 2), we will use the line integral. Since the curve is a circle, we can parameterize it using polar coordinates as follows:
x = 2cos(θ)
y = 2sin(θ)
Now, let's find the derivatives:
dx/dθ = -2sin(θ)
dy/dθ = 2cos(θ)
Next, we substitute x and y in f(x, y):
f(x, y) = 2cos(θ) + 2sin(θ)
Now, we can set up the line integral:
∫[f(x, y) * ||dr/dθ||]dθ
Since ||dr/dθ|| = sqrt((-2sin(θ))^2 + (2cos(θ))^2) = 2, the line integral becomes:
∫[2cos(θ) + 2sin(θ)] * 2 dθ
To find the limits of integration, we can use the points (2, 0) and (0, 2). In polar coordinates, these points correspond to θ = 0 and θ = π/2.
So, the line integral becomes:
∫[4cos(θ) + 4sin(θ)]dθ from 0 to π/2
Now, we can integrate and evaluate:
[4sin(θ) - 4cos(θ)] from 0 to π/2 = [4(1) - 4(0)] - [4(0) - 4(1)] = 8
Thus, the integral of f(x, y) = x + y over the given curve is 8.
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If the equation, in which n, m, and r are constants, is true for all positive values of a, b, and c, what is the value of n?
The value of n is 6
Given expression is [tex]\frac{48a^{12}b^8c^{15}}{(2a^2bc^4)^3}=6a^nb^mc^r[/tex]
To find the value of n, we need to simplify the expression:
(48 × a¹² × b⁸ × c¹⁵) / (2 × a² × b × c⁴)³
First, we can simplify the denominator:
(2 × a² × b × c⁴)³ = 2³ × (a²)³ × b³ × (c⁴)³
= 8 × a⁶ × b³ × c¹²
(48 × a¹² × b⁸ × c¹⁵) / (8 × a⁶ × b³ × c¹²) = (8 × 6a⁶ × a⁶ × b⁵ × b³ × c₁₂ × c³) / (8 × a⁶ × b³ × c¹²)
Simplifying further, we get:
= 6 × a⁶ × b⁵ × c³
on comparing with R H S
a⁶ = aⁿ
So, n=6
Therefore, the value of n is 12, since that is the exponent of the variable "a".
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Given question is incomplete, the complete question is given below
For the expression below
[tex]\frac{48a^{12}b^8c^{15}}{(2a^2bc^4)^3}=6a^nb^mc^r[/tex]
If the equation, in which n, m, and r are constants, is true for all positive values of a, b, and c, what is the value of n?
In the relations v=u+at,findv,when u=6 a=10 t=2
The value of v in the equation is 26
How to calculate the value of v in the equation?The equation is given as
v= u + at
The parameters given are
u= 6
a= 10
t= 2
v= 6 + 10(2)
v= 6 + 20
v= 26
Hence the value of v in the equation is 26
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To conserve water, many communities have developed water restrictions. The water utility charges a fee of $34, plus an additional $1.36 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $60 and $85 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.
60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.
Hown to write the inequalityThe correct compound inequality to represent the scenario is:
60 ≤ 1.36x + 34 ≤ 85
To solve for x, we need to isolate it in the middle of the inequality:
60 - 34 ≤ 1.36x ≤ 85 - 34
26 ≤ 1.36x ≤ 51
Finally, we divide by 1.36 to isolate x:
19.12 ≤ x ≤ 37.5
Therefore, the recommended range of water consumption is between 19.1 and 37.5 HCF. The answer is (D) 60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.
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complete question
To conserve water, many communities have developed water restrictions. The water utility charges a fee of $34, plus an additional $1.36 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $60 and $85 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)
60 ≤ 1.36x − 34 ≤ 85; To stay within the range, the usage should be between 69.1 and 87.5 HCF.
60 ≤ 1.36x − 34 ≤ 85; To stay within the range, the usage should be between 44.1 and 87.5 HCF.
60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 37.5 and 44.1 HCF.
60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.
Mr. Vega is going to buy a blue tractor that weighs 3/5 of a ton or a red tractor weighs 4/6 of a ton. Which tractor is heavier
The red tractor is heavier.
To determine which tractor is heavier, Mr. Vega needs to compare the weights of the blue and red tractors. The blue tractor weighs [tex]\frac{3}{5}[/tex] of a ton, and the red tractor weighs [tex]\frac{4}{6}[/tex] of a ton.
First, we need to simplify the fractions if possible. In this case, we can simplify the red tractor's fraction by dividing both the numerator and denominator by 2:
[tex]\frac{4}{6} = \frac{\frac{4}{2} }{\frac{6}{2} } = \frac{2}{3}[/tex]
Now we can compare the simplified fractions:
[tex]Blue tractor: \frac{3}{5}[/tex]
[tex]Red tractor: \frac{2}{3}[/tex]
To compare these fractions, we can find a common denominator. The least common multiple of 5 and 3 is 15. To convert the fractions to the same denominator, we multiply the numerators and denominators by the necessary factors:
[tex]Red tractor: (\frac{2}{3}) (\frac{5}{5}) = \frac{10}{15}[/tex]
[tex]Blue tractor: (\frac{3}{5}) (\frac{3}{3}) = \frac{9}{15}[/tex]
Now we can easily compare the weights:
[tex]Blue tractor: \frac{9}{15}[/tex]
[tex]Red tractor: \frac{10}{15}[/tex]
Since [tex]\frac{10}{15}[/tex] is greater than [tex]\frac{9}{15}[/tex] , the red tractor is heavier.
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A) Construct an appropriate tabular representation/summary of the random variable Number of years in operation and provide an interpretation.
b) Construct a cross-tabulation of the data on Daily Income and Type of service and provide an interpretation. Hint: Use a class width of N$ 500 for Daily Income.
c) Calculate and interpret relative measures of variability for the Daily Income for each of the three categories of Type of service
Un árbol ha sido roto por el viento de tal manera que sus dos partes forman un triángulo rectángulo. la parte superior tiene una longitud de 10 m, y la distancia medida sobre el piso hasta la cúspide del árbol es de 6 m. hallar la altura que tenía el árbol.
Se puede utilizar el teorema de Pitágoras para resolver este problema. Si se considera que la altura del árbol es la hipotenusa del triángulo rectángulo,
entonces la parte superior de la parte rota del árbol es uno de los catetos, y la distancia medida sobre el piso hasta la cúspide del árbol es el otro cateto.
Por lo tanto, se tiene que:
[tex]altura^2 = cateto1^2 + cateto2^2[/tex]
Reemplazando los valores conocidos, se tiene:
[tex]altura^2 = 10^2 + 6^2[/tex]
[tex]altura^2 = 136[/tex]
Tomando la raíz altura^2 = 136, se obtiene:
[tex]altura = √136[/tex]
altura ≈ 11.66 m
Por lo tanto, la altura que tenía el árbol antes de ser roto por el viento es de aproximadamente 11.66 metros.
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Solve for x WILL MAKE BRAINLIEST QUESTION IN PHOTI ALSO
The measure of x in the intersected chord is 16.
How to find the angle in an intersected chord?If two chords intersect in a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Using the chord intersection angle theorem,
5x - 7 = 1 / 2 (119 + 27)
5x - 7 = 1 / 2 (146)
5x - 7 = 73
add 7 to both sides of the equation
5x - 7 = 73
5x - 7 + 7 = 73 + 7
5x = 80
divide both sides of the equation by 5
x = 80 / 5
x = 16
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A circle is centered at c(0,0)c(0,0)c, left parenthesis, 0, comma, 0, right parenthesis. the point m(0,\sqrt{38})m(0, 38 )m, left parenthesis, 0, comma, square root of, 38, end square root, right parenthesis is on the circle.where does the point n(-5,-3)n(−5,−3)n, left parenthesis, minus, 5, comma, minus, 3, right parenthesis lie
The point N(-5,-3) lies inside the circle centered at C(0,0) with radius √38.
How we find the point lies inside the circle?Since the point M(0, √38) lies on the circle with center C(0,0), we can find the radius of the circle by finding the distance between M and C:
r = √[tex]((0 - 0)^2[/tex] + (√[tex]38 - 0)^2)[/tex] = √38
Now that we know the radius of the circle is √38, we can determine where the point N(-5,-3) lies relative to the circle. We can find the distance between N and the center of the circle:
d = √[tex]((-5 - 0)^2[/tex] + [tex](-3 - 0)^2)[/tex] = √34
Since the distance between N and the center of the circle is less than the radius of the circle, the point N is inside the circle. Therefore, N lies inside the circle centered at C(0,0) with radius √38.
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Ello beautiful people how are you doing today and wyd this weekend
Hello beautiful people! I hope you're all doing well today. As for me, I'm feeling great and ready for the weekend! I plan on spending some quality time with my loved ones, exploring new places, and trying out new activities.
I believe that weekends are meant for rest, relaxation, and rejuvenation, so I'm looking forward to taking a break from my busy work schedule.
One of the things I love about weekends is the opportunity to disconnect from the stresses of everyday life and focus on things that bring me joy. Whether it's going for a hike, trying out a new recipe, or catching up with friends over a cup of coffee, there's always something to look forward to.
this weekend I plan on making the most of my free time by doing things that make me happy and help me recharge. I hope you all have a great weekend as well, and that you find time to do the things you love with the people you care about. Remember, life is short, so let's make the most of every moment we have!
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One gallon of paint covers 50 square feet. A wall that measures 32 feet by 16 feet is going to be painted.
Area of Wall:
How many gallons of paint will it take?
If paint costs $27 per gallon, how much money will it take to paint the wall?
Answer:
10.24 gallons
$276.48
Step-by-step explanation:
The area of the wall can be calculated by multiplying the length and height of the wall:
Area of wall = length x height = 32 x 16 = 512 square feet
To calculate the number of gallons of paint needed, we need to divide the area of the wall by the coverage of one gallon of paint:
Number of gallons of paint = Area of wall / Coverage of one gallon of paint
Number of gallons of paint = 512 / 50
Number of gallons of paint = 10.24
Therefore, it will take approximately 10.24 gallons of paint to paint the wall.
To calculate the cost of the paint, we need to multiply the number of gallons of paint by the cost per gallon:
Cost of paint = Number of gallons of paint x Cost per gallon
Cost of paint = 10.24 x $27
Cost of paint = $276.48
Therefore, it will cost $276.48 to paint the wall.
In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:
(2, 1990) (5, 4225) (9, 7205)
Find the slope and y-intercept. Explain what each represents.
Use first two points and the slope equation to find the slope:
m = (4225 - 1990)/(5 - 2) = 745The slope is 745.
Use the first point and point-slope equation to find the y-intercept:
y - y₁ = m(x - x₁), where m- slope, (x₁, y₁) - the given pointy - 1990 = 745(x - 2)y - 1990 = 745x - 1490y = 745x - 1490 + 1990y = 745x + 500The y-intercept is 500.
The slope of 745 represents the profit per month and the y-intercept of 500 represents the initial profit.
Jerry has the following assets a house with equity of $15. 0. A car with equity of $2. 500, and household goods worth $6,000 (no single item over $400). He also has tools worth $5. 800 that he needs for his business. Using the federal list, the total amount of exemptions that Jerry would be allowed is $____. 0. Using the state list, the total amount of exemptions that jerry would be allowed is $____. 0.
00. Using the state list the total amount of exemptions that Jerry would be allowed is s
. 0. The state
list will be more favorable for him
tially Connect
Under the federal list, the total amount of exemptions that Jerry would be allowed is $27,900.
Under the state list, the total amount of exemptions that Jerry would be allowed is $37,500.
What are the exemptions?Under the federal list, Jerry's exemptions can only be be:
Equity in home: $15,000
Motor vehicle: $2,400
Household goods: $8,000
Tools (for debtor’s trade): $1,500
Total exemptions = $27,900
Under the state list, Jerry's exemptions can only be be
Equity in home: $25,000
Motor vehicle: $1,500
Household goods: $6,000
Tools: $5,000
Total exemptions = $37,500
Based on the above, the state list can be more favorable for Jerry as it will give him a lot of exemption a higher total value of assets.
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See full question below
Computing Exemptions Under Chapter 7 Bankruptcy
Assume the current federal bankruptcy exemptions are listed at the left, and the state exemptions are
listed at the right. The debtor may use the exemption table that best benefits him or her. For the two
circumstances shown below, compute the exemption amounts and decide which will be better for the
debtor—the federal list or the state list.
LIST A. FEDERAL EXEMPTIONS
Equity in home .......................................$15,000
Motor vehicle .............................................2,400
Household goods .......................................8,000
($400 limit for a single item)
Jewelry .......................................................1,000
Other property ..............................................800
Tools (for debtor’s trade) ...........................1,500
LIST B. STATE EXEMPTIONS
Equity in home ....................................... $25,000
Motor vehicle ............................................. 1,500
Household goods ..................................... 10,000
($1,000 limit for a single item)
Jewelry .......................................................... 500
Other property .............................................. 100
Tools ........................................................... 5,000
1. Jerry has the following assets: a house with equity of $15,000, a car with equity of $2,500, and household goods worth $6,000 (no single item over $400). He also has tools worth $5,800 that he needs for his business. What is the total amount of exemptions Jerry would be allowed using the federal list? The state list? Which list will be more favorable for him? SHOW YOUR WORK!
Gabby had 578
7
8
yards of fabric. she used 3215
2
15
yards of fabric. estimate the amount of fabric gabby has left.
The same method of subtracting the amount of fabric used from the amount she started with to estimate the amount of fabric Gabby has left.
How to estimate the amount of fabric Gabby has left?To estimate the amount of fabric Gabby has left, we can subtract the amount of fabric she used from the amount she started with:
57878 - 3215215 ≈ -3157337
However, we can see that this result is negative, which doesn't make sense in the context of the problem. It's not possible for Gabby to have negative yards of fabric left.
It's likely that there was a mistake in the problem statement or in the numbers given. If the problem were corrected, we could use the same method of subtracting the amount of fabric used from the amount she started with to estimate the amount of fabric Gabby has left.
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what is the product of -5 and -10 sign and result
Answer:
50, positive
Step-by-step explanation:
(-5) * (-10) = 50
When a negative multiplies by another negative, the answer is positive
So, the answer is 50 and the sign is positive
Suppose 60 seventh-grade students were surveyed.
How many can be expected to say that bike riding is
their favorite hobby?
Please IM IN NEED OF HELP
thx
We need to make some assumptions. Let's assume that the survey allowed students to choose one favorite hobby and that bike riding was one of the options.
We also need to know the percentage of students who chose bike riding as their favorite hobby. If this information is not given, we cannot accurately estimate the number of students who would say that bike riding is their favorite hobby.
Suppose that 30% of the surveyed students chose bike riding as their favorite hobby. To find out how many students this represents, we can use the following formula:
Expected number of students = Percentage of students x Total number of students surveyed
Plugging in the values we have, we get:
Expected number of students who say bike riding is their favorite hobby = 0.30 x 60 = 18
Therefore, we can expect that approximately 18 of the 60 seventh-grade students surveyed would say that bike riding is their favorite hobby, based on the assumption that 30% of the students chose this option.
It's important to remember that this is just an estimate based on the information we have. The actual number may be different depending on the survey results.
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AutoTrader would like to estimate the number of years owners keep the cars that they purchased as a new vehicle. The following data shows the age of seven vehicles that were sold for the first time by their owners. Using this sample, the 90% confidence interval that estimates the average age of cars sold for the first time is ________. Group of answer choices (2. 56, 10. 30) (5. 14, 7. 72) (1. 27, 11. 59) (3. 93, 8. 93)
The 90% confidence interval that estimates the average age of cars sold for the first time is (2.56, 10.30).
To calculate the confidence interval, we can use the formula:
CI =[tex]\bar{X}[/tex] ± tα/2 * (s/√n)
where [tex]\bar{X}[/tex] is the sample mean, s is the sample standard deviation, n is the sample size, tα/2 is the critical value from the t-distribution table with (n-1) degrees of freedom and a confidence level of 90%.
Using the given data, we find that the sample mean is 6.43 years and the sample standard deviation is 2.69 years. With a sample size of 7, the critical value from the t-distribution table is 1.895.
Plugging in these values, we get:
CI = 6.43 ± 1.895 * (2.69/√7)
Simplifying this expression gives us the confidence interval (2.56, 10.30). Therefore, we can say with 90% confidence that the average age of cars sold for the first time is between 2.56 and 10.30 years.
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A van can ferry a maximum of 12 people. By setting up an inequality, find the maximum number of vans that are needed to ferry 80 people
By setting up an inequality, the maximum number of vans that are needed to ferry 80 people are 7 vans.
To find the maximum number of vans needed to ferry 80 people using the given terms, let's set up an inequality. Let's use the variable "v" to represent the number of vans.
Since a van can ferry a maximum of 12 people, we can write the inequality as:
12v ≥ 80
Now, let's solve for "v":
Divide both sides of the inequality by 12.
v ≥ 80/12
Simplify the inequality.
v ≥ 6.67
Since we cannot have a fraction of a van, we need to round up to the nearest whole number:
v ≥ 7
Therefore, the maximum number of vans needed to ferry 80 people is 7 vans.
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how many shortest lattice paths start at (2, 2) and
a) end at (11, 11) and pass through (8, 10)?
b) end at (11,11) and avoid (8,10)
A. The number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is 28 * 4 = 112.
B. The number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10) is the total number of paths minus the number of paths that pass through (8, 10), which is 48620 - 112 = 48508.
What is combinatorics?
Combinatorics is a branch of mathematics that deals with counting and arranging the possible outcomes of different arrangements and selections of objects.
For part (a), the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is given by the product of the number of shortest lattice paths from (2, 2) to (8, 10) and from (8, 10) to (11, 11).
To find the number of shortest lattice paths from (2, 2) to (8, 10), we can count the number of ways to choose 6 steps up out of 8 total steps (the remaining 2 steps are to the right), which is 8 choose 6 = 28.
Similarly, the number of shortest lattice paths from (8, 10) to (11, 11) is the number of ways to choose 1 step up out of 4 total steps (the remaining 3 steps are to the right), which is 4 choose 1 = 4.
Therefore, the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is 28 * 4 = 112.
b) To find the number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10), we can use the principle of inclusion-exclusion.
Let's first count the number of shortest lattice paths from (2, 2) to (11, 11) without any restrictions. Since we can only move up or to the right, the number of such paths is the number of ways to choose 9 steps up out of 18 total steps (the remaining 9 steps are to the right), which is 18 choose 9 = 48620.
Next, we count the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10). Using the method described in part (a), we found that the number of such paths is 28 * 4 = 112.
Therefore, the number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10) is the total number of paths minus the number of paths that pass through (8, 10), which is 48620 - 112 = 48508.
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Using the formulas, answer the question.
A = P(1 + =)nt
A = Pert
Ted invests $500 in an account that compounds interest quarterly with a 3.5%
rate. How much money will he have after 15 years? Round to the nearest
dollar.
Answer:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.5/100
r = 0.035 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 500.00(1 + 0.035/4)(4)(15)
A = 500.00(1 + 0.00875)(60)
A = $843.30
A = $843 (round-off)
