For this case we have to:
n: It's the variable that represents the number of lawns that mowed Wally last week.
If you tell us as a fact that this week Wally mowed two more lawns, then we have the following expression:
[tex]n + 2[/tex]
Finally, the expression is:
[tex]n + 2[/tex]
Answer:
[tex]n + 2[/tex]
Option A
The histogram shows a city’s daily high temperatures recorded for four weeks.
Which phrase describes the shape of the temperature data?
symmetrical
left-skewed
right-skewed
normal
Answer:
Step-by-step explanation:
The answer is b. left skewed
Left-skewed describes the shape of the temperature data.
left-skewed distribution
A distribution exists skewed if one of its tails is longer than the other. The first distribution shown includes a positive skew. This suggests that it has a long tail in the positive direction. The distribution below it has a negative skew since it includes a long tail in the negative direction.
In statistics, left-skewed simply represents a distribution where the value is concentrated on the right side of the distribution graph.In this case, the shape of the temperature data stands left-skewed as the left tail of the distribution graph exists longer.In this distribution, the majority of the data is to the right of the graph. The "tail" of the distribution is to the left. This defines a left-skewed distribution.
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Solve Ax + By = −C for x.
x equals the quantity negative B times y minus C all over A
x equals the quantity negative B times y plus C all over A
x equals the quantity B times y plus C all over A
x equals the quantity B times y minus C all over A
Answer:
x equals the quantity negative B times y minus C all over A
Step-by-step explanation:
Subtract By and divide by A:
Ax + By = -C . . . . starting equation
Ax = -By -C . . . . . subtract By from both sides
x = (-By -C)/A . . . . divide both sides by A
Answer:
A
Step-by-step explanation:
Determine there relationship
Answer:
Parallel
Step-by-step explanation:
Note for any function h(x) = mx + b
m = slope of the function
in this case, both functions have the same slope of [tex]\frac{3}{5}[/tex]
Hence the functions must parallel
the function f(x)=18000(0.7)^x represents the penguin population on an island x years after it was first studied.what was the original population of the penguins on island?
Answer:
1800
Step-by-step explanation:
The original population occurs when time (i.e x) is zero.
hence we substitute x = 0 into the function
Original population, f(0),
= 1800 [tex](0.7)^{0}[/tex] .......... recall anything raised to power of zero is 1
= 1800 (1)
= 1800
The original population of the penguins on island be, 1800.
The correct option is (c)
What is function?A function is defined as a relation between a set of inputs having one output each. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given: f(x)=18000[tex](0.7)^{x}[/tex]
The original population will occurs when time is zero.
So, put x = 0 into the function f(x),
we have,
f(0)= 1800[tex](0.7)^{0}[/tex]
f(0)= 1800*1
f(0)=1800
Hence, the original population of the penguins on island is 1800.
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The function arcsine can also be defined as A. csc(θ) B. sin-1(θ) C. sec(θ) D. 1/sin(θ)
Answer:
B
Step-by-step explanation:
arcsine is just sin -1 (theta) and can be entered in the calculator as such.
The function arcsine is represented as sin-1(θ). It is the inverse of the sine function, and it helps find the angle whose sine is a given value like 0.44. The arcsine function can be accessed using the sin-1 button on calculators, allowing for easy calculations.
I posted a question similar to this yesterday and I understand how to do it now, but I want to make sure that I did this question correctly.
Answer:
Your choice is correct.
Step-by-step explanation:
magnitude = √(6² +5²) = √61 ≈ 7.81
direction = arctan(5/6) ≈ 39.81°
The polar coordinates are (7.81, 39.81°).
Find the possibility of rolling even numbers three times, using a six-side die number from 1 to 6
Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
Number of sides of die = 6
Number of sides with even numbers = 3
P( rolling an even number 1 time) = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
P(rolling even number 3 times) = [tex]\frac{1}{2}[/tex] x [tex]\frac{1}{2}[/tex] x [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{8}[/tex]
Please answer this multiple choice question for 23 points and brainliest!!
Answer:
A. T = 20°C - (2.8°C/h × 4h)
Step-by-step explanation:
The rate of change of temperature (-2.8°C/h) is multiplied by time (4h) to get the change in temperature (-11.2°C). That change is added to the initial temperature (20°C) to find the temperature after 4 hours.
Only equation A properly expresses this calculation.
In choice B, the rate of change is (wrongly) shown as +2.8°C/h. In the other choices, the combinations of units are nonsense. (What is a °C·h?)
A publisher claims that the average salary paid at its company is $37,500, but it could differ by as much as $4,500. Write an absolute value inequality to determine the range of salaries at this company.
|x − 37,500| ≤ 4,500
|x − 4,500| ≤ 37,500
|x − 37,500| ≥ 4,500
|x − 4,500| ≥ 37,500
Answer:
|x − 37,500| ≤ 4,500
Step-by-step explanation:
salary - 37,500 can be up +4500 or as negative -4500
as much as means less than or equal to
We use absolute values to indicate this
|x − 37,500| ≤ 4,500
Answer:
|x − 37,500| ≤ 4,500
Step-by-step explanation:
Let x represents the new salary paid (In dollars ),
∵ The actual salary = $ 37,500
∵ Maximum difference in salaries = $ 4500
Case 1 : If x > 0
⇒ x - 37500 ≤ 4500 -----(1)
Case 2 : If x < 0
⇒ 37500 - x ≤ 4500
⇒ -(x-37500) ≤ 4500 -----(2)
By combining inequalities (1) and (2),
| x - 37500 | ≤ 4500 ( ∵ |a| < b ⇒ -a < b or a < b )
Which is the absolute value inequality to determine the range of salaries at this company.
FIRST option is correct.
PLEASE HELP ME, I NEED HELP, THANK YOU SO MUCH !!!!!
1.
[tex]3x-6=36\\3x=42\\x=14[/tex]
2.
[tex]8y-5=99\\8y=104\\y=13[/tex]
A map uses a scale of 1 in. : 25 mi. If the distance between two cities on the map is 3.5 inches, what've is the actual distance between the cities
Answer:
if the distance in the map is 3.5 inches the actual distance is 87.5 miles
*will give brainlist* PLEASE ANSWER ASAP
what is the value of x?
Answer:
I don't know for sure but is 69 an option? is so that might be it
Answer:
x = 58
Step-by-step explanation:
Given an angle outside a circle formed by a tangent and a secant then
angle = [tex]\frac{1}{2}[/tex] difference of the measures of the intercepted arcs, that is
51 = [tex]\frac{1}{2}[/tex] (160 - x) ← multiply both sides by 2
160 - x = 102 ( subtract 160 from both sides )
- x = - 58 ( multiply both sides by - 1 )
x = 58
What conic section is defined by all points in a plane where the difference between the lengths of segments x and y remains constant?
Answer:
hyperbola
Step-by-step explanation:
If the sum is constant, the figure is an ellipse.
If the difference is constant, you get a hyperbola.
If one length is constant, you get a circle.
If the length to a point is the same as the length to a line, you get a parabola.
Answer:
There are four type of conic generated when a double napped cone is cut by a plane
1.Circle
2.Parabola
3.Ellipse
4.Hyperbola
Among these four, Hyperbola is the conic , ,all points in a plane where the difference between the lengths of segments x and y remains constant.
A point on Semi major Axis=(a,0),lying on the Hyperbola.
A point on Semi Minor axis =(0,b),not lying on the Hyperbola.
Take a point D lying on the hyperbola,and two points M and N not lying on the hyperbola.
DM-DN=2a(Length of major axis)
The vet told Jake that his dog, Rocco, who weighed 55 pounds, needed to lose 10 pounds. Jake started walking Rocco every day and changed the amount of food he was feeding him. Rocco lost half a pound the first week. Jake wants to determine Rocco's weight in pounds, p, after w weeks if Rocco continues to lose weight based on his vet's advice. The equation of the scenario is . The values of p must be
Final answer:
Explanation on solving the equation p = 55 - 0.5w to find Rocco's weight after w weeks.
Explanation:
Solving the Equation:
Since Rocco lost half a pound per week, the equation would be: p = 55 - 0.5w, where p is Rocco's weight in pounds and w is the number of weeks.
Substitute the value for the first week: p = 55 - 0.5(1) = 55 - 0.5 = 54.5 pounds.
Therefore, Rocco's weight after w weeks would be p = 55 - 0.5w.
Answer:
The equation of the scenario is
✔ p = 55 – 0.5w
.
The values of p must be
✔ any real number 45 to 55
Step-by-step explanation:
The area of a parking lot is 805 square meters. A car requires 5 meters and a bus requires 32 square meters of space. There can be at most 80 vehicles parked at one time. If the cost to park a car is $2.00 and a bus is $6.00, how many should be in the lot to maximize income?
Answer:
80 cars will maximize revenue
Step-by-step explanation:
The revenue per square meter for parked cars is ...
$2.00/5 = $0.40
The revenue per square meter for buses is ...
$6.00/32 = $0.1875
Thus the available space should be used to park the maximum number of cars.
80 cars should be in the lot to maximize income.
To maximize income, the parking lot should have 69 cars and 11 buses parked, resulting in a total income of $282.
To maximize income, we need to maximize the revenue generated from parking fees. Let's denote the number of cars as x and the number of buses as y.
Given:
- Area of parking lot: 805 square meters
- Space required for a car: 5 square meters
- Space required for a bus: 32 square meters
- Maximum number of vehicles: 80
We have the following constraints:
1. [tex]\( 5x + 32y \leq 805 \)[/tex] (total area constraint)
2. [tex]\( x + y \leq 80 \)[/tex] (maximum number of vehicles constraint)
The objective function to maximize income is:
Income [tex]\( I = 2x + 6y \)[/tex]
To solve this problem, we'll analyze the feasible region defined by these constraints and find the combination of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that maximizes income.
By solving these constraints, we find that the maximum income occurs at the vertex where [tex]\( x = 69 \) and \( y = 11 \)[/tex].
Therefore, to maximize income, there should be 69 cars and 11 buses parked in the lot.
The top and bottom of the polyhedron below are equilateral triangles. A plane that perpendicularly bisects corresponding sides of both triangles would form two sets of two consecutive interior dihedral angles with measures of _______ and _________ .
Answer:
30° and 90°
Step-by-step explanation:
The perpendicular bisector of an equilateral triangle forms a 90° angle with one side and a 30° angle with the other side.
Caroline replaced the original factory tires (P240/75 R 16) on her pickup truck with P290/70R16 tires. If the speedometer on Cassie’s truck reads 60 mph, how fast is Cassie actually traveling?
Cassie is traveling 65.7 mph
Cassie is traveling 66.6 mph
Cassie is traveling 68.9 mph
Cassie is traveling 63.6 mph
Answer:
Cassie is traveling 63.6 mph
Step-by-step explanation:
If the three numbers, left to right, are A, B, C, then the tire radius in millimeters is ...
A×B/100 + 12.7×C
For the factory tires, the tire radius is ...
240·75/100 + 12.7·16 = 180 +203.2 = 383.2 . . . . millimeters
For the replacement tires, the tire radius is ...
290·70/100 +203.2 = 406.2 . . . . millimeters
The speedometer is calibrated based on the number of revolutions the tire makes in a given time period. If the truck goes farther for each revolution, its speed is higher by the same proportion.
If the speedometer on the truck with these replacement tires reads 60 mph, the actual speed is ...
(406.2/383.2)×60 mph = 63.6 mph
_____
Comment on the problem statement
Caroline's truck has the replacement tires. If Cassie's speedometer reads 60 mph, we have no reason to assume Cassie is traveling at any speed other than 60 mph.
given that (-5,8)is on the graph of f(x) find the corresponding point for the function f(x)-2
I never came across a question like this one. Time to reason my way to the answer.
We know that f(x) = y.
In the point given, y = 8.
So, f(x) - 2 = y - 2 = 8 - 2 = 6.
The corresponding point should be (-5, 6).
Identify m∠MNP. I CAN'T FAIL THIS!! ANSWER FAST PLEASE!!
Answer:
It's 90 degrees.
Step-by-step explanation:
You have to use your instincts here, the angle is not acute, so it can't be 60. The angle is not obtuse either, so it can't be 120 or 180, leaving 90. Also the degree of the arc of a circle is usually 2x the measure of the corresponding angle.
Answer:
90 degrees
Step-by-step explanation:
Consider this number in scientific notation.
3.75 × 10^8
Which is true about writing the number in standard form? Check all that apply.
Move the decimal point eight places to the left.
This will convert to a very large number.
Move the decimal point ten places to the right.
This will convert to a very small number.
This is the same as the product of 3.75 and 100,000,000.
Answer:
This will convert to a very large numberThis is the same as the product of 3.75 and 100,000,000Step-by-step explanation:
[tex]3.75\times 10^8=3.75\times 100,000,000=375,000,000.[/tex]
The decimal point is moved 8 places to the right. The number is "very large" in relation to most folks' personal experience with counting things, but is "very small" in relation to quantities and sizes in the known universe.
Answer:
This will convert to a very large number.
This is the same as the product of 3.75 and 100,000,000.
Step-by-step explanation:
scientific notation.
[tex]3.75 \cdot 10^8[/tex]
To get the standard form we multiply the decimal number by 10^8
When we multiply by 10^8, move the decimal 8 places the right
This will convert to a very large number
[tex]10^8 = 100,000,000[/tex]
[tex]3.75 \cdot 100000000[/tex]
This is the same as the product of 3.75 and 100,000,000.
Counting back from 5 what number follows 4
I believe your answer should be 3.
Really?
5 down to 4 down to 3.
I think 3 is the best answer.
Determine the product: (46.2 × 10–1) ⋅ (5.7 × 10–6). Write your answer in scientific notation.
A. 2.6334 × 10–5
B. 2.6334 × 10–7
C. 2.6334 × 10–1
D. 2633.4 × 10–5
Answer:
A
Step-by-step explanation:
10-6 X 10-1 = 10-7
5.7*46.2=263.34
263.34=2.6334 x 10^2
10^2 x 10^-7 = 10^-5
so
=2.6334 x 10-5
The standard form of the product of the mathematical expression (46.2×10⁻¹)(5.7×10⁻⁶) is 2.6334×10⁻⁵ option (A) is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have a mathematical expression:
= (46.2×10⁻¹)(5.7×10⁻⁶)
= 46.2×5.7×10⁻⁷
= 263.34×10⁻⁷
= 2.6334×10⁻⁵
Thus, the standard form of the product of the mathematical expression (46.2×10⁻¹)(5.7×10⁻⁶) is 2.6334×10⁻⁵ option (A) is correct.
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Which equation is equivalent to square root x^2+81 =x+10
Answer:
x² +81 = x² +20x +100
Step-by-step explanation:
Square both sides of the original equation:
(√(x² +81))² = (x +10)²
x² +81 = x² +20x +100
I'm terrible at math any help here is appreciated.
Answer:
d. 12 units, 14 units, 10 units
Step-by-step explanation:
The side lengths differ by 2 units from one to the next larger one:
(2t+2) - (2t) = 2
(2t+4) - (2t+2) = 2
So, you're looking for answer numbers that can make a sequence with differences of 2, and that add to 36. Only the last choice matches that description.
_____
You can solve this "directly" by adding up the side lengths and setting that result to the perimeter length.
(2t+2) + (2t+4) + (2t) = 36
6t +6 = 36 . . . . . collect terms
6t = 30 . . . . . . . . subtract 6
t = 30/6 = 5 . . . . divide by 6
The shortest side is 2t, so is 2·5 = 10 units. Only the last answer choice matches this.
Side lengths are 12 units, 14 units, 10 units.
A circle is centered at the point (-7, -1) and passes through the point (8, 7). The radius of the circle is units. The point (-15, ) lies on this circle.
Answer:
Part 1) The radius of the circle is [tex]r=17\ units[/tex]
Part 2) The point (-15,14) and the point (-15,-16) lies on the circle
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
To find the radius of the circle calculate the distance between the center of the circle and the point (8,7)
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex](-7,-1)\\(8,7)[/tex]
substitute
[tex]r=\sqrt{(7+1)^{2}+(8+7)^{2}}[/tex]
[tex]r=\sqrt{(8)^{2}+(15)^{2}}[/tex]
[tex]r=\sqrt{289}[/tex]
[tex]r=17\ units[/tex]
step 2
Find the equation of the circle
The equation of the circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center
r is the radius
substitute
[tex](x+7)^{2}+(y+1)^{2}=17^{2}[/tex]
[tex](x+7)^{2}+(y+1)^{2}=289[/tex]
step 3
Find the y-coordinate of the point (-15.y)
substitute the x-coordinate in the equation of the circle and solve for y
[tex](-15+7)^{2}+(y+1)^{2}=289[/tex]
[tex](-8)^{2}+(y+1)^{2}=289[/tex]
[tex]64+(y+1)^{2}=289[/tex]
[tex](y+1)^{2}=289-64[/tex]
[tex](y+1)^{2}=225[/tex]
square root both sides
[tex](y+1)=(+/-)15[/tex]
[tex]y=-1(+/-)15[/tex]
[tex]y1=-1(+)15=14[/tex]
[tex]y2=-1(-)15=-16[/tex]
therefore
The point (-15,14) and the point (-15,-16) lies on the circle
see the attached figure to better understand the problem
Answer:
plato users the answer is 17 units and (-15,14)
Step-by-step explanation:
The average person drinks 16 ounces of milk a day. At this rate, how many gallons will a person drink in a leap year?
bearing in mind a leap year has 366 days, with February 29th.
[tex]\bf \begin{array}{ccll} ounces&days\\ \cline{1-2} 16&1\\ x&366 \end{array}\implies \cfrac{16}{x}=\cfrac{1}{366}\implies 5856=x[/tex]
that many ounces, how many gallons(US) is that?
well, there are 128 oz in 1 gallon(US), so in 5856 oz there are 5856 ÷ 128 = 45.75 gallons(US).
58.56 gallons of milk,a person will drink in a leap year.
What is leap year?
A Leap Year has 366 days (the extra day is the 29th of February).
How to know if it is a Leap Year:
Leap Years are any year that can be exactly divided by 4 (such as 2016, 2020, 2024, etc)
except if it can be exactly divided by 400, then it is (such as 2000, 2400)
How many galllons will a person drink in a leap year?
We have given,
Average person drinks 16 ounces of milk in 1 day.
We have to find milk consume by average person in 366 days in gallons.
We know, 1 ounce (oz)=0.01 gallons
So, 16 ounce = 16×0.01 gallons
=0.16 gallons
We can say milk consume in one day = 0.16 gallons
Therefore,milk consume in 366 days(in gallons)=366×milk consume in 1 day.
=366×0.16
=58.56 gallons.
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PLEASE HELP ME WITH THIS QUESTION ITS URGENT ITS ABOUT COMPLETING A EQUATION
Answer:
(x - 2)² + (y +8)² = 49
Step-by-step explanation:
Points to remember
Equation of a circle passing through the point (x₁, y₁) and radius r is given by
(x - x₁)² + (y - y₁)² = r ²
To find the radius
It is given that, center of circle = (-5, -8) and passes through the point (2 -8)
By using distance formula,
r = √[(2 --5)² + (-8 --8)²]
= √7²
r = 7
To find the equation of the circle
Here (x₁, y₁) = (2, -8)
Equation of circle is,
(x - x₁)² + (y - y₁)² = r ²
(x - 2)² + (y - (-8))² = 7²
(x - 2)² + (y +8)² = 49
Answer:
The equation of circle is [tex](x+5)^2+(y+8)^2=49[/tex].
Step-by-step explanation:
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex] .... (1)
where, (h,k) is the center of the circle and r is the radius.
It is given that the center of the circle is (-5,-8). it means h=-5 and k=-8.
The circle passes through the point (2,-8). So, the radius of the circle is the distance between point (-5,-8) and (2,-8).
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]r=\sqrt{(2-(-5))^2+(-8-(-8))^2}[/tex]
[tex]r=\sqrt{7^2+0}[/tex]
[tex]r=7[/tex]
Substitute h=-5, k=8 and r=7 in equation (1), to find the equation of circle.
[tex](x-(-5))^2+(y-(08))^2=(7)^2[/tex]
[tex](x+5)^2+(y+8)^2=49[/tex]
Therefore the equation of circle is [tex](x+5)^2+(y+8)^2=49[/tex].
Let f(x) = x + 7 and g(x) = x − 4. Find f(x) ⋅ g(x).
For this case we have the following functions:
[tex]f (x) = x + 7\\g (x) = x-4[/tex]
We must find the product of the functions:
[tex]f (x) * g (x) = (x + 7) (x-4)[/tex]
We apply distributive property:
[tex]f (x) * g (x) = x ^ 2-4x + 7x-28\\f (x) * g (x) = x ^ 2 + 3x-28[/tex]
Finally, the product of the functions is:
[tex]x ^ 2 + 3x-28[/tex]
Answer:
[tex]x ^ 2 + 3x-28[/tex]
NEED HELP WITH A MATH QUESTION
Answer:
[tex]x =18.0[/tex]
Step-by-step explanation:
To solve this problem use the Law of cosine.
The law of cosine says that:
[tex]c^2 = a^2 + b^2 -2abcos(C)[/tex]
In this case we have that:
[tex]c = x\\\\a=30\\\\b=16\\\\C=30\°[/tex]
Therefore
[tex]x^2 = 30^2 + 16^2 -2(30)(16)cos(30\°)[/tex]
[tex]x = \sqrt{30^2 + 16^2 -2(30)(16)cos(30\°)}[/tex]
[tex]x = \sqrt{1156 -831.38}[/tex]
[tex]x = \sqrt{324.62}[/tex]
[tex]x =18.0[/tex]
Two students from a group of eight boys and 12 girls are sent to represent the school in a parade.If the students are chosen at random, what is the probability that the students chosen are not both girls?a. 12/190b. 33/95c. 62/95d. 178/190
Answer:
The probability that the students chosen are not both girls is 62/95 ⇒ (c)
Step-by-step explanation:
* Lets explain how to find the probability of an event
- The probability of an Event = Number of favorable outcomes ÷ Total
number of possible outcomes
- P(A) = n(E) ÷ n(S) , where
# P(A) means finding the probability of an event A
# n(E) means the number of favorable outcomes of an event
# n(S) means set of all possible outcomes of an event
- Probability of event not happened = 1 - P(A)
- P(A and B) = P(A) . P(B)
* Lets solve the problem
- There is a group of students
- There are 8 boys and 12 girls in the group
∴ There are 8 + 12 = 20 students in the group
- The students are sent to represent the school in a parade
- Two students are chosen at random
∴ P(S) = 20
- The students that chosen are not both girls
∴ The probability of not girls = 1 - P(girls)
∵ The were 20 students in the group
∵ The number of girls in the group was 12
∴ The probability of chosen a first girl = 12/20
∵ One girl was chosen, then the number of girls for the second
choice is less by 1 and the total also less by 1
∴ The were 19 students in the group
∵ The number of girls in the group was 11
∴ The probability of chosen a second girl = 11/19
- The probability of both girls is P(1st girle) . P(2nd girl)
∴ The probability of both girls = (12/20) × (11/19) = 33/95
- To find the probability of both not girls is 1 - P(both girls)
∴ P(not both girls) = 1 - (33/95) = 62/95
* The probability that the students chosen are not both girls is 62/95