Answer:
I believe you mean what square number that is less than 100 has the most factors.
The square numbers under 100 are 1, 4, 9, 16, 25, 36, 49, 64, and 81.
1 obviously only factors to 1*1.
4, 9, 25, and 49 are square of prime numbers. If we call the original number n and the root p (for prime) each of them can only be factored as 1*n or p*p. example: 1*4, 2*2 .We can eliminate those.
16 and 81 are not only squares, but the fourth power of a prime (2 and 3) respectively. They can be factored as 1*n, (p^3)*p, or (p^2*p^2). Example: 1*16, 8*2, or 4*4.
But 36 is 2*2*3*3 as it’s prime factoring. This allows us to find more combinations of factors: 1*36, 2*18, 4*9, 12*3, or 6*6.
Final answer:
The largest even square number smaller than 100 is 64, which is the square of 8.
Explanation:
To find an even square number smaller than 100, we can look at the squares of the even numbers less than 10, since 10² (which is 10 times 10) equals 100. Squaring each even number from 2 to 8, we get the following even square numbers: 2²=4, 4²=16, 6²=36, and 8²=64. Among these, 64 is the largest even square number that is less than 100.
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]
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]
in order to come up with a realistic schedule, a manager wants to know how long it usually takes an employee to complete a task. which statistical measurement is the manager most likely to use? A. mean B. median C. mode D. sum
Answer:
A. mean
Step-by-step explanation:
The mean of data is given by the ratio of the sum of all the values to the total number of values. It gives the average value of the set of values.
[tex]\bar{x}=\frac{1}{n}}\left(\sum _{i=1}^{n}{x_{i}}\right)[/tex]
Here, the manager wants to get an estimate of how much time it takes by each employee to complete a task. The mean will be the sum of time taken by each person to complete a task divided by the number of employees.
A vegetable garden and a surrounding path are shaped like a square together are 12 ft wide. The path is 1 feet wide. If one bag of gravel covers 8 square feet, how manu bags are needed to cover the path? Round your answers to the nearest tenth.
Step-by-step answer:
There are two squares, the inner one of which is a garden, surrounded by a path 1 foot wide.
The outer square represents the periphery of the path, as shown in the attached image.
One bag of gravel covers 8 square-feet. Need the number of bags required to cover the path.
Solution:
We first need to find the total area of the path by subtracting the area of garden from the overall area, namely the outer square.
Area of path = 12^2 - 10^2 = 144-100 = 44 sq. ft.
Number of bags required
= area (sq.ft) / area each bag covers
= 44 sq.ft / 8 (sq.ft / bag)
= 5.5 bags
Answer: 6 bags need to be purchased.
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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What is magma? a. The molten mixture of rock-forming substances, gases, and water from the mantle.. c. Hardened lava on the surface of the Earth. b. Liquid rock that reaches the surface. d. All of the above Please select the best answer from the choices provided A B C D
Answer: A. The molten mixture of rock-forming substances, gases, and water from the mantle
Magma is a mass of molten rock that is found in the deepest layers of the Earth at high temperature and pressure, and that can flow out through a volcano.
The composition of this mass is a mixture of liquids, volatile and solids that when they reach the surface in an eruption becomes lava, which when cooled crystallizes and gives rise to the formation of igneous rocks.
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?)
Please answer this question correctly for 35 points and brainliest!!
Answer:
11
Step-by-step explanation:
49-5=44
44/4=11
how much larger then 1/4 mile is 9/10 mile please show work
Answer:
13/20 = 0.65 mile
Step-by-step explanation:
Finding the difference of two fractions is usually done by first expressing each of them using a common denominator. Here, both 4 and 10 are factors of 20, so 20 is a suitable common denominator.
9/10 - 1/4 = 18/20 - 5/20 = (18 -5)/20 = 13/20
This can be expressed as a decimal:
13/20 = (13·5)/(20·5) = 65/100 = 0.65
9/10 of a mile is 13/20 of a mile larger than 1/4 of a mile. In decimal, that is 0.65 miles larger.
Which function has an inverse that is a function?
A. b(x)=x^2+3
B. d(x)=-9
C. -7x
D. p(x)=lxl
Answer:
C. -7x
Step-by-step explanation:
Only one of the offered choices passes the horizontal line test: at most one point of intersection with any horizontal line.
__
A: a parabola opening upward, so will have two points of intersection with a general horizontal line (only one at the vertex).
B: a horizontal line, so will have an infinite number of points of intersection with a horizontal line.
D. A "V-shaped" graph that will generally have two points of intersection with a horizontal line (only one at the vertex).
Answer:
m(x)=-7x C
Step-by-step explanation:
Edge
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:
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.
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 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.
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
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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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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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
Which circle shows AB that measures 60 degrees?
I say the third circle from the top down. The central angle is the measure of minor arc AB.
The central angle here is 60 degrees, shown by the third circle down from the top. This is the right answer.
The circle that shows chord AB to measure 60 degrees is Option(C).
What is minor chord ?A chord of a circle divides the circle into two regions, which are called the segments of the circle. The minor chord is the shorter arc connecting two endpoints on a circle . The measure of a minor chord is always less than 180° .
How to identify chord AB to measure 60° ?In the four Options given alongside diagram, Option(C) represents a minor chord with its central angle subtended by the minor segment as 60°.
Thus AB is the minor sector of the circle and the angle measures 60° with that chord itself. The other three options do not define the minor chord or segment AB therefore not measuring its central angle.
Therefore, the circle that shows chord AB to measure 60 degrees is Option(C).
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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 group of numbers arranged in a specific order is called a sequence. Create two groups of numbers- one that can be classified as a sequence and another that cannot. Use complete sentences to differentiate between the two groups of numbers. In your final answer, include both groups of numbers and your explanation.
Answer:
1, 3, 6, 7, 9...
1, 4, 8, 7, 11...
Step-by-step explanation:
(1, 3, 6, 7, 9...)
This one is the sequence because it follows a specific pattern, which is 2n-1, or (2 x figure number) - 1. 1x2-1=1. 2x2-1=3. 3x2-1=7. And so on.
(1, 4, 8, 7, 11...)
This one, no matter how you look at it, has no pattern. Its not a proper sequence of numbers.
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].
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.
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]
what is the exponential form of log5 9 = x?
Step-by-step explanation:
log₅ 9 = x
5^(log₅ 9) = 5^x
9 = 5^x
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:
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°).
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:
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]
The total cost to rent a row boat is $14 times the number of hours the boat is used. Write an equation to model this situation if c= total cost and h= number of hours.
Answer:
14h=c
Step-by-step explanation:
14 times total hours boat of used (h) is the total cost of the boat > 14h=c