Which of the following is a statistical question that can result in numerical data?
What is the name of the librarian at your local library?
Which park is the best one to take your dogs to play?
What is the name of a local farm in your area?
How many students at your school ride horses?
what type of number is 15/10?
Answer:
1.5
Step-by-step explanation:
its a decimal number
Answer: the number 15/10 is a fraction.
Step-by-step explanation:
any two numbers that have a slash in the middle are fractons. :)
what are the coordinates of the point that corresponds to -5pi/4 on the unit circle
The coordinates of the point that corresponds to -5π/4 on the unit circle is (-1/√2, 1/√2).
Given that,
We have to find the coordinates of the point that corresponds to -5π/4 on the unit circle.
We know that any point on the unit circle can be defined as,
(cos θ, sin θ)
where θ is the angle formed with the X axis.
-5π/4 will be the point the corresponds to -225°.
Cos(-5π/4) = cos (5π/4)
= cos (π + π/4)
= -cos (π/4)
= -1/√2
sin (-5π/4) = -sin (5π/4)
= -sin (π + π/4)
= sin (π/4)
= 1/√2
Hence the coordinate of the unit circle is (-1/√2, 1/√2).
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a rock is thrown straight up with an initial velocity of 3m/s. The mass of the rock is approximately 0.2kg. Air resistance acts on the rock with a force numerically equal to 0.5v where v is the velocity of the rock. Acceleration due to gravity is 9.8 m/s^2. Set up and solve a differential equation to find the velocity of the rock as a function of time
The velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
The forces acting on the rock are the force due to gravity and the force due to air resistance. The force due to air resistance is given by 0.5v, where v is the velocity of the rock.
The force due to gravity is given by the mass of the rock (0.2 kg) times the acceleration due to gravity [tex](9.8 m/s^2)[/tex]. Using Newton's second law, we can set up the following differential equation:
[tex]m(dv/dt) = -mg - 0.5v[/tex]
where m is the mass of the rock, g is the acceleration due to gravity, and v is the velocity of the rock as a function of time t.
We can simplify this differential equation by dividing both sides by m:
[tex]dv/dt = (-g - 0.5v/m)v[/tex]
This is a separable differential equation, which we can solve using the separation of variables:
[tex](1/(-g - 0.5v/m)) dv = dt[/tex]
Integrating both sides gives:
[tex]-2ln(-g - 0.5v/m) = t + C[/tex]
where C is a constant of integration.
Solving for v gives:
[tex]v(t) = -0.5mg + C'exp(-2t/m)[/tex]
where C' = exp(C).
We can find the value of C' using the initial condition that the initial velocity of the rock is 3 m/s:
[tex]v(0) = -0.5mg + C' = 3[/tex]
[tex]C' = 0.5mg + 3[/tex]
Substituting this into the equation for v(t) gives:
[tex]v(t) = -0.5mg + (0.5mg + 3)exp(-2t/m)[/tex]
Therefore, the velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
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2y+3y-18=-83?????????????
Answer:
-13
Step-by-step explanation:
Consider the line y=8x-7
Find the equation of the line that is parallel to this line and passes through the point (5,-3)
Find the equation of the line that is perpendicular to this line and passes through the point (5,-3)
Answer:
Parallels lines:
y = 8x - 43
Perpendicular line:
y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]
Step-by-step explanation:
y = 8x -7
Parallel lines have the same slope.
The slope will be 8. We will use the x from the point (5,-3) and the y from the point (5,-3) to find the y-intercept (b)
y = mx + b Substitute in -3 for y, 8 for m, and 5 for x.
-3 = 8(5) + b
-3 = 40 + b Subtract 40 from both sides
-3 - 40 = 40 - 40 + b
-43 = b
Substitute in 8 for m and -43 for b to write the equation
y = mx + b
y = 8x - 43
Perpendicular slope are opposite reciprocals of each other, so the perpendicular slope is [tex]\frac{-1}{8}[/tex]
Substitute [tex]\frac{-1}{8}[/tex] doe m, -3 for y and 5 for x.
y = mx + b
-3 = [tex]\frac{-1}{8}[/tex](5) + b
-3 = [tex]\frac{-5}{8}[/tex] + b add [tex]\frac{5}{8}[/tex] from both sides
-3 + [tex]\frac{5}{8}[/tex] = [tex]\frac{-5}{8}[/tex] + [tex]\frac{5}{8}[/tex] + b
[tex]\frac{-24}{8}[/tex] + [tex]\frac{5}{8}[/tex] = b
[tex]\frac{-19}{8}[/tex] = b
Substitute [tex]\frac{-1}{8}[/tex] for m and [tex]\frac{-19}{8}[/tex] for b
y = mx + b
y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]
Helping in the name of Jesus.
sketch the graph of each function.
22. g(x)= -2x³-8x2 +18x+72
The graph of the cubic equation is in the equation of the end.
How to sketch the graph of the function?To do it, we need to find some points that are solutions of the equation. Then we can graph these points on a coordinate axis and then connect these points with a curve proper of a cubic relation.
when x = 0
g(0) = -2*0³-8*0² +18*0+72 = 72
So we have the point (0, 72)
when x = 1
g(1) = -2*1³-8*1² +18*1+72
= -2 - 8 + 18 + 72 = 80
So we have the point (1, 80)
when x = -1
g(-1) = -2*-1³-8*-1² +18*-1+72
= 2 - 8 - 18 + 72 = 48
(-1, 48)
And so on, when you have enough points, you can connect them. The graph that should you get is one like the graph in the image at the end.
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11. Which of the following are not meaningful?
(b) XXXI
(a) VXXIX
(C) XLIV
12. Write 'Divide the difference of 91 and 7 by 6' using brackets and solve.
(d) CXCLXV
Prove by mathematical induction that:
[tex]2 + 4 + 8 + ... + {2}^{n} = {2}^{n + 1} - 2 [/tex]
By the principle of mathematical induction, the statement holds for all positive integers n.
How did we arrive at this assertion?Using mathematical induction:
Base case:
For n=1, results into:
2 = 2^2 + 1 - 2
which is true.
Inductive step:
For some positive integer k, we have:
2+4+8+...+2^k = 2^(k+1) + 1 - 2
This implies the statement for n=k+1, i.e.,
2+4+8+...+2^k+2^(k+1) = 2^(k+2) + 1 - 2
From the left-hand side of the equation, we can rewrite it as:
2+4+8+...+2^k+2^(k+1) = (2+4+8+...+2^k) + 2^(k+1)
Applying the induction hypothesis, substitute the expression for 2+4+8+...+2^k:
2+4+8+...+2^k+2^(k+1) = (2^(k+1) + 1 - 2) + 2^(k+1)
Simplify:
2+4+8+...+2^k+2^(k+1) = 2^(k+2) - 1
Using the formula for the sum of a geometric series to simplify the right-hand side of the original statement:
2^(k+2) + 1 - 2 = 2^(k+2) - 1
Thus, the statement holds for n=k+1, supposing it holds for n=k. By the principle of mathematical induction, the statement holds for all positive integers n.
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Need help with this 50 Points
Answer:
8.) is D
9.) is B
10.) is A
Step-by-step explanation:
mark brainliest
Answer: D, B, A
Step-by-step explanation:
When multiplying or dividing - and + numbers, rules are as follows:
If the signs are the same, your answer will be +
[tex]\frac{-a}{-b} =+\frac{a}{b}[/tex]
[tex]\frac{+a}{+b} =+\frac{a}{b}[/tex]
If the signs are different, your answer will be -
[tex]\frac{-a}{+b} =-\frac{a}{b}[/tex]
[tex]\frac{+a}{-b} =-\frac{a}{b}[/tex]
If there is no sign in front of number, it is positive
8.
a. 18 / -9 = -2 negative because signs are diff
b. -35 / -7 +5 signs same so +
c. -12 / -6 = +2 same signs so +
d. 70 / -10 = -7 diff signs so -
Order from least to greatest:
-7 -2 2 5
Answer: D
9. Follow rules from above:
Be careful with fractions 1/5 is not the same as 5/1.
With the fraction problems they do not divide into the number because 1 cannot be divided by 5 evenly, leave as a fraction and we are only taking care of the signs.
a. +1/5
b. -1/5
c. +1/10
d. +1/10
Order from least to greatest:
-1/5 1/5 1/10 1/10
Answer: B
10.
a. -2/3
b. +1/25
c. +3/25
d. +1/50
The smallest number is the negative number
Answer A
Which of the following has the polar coordinates negative five comma two pi over 3
Options:
Q
R
U
W
Use the graph of g(x) to answer the following question. The graph of g(x) is a translation of f(x)=x^2 Write the equation for g(x) in vertex form.
The equation for g(x) in vertex form is g(x) = (x - 2)^ + 3
Writing the equation for g(x) in vertex form.From the question, we have the following parameters that can be used in our computation:
The graph of g(x)
Also, we have
The graph of g(x) is a translation of f(x)=x^2
From the graph, we can see that
Using the above as a guide, we have the following:
g(x) = f(x - 2) + 3
Substitute the known values in the above equation, so, we have the following representation
g(x) = (x - 2)^ + 3
Hence, the equation for g(x) in vertex form is g(x) = (x - 2)^ + 3
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Find the area of the triangle:
(Please show work so I can learn how to do it)
Step-by-step explanation:
Area of a traingle = 1/2 * base * height
area = 1/2 * 6 * 4 = 12 cm^2
3x+10<3 or 2x-5 ≥ 5 solve the inequality
Answer: x is greater than or equal to 5 (I can't put the symbol in)
Step-by-step explanation:
Add 5 to both sides then simplify, which will get you 2x is greater than or equal to 10, then divide by 2.
Answer:
Step-by-step explanation:
3x+10<3
3x<3-10
3x<-7
x<-7/3
2x-5≥5
2x≥5+5
2x≥10
x≥10/2
x≥5
so x<-7/3 or x≥5
POSSIBLE POINTS: 10
Find the area of the composite figure below. Area of Triangle = bh, Area of Rectangle = lb Use Pythagorean formula to find the length () of the
Rectangle.
7 mm
10.4 mm
15.3 mm
The total surface area of the composite figure is: 288.62 mm²
What is the area of the composite figure?From the attached image, we can see that the composite figure is made up of 2 triangles and one rectangle. Thus:
Formula for area of rectangle is:
A = Length * Width
Formula for area of triangle is:
A = ¹/₂ * base * height
Using Pythagoras theorem, length of rectangle is:
L = √(10.4² + 15.3²)
L = 18.5 mm
Thus:
TSA = (18.5 * 7) + 2(¹/₂ * 15.3 * 10.4)
TSA = 129.5 + 159.12
TSA = 288.62 mm²
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Solve (x+1)2 =13/4 using the square root property
Answer:
Starting with the equation:
(x + 1)^2 = 13/4
We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.
Taking the square root of both sides, we get:
x + 1 = ±√(13/4)
Simplifying under the radical:
x + 1 = ±(√13)/2
Now we can solve for x by subtracting 1 from both sides:
x = -1 ± (√13)/2
Therefore, the solutions to the equation are:
x = -1 + (√13)/2 or x = -1 - (√13)/2
Step-by-step explanation:
Calculator
What is the volume of this figure?
Enter your answer in the box.
ft³
4
3 ft
5 ft
6 ft
7 ft
2 ft
Answer:
The answer should be 1,260
Answer:
75
Step-by-step explanation:
.
The distance between cities A and B on a map is 12.5 in. The distance from city B to city C, is 8.5 in, and the distance from C to A is 16.25 in. If the bearing
from A to B is N75°E, find the bearing from C to 4. Round to the nearest tenth of a degree.
Answer:
90
Step-by-step explanation:
Answer:
It seems like the chat transitioned to a different topic. However, based on the search results, it appears that the query was related to solving distance problems using linear equations. One common application of linear equations is in distance problems, where you can create and solve linear equations to find the distance between two points or the rate of travel. Here's an example problem:
Joe drove from city A to city B, which are 120 miles apart. He drove part of the distance at 60 miles per hour (mph) and the rest at 40 mph. If the entire trip took three hours, how many miles did he drive at each speed?
To solve this problem, you can use a system of two linear equations. Let x be the number of miles driven at 60 mph, and y be the number of miles driven at 40 mph. Then you have:
x + y = 120 (total distance is 120 miles) x/60 + y/40 = 3 (total time is 3 hours)
To solve for x and y, you can multiply the second equation by 120 to eliminate fractions and then use the first equation to solve for one of the variables. For example:
x/60 + 3y/120 = 3 x/60 + y/40 = 3 2x/120 + 3y/120 = 3 x/60 + y/40 = 3 x/60 = 3 - y/40 x = 180 - 3y/2 (from the first equation)
Substitute the expression for x into the second equation and solve for y:
x/60 + y/40 = 3 (180 - 3y/2)/60 + y/40 = 3 3 - 3y/160 + y/40 = 3 3 - 3y/160 = 2.75 -3y/160 = -0.25 y = 20
Substitute y = 20 into the expression for x to get:
x = 180 - 3y/2 x = 120
Therefore, Joe drove 120 - 20 = 100 miles at 60 mph and 20 miles at 40 mph.
Step-by-step explanation:
Pls help
The shape below contains a rectangle and four semi-circles.
Round your responses to two decimal places.
What is the perimeter of the shape above?
What is the area of the shape above?
Answer:
perimeter: 47.12 unitsarea: 151.60 square unitsStep-by-step explanation:
You want the perimeter and area of a figure consisting of a 4 × 11 rectangle with semicircles attached to each straight edge.
PerimeterIf you trace the perimeter of the figure, you see you are tracing the circumference of a circle 4 units in diameter and the circumference of a circle that is 11 units in diameter. The circumference of a circle is given by ...
C = πd
so the total circumference is ...
C1 +C2 = π(4) +π(11) = π(4+11) ≈ 47.12 . . . . units
The perimeter of the figure is about 47.12 units.
AreaThe area of two half-circles is the area of one whole circle of the same diameter. The area of a circle of diameter d is given by ...
A = (π/4)d²
The total area of the circles of diameters 4 and 11 is ...
A1 +A2 = (π/4)·4² +(π/4)·11² = (π/4)(4² +11²)
The area of the central rectangle is added to the areas of the semicircles. Its area is ...
A = LW
A = (11)(4)
TotalThe area of the entire figure is the sum of the circle areas and the rectangle area:
total area = (π/4)(4² +11²) +(4)(11) ≈ 151.60 . . . . square units
The area of the figure is about 151.60 square units.
__
Additional comment
You usually see the formula for the area of a circle as ...
A = πr²
Since r = d/2, we can express this using d as ...
A = π(d/2)² = π(d²)/(2²) = (π/4)d²
You may notice that a square that circumscribes the circle will have a side length of d, and an area of d². The fraction π/4 tells you the fraction of that enclosing square that is covered by the circle. This fact can help you estimate areas and volumes of circles and cylinders.
Pls help Thanks!!!!!!!!!!!
Answer:
Put your calculator in degree mode.
[tex] \cos(x) = \frac{12}{13} [/tex]
[tex]x = {cos}^{ - 1} \frac{12}{13} = 22.6[/tex]
Angle x measures 22.6°.
Use mathematical induction to prove that the statement is true for all positive integers: 30 + 138 + 318...
The mathematical induction has been used to prove that the statement is true for all positive integers: 30 + 138 + 318.
What is mathematical induction?In mathematics, mathematical induction is a way of proving propositions. The method entails demonstrating that a statement is true for a base case, usually the smallest feasible value, and then demonstrating that if the statement is true for some value, it is likewise true for the next value.
The key to the proof is the inductive step. It is typically accomplished by assuming that the statement is true for some value and then utilizing that assumption to establish that the statement is true for the following value.
Check the attachment.
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Find the surface area of the prism
The surface area of the triangular prism is 70.2 yd²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as ;
SA = 2B +ph
where h is the height,
B is the base area and
p is the perimeter of the base
Base area = 1/2 bh( since the base Is a triangle)
Base area = 1/2 × 3 ×3 = 4.5yd²
The other side of the triangle is calculated as;
x= √ 3²+3²
x = √9+9
x = √18
x = 4.2
Therefore perimeter = 4.2 + 3+3 = 10.2yds
SA = 2× 4.5 + 10.2 × 6
SA = 9 + 61.2
SA = 70.2 yd²
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You invest $4000 in an account to save for college.
a. Option 1 pays 5% annual interest compounded semi-annually. What would
be the balance in the account after 2 years?
b. Option 2 pays 4.5% annual interest compounded continuously. What would
be the balance in the account after 2 years?
c. At what time t (in years) would Option 1 give you $100 more than Option 2?
The answers to the given questions about annual interest are given below:
a. $4,415.25b. $4,376.70c. 2.27986 yearsHow to solvea.
A = 4,000 (1 + 0.05/2)^(2 x 2)
= $4,415.25
b.
A = 4,000 x e^(0.045 x 2)
= $4,376.70
c. $100 more than option 2 = 4,376.70 + 100
= $4,476.70
t (in years) = ln(4,476.70/4,000) / ln(1 + 0.05/2)
= 2.27986 years
Annual interest denotes the rate of interest levied or gained on a loan or investment for a duration of one year. This indicates the portion, expressed as a percentage, of the original amount that is utilized for interest payments or gained as a profit within a twelve-month period.
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Can someone help me please
The expansion and simplification of the expression (x - 2)² is x² - 4x + 4.
What is an expression?An algebraic expression is a combination of variables with constants, numbers, and values using the mathematical operands addition, subtraction, multiplication, or division.
Algebraic Expression:(x - 2)²
Expanding the square:
(x - 2)² = (x - 2)(x -2)
Distributing the square:
x(x - 2) - 2(x - 2)
x² - 2x - 2(x -2)
x² - 2x - 2x + 4
Solution:x² - 4x + 4
Thus, after expanding and simplifying the algebraic expression (x - 2)², the solution is x² - 4x + 4.
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I am unsure about how to do this problem, pictured below.
Answer:
Step-by-step explanation:
150/2 = 75
500/75 = 6.6666666667 hours
it will take 6.2/3 hours to reach 500 bacteria cells
NOT SURE ABOUT EXPERSION BUT YOU COULD TRY THIS
p = 75t
Given that a culture of bacteria grows at a rate proportional to its size. Where the culture starts with 50 cells, then grows 150 after time, "t" equals 2 hours.
We are asked to:
> (a) Find an expression, P(t), to model the number of cells present after "t" hours.
> (b) Determine the time at which the population is at 500 cells.
For part (a):
Since the culture of bacteria grows at a rate proportional to its size, we can model it as the following differential equation.
[tex]\Rightarrow \frac{dP}{dt}=kP; \ Where \ P =P_0 \ at \ t=0 \ and \ P=3P_0 \ at \ t=2[/tex]
Solve the first-order separable differential equation with the given initial condition.
[tex]\Longrightarrow \frac{dP}{dt}=kP \Longrightarrow \frac{1}{P}dP=kdt \Longrightarrow \int\limits {\frac{1}{P} } \, dP=\int\ {k} \, dt \Longrightarrow ln(P)=kt+c[/tex]
[tex]\Longrightarrow e^{ln(P)}=e^{kt}+e^{c} \Longrightarrow P=ce^{kt}[/tex]
Plug in the initial condition.
[tex]\Longrightarrow P_0=ce^{k(0)} \Longrightarrow P_0=c(1) \Longrightarrow \boxed{c=P_0}[/tex]
[tex]\Longrightarrow P=ce^{kt} \Longrightarrow \boxed{P=P_0e^{kt}}[/tex]
Use the second initial condition to find "k."
[tex]\Longrightarrow 3P_0=P_0e^{k(2)} \Longrightarrow 3=e^{k(2)} \Longrightarrow 3=e^{2k} \Longrightarrow ln(3)=ln(e^{2k})[/tex]
[tex]\Longrightarrow k=\frac{ln(3)}{2} \Longrightarrow \boxed{k \approx 0.5493}[/tex]
Thus, the equation to model the situation is,
[tex]\boxed{\boxed{P(t)=50e^{0.5493t}}} \therefore Sol.[/tex]
For part (b):
[tex]P=10P_0[/tex]
[tex]\Rightarrow 10P_0=P_0e^{0.5493t} \Longrightarrow 10=e^{0.5493t} \Longrightarrow ln(10)=ln(e^{0.5493t})[/tex]
[tex]\Longrightarrow ln(10)=0.5493t \Longrightarrow t=\frac{ln(10)}{0.5493} \Longrightarrow \boxed{t=4.192 \ hrs}[/tex]
Thus, the time it takes the population to reach 500 is approx. 4.192 hours.
Question 4 A study has been conducted to compare male and female test performance on a standardised science exam. In this hypothetical study, the researchers reported with a sample size of n = 50, the 95% confidence interval was found to be between 0.15 and 0.55.
What would happen to the 95% confidence interval if the sample size was increased?
The 95% confidence interval would remain the same Cannot be determined from the information provided The 95% confidence interval would decrease The 95% confidence interval would increase
If the sample size was increased, the 95% confidence interval would decrease. A larger sample size would provide more precise and accurate data, resulting in a narrower confidence interval.
A confidence interval is a range of values within which a population parameter is estimated to lie with a certain level of confidence. It is commonly used in statistical inference to estimate the true value of a population parameter based on a sample from that population.
If the sample size was increased, the 95% confidence interval would likely decrease. This is because a larger sample size typically leads to more precise estimates and less variability in the data, resulting in a narrower confidence interval. However, the exact size of the decrease would depend on various factors such as the amount of variability in the data and the level of statistical significance chosen for the study.
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Find the amount in the account for the given principal, interest rate, time, and compounding period. P = $700, r=7%, t=8 years; compounded quarterly
Answer:
$1092
Step-by-step explanation:
What meaning of the statement this?
We can see here that the statement means that H is a subgroup of a group, and aЄ H is an element of that subgroup.
What is a mathematical statement?We can define a mathematical statement to be a claim that, depending on the circumstances, may be true or false. It frequently incorporates mathematical objects and their relationships or characteristics, such as integers, sets, functions, or geometric shapes.
We can see here that it shows that a is an element of the subgroup of H.
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I'm needing help with setting up these equations
The sides show that we have an equilateral triangle
What is the measure of each of the sides?An equilateral triangle is a triangle in which all three sides are of equal length. Since all three sides are equal, all three angles are also equal and measure 60 degrees each.
We know that;
12x - 22 = 10x - 6
Collect like terms;
12x - 10x = -6 + 22
2x = 16
x = 8
Thus the sides of the triangle are;
12(8) - 22 = 74
10(8) - 6 = 74
7(8) + 18 = 74
In the second triangle;
4x - 25 = x + 14
4x - x= 14 + 25
3x = 39
x = 13
Thus the sides are;
4(13) - 25 = 27
13 + 14 = 27
6(13) - 51 = 27
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Find the multiplying integers -2x24=
The multiplying integers -2x24= -48
Multiplication of Integers:Here is some rules of multiplication of integers:
1. Positive integer × negative integer = negative.
2. Positive integers × Positive integers = positive.
3. Negative integers × Negative integers = positive.
Here, To find the the multiplying integers
-2x24 = -48
When you multiply integers :
Negative x Positive = Negative
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