To evaluate the limit of f(x) as x approaches 3 from the left, we substitute the value of x that is slightly less than 3 into the first part of the piecewise function. Therefore[tex], lim f(x)[/tex]as x approaches 3- is equal to lim (3 - 2 + x) as x approaches 3-. Simplifying further, we get lim f(x) as x approaches 3- = 3 - 2 + 3 = 4.
To evaluate the limit of f(x) as x approaches 3 from the right, we substitute the value of x that is slightly greater than 3 into the second part of the piecewise function. Therefore, lim f(x) as x approaches 3+ is equal to lim (4 - x) as x approaches 3+. Simplifying further, we get lim f(x) as x approaches 3+ = 4 - 3 = 1. Now, to determine whether the function f is continuous at x = 3, we compare the left-hand limit[tex](lim f(x)[/tex]as x approaches 3-) and the right-hand limit [tex](lim f(x)[/tex] as x approaches 3+).
If the two limits are equal and the function value at x = 3 (f(3)) is equal to the limits, then the function is continuous at x = 3. In this case, the left-hand limit is 4, the right-hand limit is 1, and the function value at x = 3 is not given. Since the left-hand and right-hand limits are not equal, the function f is not continuous at x = 3.
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What are independent variables and dependent variables when
conducting a research design to investigate the impact of a school
nutrition program on grade performance of students at high
school?
Independent variables are the factors that are manipulated or controlled by the researcher in a study. In the context of investigating the impact of a school nutrition program on grade performance of high school students, the independent variable would be the school nutrition program itself.
The researcher would design and implement the program, and this variable would be under their control.
Dependent variables, on the other hand, are the outcomes or variables that are measured in a study and are expected to change as a result of the independent variable. In this case, the dependent variable would be the grade performance of the students. The researcher would collect data on the grades of the students before and after the implementation of the nutrition program, and this would be the variable that is expected to be influenced by the independent variable.
In summary, the independent variable in this research design is the school nutrition program, while the dependent variable is the grade performance of the students. The researcher would manipulate the independent variable (implement the nutrition program) and then measure the dependent variable (student grades) to determine if there is an impact of the program on grade performance.
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These are my last point I’ve been trying to get someone to answer this :(
Answer:
[tex]\huge\boxed{\text{(C), (D), and (E)}}[/tex]
Step-by-step explanation:
We can use basic angle relationships to find which statements are true.
Since we know that the horizontal line is being intersected by two vertical lines that are parallel, we know the corresponding angles are equivalent.
A can’t be true because alternate exterior angles come from the same line. 4 and 7 are from two different lines.
B can’t be true because the 50° angle and 1 and 2 are supplementary. In order for 1 and two to be complementary, the 50° angle would have to be 90°. So this isn’t true.
C must be true because angles 8 and 5 come together to form one of the parallel lines that intersects the horizontal line. Since it’s a line intersection, the two angles must be supplementary.
D must be true because we have two angles that are formed by parallel lines intersecting the same line. Since the lines are parallel, the angles on either side are equivalent. These are called corresponding angles.
E must be true because the angles are equivalent to each other. 5 and 7 are equivalent, and so are 8 and 6. Therefore, these are vertical angles.
Hope this helped!
Jadia was at the state fair from 8:45 AM until 11:00 AM. How much time did Jada spend at the state fair?
Answer: 2 hours 45 minutes
Step-by-step explanation: Your welcome
tStep-by-step explanation:
Mr. Johnson is driving to Flagstaff at a constant speed. He plans on getting there in 3 hours. If the distance from his home is 246 miles, what should be his rate of change?
____ miles per hour.
Answer: 82 miles per hour
Step-by-step explanation:
246/3
82 miles per hours
Answer:
82 miles per hour
Step-by-step explanation:
246/3
Hi hope your having a good day please answer this
2 1/6 − 11/15x=0.15
please solve for x asap
x=
44
------ <-------- fraction
201
=4.568
Step-by-step explanation:
Darcy and Harper work for different catering companies. Darcy earns a weekly salary of $982 and an 18% commission on her food
sales. Harper earns a weekly salary of $807 and a 25% commission: What amount of food sales will result in Darcy and Harper
earning the same amount for the week?
Answer:
$2500
Step-by-step explanation:
Given that:
Darcy's weekly earning = $982 plus 18% commission on food sales
Harper's weekly earning = $807 plus 25% commision
amount of food sales will result in Darcy and Harper earning the same amount for the week
Let amount of food sales = f
Darcy's earning = Harper's earning
(982 + 18%*f) = (807 + 25% * f)
(982 + 0.18f) = (807 + 0.25f)
982 + 0.18f = 807 + 0.25f
982 - 807 = 0.25f - 0.18f
175 = 0.07f
f = 175 / 0.07
f = 2500
Hence amount of food sales that will result in both Darcy and Harper earning the same amount = $2500
Please please help me!!
Answer:
D because it’s D
x+2-3=7
x-1=7
x=8
Answer:Eight 8 8 The answer is 8
Step-by-step explanation:
Se encontro que la arista de un cubo es de 30cm, con un posible error en la medicion de 0.1. Utilice diferenciales para estimar el error maximo posible, el error relativo y el porcentaje de error al calcular a) el volumen del cubo b) el area superficial del cubo
Answer:
a) El error máximo posible es 270 centímetros cúbicos. El error relativo asociado al volumen es 0.01. El error asociado al volumen es 1 por ciento.
b) El máximo error posible del área superficial es 36 centímetros cuadrados. El máximo error posible del área superficial es 36 centímetros cuadrados. El porcentaje de error del área superficial es 0.667 por ciento.
Step-by-step explanation:
Recordemos que el volumen y el área superficial de un cubo quedan representados por las respectivas fórmulas:
[tex]V = l^{3}[/tex] (Ec. 1)
[tex]A_{s} = 6\cdot l^{2}[/tex] (Ec. 2)
Donde:
[tex]l[/tex] - Longitud de la arista, medida en centímetros.
[tex]A_{s}[/tex] - Área superficial, medida en centrímetros cuadrados.
[tex]V[/tex] - Volumen, medido en centímetros cúbicos.
a) El error máximo posible del volumen del cubo se estima por el siguiente diferencial:
[tex]\Delta V = \frac{\partial V}{\partial l}\cdot \Delta l[/tex] (Ec. 3)
Donde:
[tex]\Delta V[/tex] - Error máximo posible del volumen, medido en centímetros cúbicos.
[tex]\frac{\partial V}{\partial l}[/tex] - Primera derivada parcial del volumen con respecto a la longitud de la arista, medida en centrímetros cuadrados.
[tex]\Delta l[/tex] - Error máximo de medición, medido en centímetros.
La derivada parcial de la función de volumen es:
[tex]\frac{\partial V}{\partial l} = 3\cdot l^{2}[/tex] (Ec. 4)
Ahora expandimos (Ec. 3):
[tex]\Delta V = 3\cdot l^{2}\cdot \Delta l[/tex]
Si conocemos que [tex]l = 30\,cm[/tex] y [tex]\Delta l = 0.1\,cm[/tex], el máximo error posible del volumen es:
[tex]\Delta V = 3\cdot (30\,cm)^{2}\cdot (0.1\,cm)[/tex]
[tex]\Delta V = 270\,cm^{3}[/tex]
El error máximo posible del volumen es 270 centímetros cúbicos.
Obtenemos el error relativo al dividir el resultado anterior por el volumen, es decir:
[tex]\epsilon_{V} = \frac{\Delta V}{V}[/tex] (Ec. 5)
El volumen del cubo es: ([tex]l = 30\,cm[/tex])
[tex]V = (30\,cm)^{3}[/tex]
[tex]V = 27000\,cm^{3}[/tex]
Ahora sustituimos (Ec. 5):
[tex]\epsilon_{V} = \frac{270\,cm^{3}}{27000\,cm^{3}}[/tex]
[tex]\epsilon_{V} = 0.01[/tex]
El error relativo asociado al volumen es 0.01.
Por último, encontramos el porcentaje de error asociado al volumen:
[tex]\%\epsilon_{V} = 0.01\times 100\,\%[/tex]
[tex]\%\epsilon_{V} = 1\,\%[/tex]
El error asociado al volumen es 1 por ciento.
b) El error máximo posible del área superficial del cubo se estima por el siguiente diferencial:
[tex]\Delta A_{s} = \frac{\partial A_{s}}{\partial l}\cdot \Delta l[/tex] (Ec. 6)
Donde:
[tex]\Delta A_{s}[/tex] - Error máximo posible del área superficial, medido en centímetros cuadrados.
[tex]\frac{\partial A_{s}}{\partial l}[/tex] - Primera derivada parcial del área superficial con respecto a la longitud de la arista, medida en centrímetros.
[tex]\Delta l[/tex] - Error máximo de medición, medido en centímetros.
La derivada parcial de la función de área superficial es:
[tex]\frac{\partial A_{s}}{\partial l} = 12\cdot l[/tex] (Ec. 7)
Ahora expandimos (Ec. 6):
[tex]\Delta A_{s} = 12\cdot l\cdot \Delta l[/tex]
Si conocemos que [tex]l = 30\,cm[/tex] y [tex]\Delta l = 0.1\,cm[/tex], el máximo error posible del área superficial es:
[tex]\Delta A_{S} = 12\cdot (30\,cm)\cdot (0.1\,cm)[/tex]
[tex]\Delta A_{S} = 36\,cm^{2}[/tex]
El máximo error posible del área superficial es 36 centímetros cuadrados.
Obtenemos el error relativo al dividir el resultado anterior por el volumen, es decir:
[tex]\epsilon_{A_{S}} = \frac{\Delta A_{S}}{A_{S}}[/tex] (Ec. 8)
El área superficial del cubo es: ([tex]l = 30\,cm[/tex])
[tex]A_{S} = 6\cdot (30\,cm)^{2}[/tex]
[tex]A_{S} = 5400\,cm^{2}[/tex]
Ahora sustituimos (Ec. 8):
[tex]\epsilon_{A_{S}} = \frac{36\,cm^{2}}{5400\,cm^{2}}[/tex]
[tex]\epsilon_{A_{S}} = 6.667\times 10^{-3}[/tex]
El error relativo del área superficial es 6.667 × 10⁻³.
Por último, encontramos el porcentaje de error asociado al área superficial:
[tex]\%\epsilon_{A_{S}} = 6.667\times 10^{-3}\times 100\,\%[/tex]
[tex]\%\epsilon_{A_{S}} = 0.667\,\%[/tex]
El porcentaje de error del área superficial es 0.667 por ciento.
I need help plz help me
Answer:
$38.10
Step-by-step explanation:
because -46.90+86 is 38.1
ur welcome!
pls marbeanibrainliest!
what is the slope of the line??
{math}
Answer:
A
Step-by-step explanation:
From 0 the graph goes up 1 and to the right 2 times
Rise over run
1/2
High Hopes^^
Barry-
Equation of straight line is given by
y = mx + cy denotes y coordinate
x denotes x coordinate
m denotes slope
c denotes intercept
ATQ,
y = 5 when x = 10Intercept (c) = 0⭆ y = mx + c
⭆ 5 = m(10) + 0
⭆ 5 = 10m
⭆ m = 5/10
⭆ m = 1/2
∴ (F) is the correct answer[tex].[/tex]
Hope It Helps!evaluate the expression 15x+4 for x = 2 and 1/3
Show your Work.
a. -18
b. 39
c. 20 and 1/2
d. 29 and 1/2
Answer:
b. 39
Step-by-step explanation:
x = 2 and 1/3
15(2 [tex]\frac{1}{3}[/tex] )+4
15 (7/3) + 4
[tex]\frac{15}{1} * \frac{7}{3}[/tex]+ 4
[tex]\frac{3*5}{1} *\frac{7}{3}[/tex] cross cancel
[tex]\frac{5}{1} * \frac{7}{1}[/tex] = 35
35 + 4 = 39
What value of x makes the equation true?
0.2x + 0.7 = 0.8 - 0.3x
Answer:
6
Step-by-step explanation:
Answer:
[tex]x = \frac{1}{5}[/tex] or [tex]0.2[/tex] (they're the same)
I hope this helps!
i dont know how to do this and considering i don't have a graph on the paper i'm using, i need help on how to solve this without a graph or having to plot anything :( plz help!! even if you just give me the formula or steps to do this, i will be much appreciative!
Answer:-5,1
Step-by-step explanation: Find the average of the the x and the y separately
-3-7=-10 -10÷2=-5
8-6=2 2÷2=1
The Mariana Trench is-35,840 feet deep. The Puerto Rico Trench is -28,374. What is the difference between the two depths?
Answer: -7,466 I would think.
Step-by-step explanation:
.In the least-squares line y=5-2x,
a. what are the values of the slope and the intercept?
b. when x changes by 1 unit, how much does y change?
c. if two variables have a negative linear correlation, is the slope of the least-squares lines positive or negative?
a) In the least-squares line y = 5 - 2x, the slope is -2 and the y-intercept is 5. b) Since the slope of the line is -2, a change of 1 unit in x would cause a change of 2 units in y. c) When two variables have a negative linear correlation, the slope of the least-squares line is negative.
The least-squares line, also known as the linear regression line, is a straight line that shows the connection between two variables that are linearly related.
A straight line is used to connect two points, and the least-squares line is the line that connects the points with the smallest amount of error or the smallest amount of distance between the points and the line.
The formula for the least-squares line is given by y = mx + b,
where m is the slope of the line and b is the y-intercept.
In the least-squares line
y = 5 - 2x,
the slope is -2, and the y-intercept is 5.
The slope of the line tells us how much y changes when x changes by one unit. In this case, since the slope is -2, a change of 1 unit in x would cause a change of 2 units in y.
When two variables have a negative linear correlation, the slope of the least-squares line is negative.
A negative correlation means that when one variable increases, the other variable decreases.
For example, if we look at the correlation between temperature and snowfall, we would expect a negative correlation. As temperature increases, we would expect snowfall to decrease.
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Evelyn and her father collects rocks Evelyn’s father has 5 more rocks than four times Evelyn’s rock. How many rocks does Evelyn name when her father has 49 rocks?
Answer:
Evelyn has 11 rocks.
Step-by-step explanation:
I first made an equation for the father's rocks.
5 + 4x = 49
X is Evelyn's rocks. We subtract the 5 from each side to get,
4x = 44, dividing each side by 4, we get X = 11.
We can double-check our answer by multiplying 11 by 4 and adding 5 to it. We get 49 doing this, proving our answer.
an international math 150 class has 5 african students, 4 european students, 8 american stu- dents, and 7 asian students.(a) in how many ways can a president, a vice-president, and a secretary be chosen?b) what is the probability that the president will be American, the vice president Asian, and the secretary American? Just the expression c) What is the probability that the president vice president and secretary will be American ? Just write the expression
a) To find the number of ways a president, a vice-president, and a secretary can be chosen from the international math class, we multiply the number of choices for each position.
Number of ways = Number of choices for president * Number of choices for vice-president * Number of choices for secretary
Since each position can have a different person, we have the following choices:
- President: Any student from the class (5 African + 4 European + 8 American + 7 Asian) = 24 choices.
- Vice-President: Any student from the class except the one chosen as president (23 choices remaining).
- Secretary: Any student from the class except the ones chosen as president and vice-president (22 choices remaining).
Number of ways = 24 * 23 * 22 = 12,144
Therefore, there are 12,144 ways to choose a president, a vice-president, and a secretary from the international math class.
b) To find the probability that the president will be American, the vice-president Asian, and the secretary American, we need to calculate the probability of each event happening and multiply them together.
Probability (president = American) = Number of American students / Total number of students = 8 / 24 = 1/3
Probability (vice-president = Asian) = Number of Asian students / Remaining number of students = 7 / 23
Probability (secretary = American) = Number of American students / Remaining number of students = 8 / 22
Probability (president = American, vice-president = Asian, secretary = American) = (1/3) * (7/23) * (8/22)
c) The probability that the president, vice-president, and secretary will be American can be expressed as:
Probability (president, vice-president, and secretary = American) = (Number of American students / Total number of students) * ((Number of American students - 1) / (Total number of students - 1)) * ((Number of American students - 2) / (Total number of students - 2)) = (8/24) * (7/23) * (6/22)
Simplifying this expression further is possible, but it is left in this form for clarity.
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linear equations
a+2b=-1
2a+3b=23
Answer:
.2a + 4b = -2 2a + 3b = 23We subtract.. 0 + b = -25a + (2×-25) = -1a - 50 = -1a = -1+50a = 49.a = 49b = -25.Step-by-step explanation:
proving my answer.a + 2b = -149 + (2×-25) = -149 - 50 = -12a + 3b = 23(2×49) + (3×-25) = 2398 + (-75) = 2398 - 75 = 23Can you help me plz on this
Answer: A
Step-by-step explanation: I think it's point A.
| y-5) = 45
how you find y ?
Answer:
y=45+5
=50
Step-by-step explanation:
Answer:
Transpose -5 to the other side so it becomes 45 + 5 which is equal to 50. Therefore, the value of y is 50.
What is the quotient in the expression
45
o?
Answer:
the quotient of 45 or o is 45/o. A quotient is the result of a division . For example 8/4=2 so, 2 is the quotient.
-x + 4 = -9
Please help
Answer:
13
Step-by-step explanation:
-x + 4 = -9
-x = -13
x = 13
Answer:
x=13
Step-by-step explanation:
subtract 4 from both sides and you get -13
the answer can't say -x=-13 because the x has to be positive
so move the negative sign to the other side which would make -13 positive.
then you have x=13 which is correct...hopefully that helps
Suppose an industry with four firms1) having the same constant marginal cost c, = C2 = C = C4 = 4;2) incurring no fixed cost of production; 3) producing a homogeneous good and choosing output simultaneously (i.e., being Cournot competitors); and 4) facing the linear inverse demand P = 10-Q with Q = q1 + q2 + q3 +q4
Q11) Determine the value for c such that the merger becomes profitable
Q12) Determine the value for c, such that the price decreases post-merger
The merger profitable is c ≤ 2.5. The value of c that makes the price decrease is c > 0.
1) Value for c such that the merger becomes profitable:
To calculate the value of c that makes the merger profitable, we must follow the following steps:
First, let's calculate the total output of the industry, which is:
Q = q1 + q2 + q3 + q4
Second, we must determine the total cost of production (TC) of each firm, which is:
TC = C*q,
where C is the marginal cost of each firm.
Third, we must determine the total cost of production of the industry, which is:
TC = C*(q1 + q2 + q3 + q4)
Fourth, we must determine the total revenue of the industry, which is:
TR = P*Q, where P = 10 - Q
Then, we can calculate the profit (Π) of each firm, which is given by:
Π = TR - TC
And, finally, we can calculate the total profit (Π) of the industry, which is given by:
Π = TR - TC * 4, where 4 is the number of firms in the industry.
Now, let's substitute the expressions we found for TR and TC into the equation for Π:
Π = (10 - Q)*Q - C*(q1 + q2 + q3 + q4) * 4
Π = (10 - (q1 + q2 + q3 + q4))*(q1 + q2 + q3 + q4) - C*(q1 + q2 + q3 + q4) * 4
Π = (10 - Q)*(Q) - C*Q * 4
Π = 10Q - Q² - 4CQ
Now, we must differentiate Π with respect to Q and equate it to zero to find the value of Q that maximizes profit:
Π' = 10 - 2Q - 4C = 0
Π' = 10 - 2(Q) - 4(C)
= 0Q
= 5 - 2C
The value of c that makes the merger profitable is c ≤ 2.5.
To verify that this is true, we can substitute this value of Q into the equation for Π and check if it is positive:
Π = 10Q - Q² - 4CQ
Π = 10(5 - 2C) - (5 - 2C)² - 4C(5 - 2C)
Π = 50 - 20C - (25 - 20C + 4C²) - 20C + 8C²
Π = 3C² - 30C + 25
Π = 3(C - 2.5)² - 3.75
Since Π is positive for c ≤ 2.5, the merger is profitable for c ≤ 2.5.2) Value for c such that the price decreases post-merger:
To calculate the value of c that makes the price decrease after the merger, we must follow the following steps:
First, let's calculate the output of each firm before the merger, which is given by:
q = (10 - C - q)/3, where q is the output of each firm.
Second, let's calculate the total output of the industry before the merger, which is given by:
Q = 4q
Third, let's calculate the price before the merger, which is given by:
P = 10 - Q
Substituting Q and q into this equation, we get:
P = 10 - 4q
Since the firms have the same marginal cost, their output levels are the same.
Thus, after the merger, the new output level of the merged firm is Q' = 4Q/2 = 2Q, and the price is given by:
P' = 10 - Q'
To find the value of c that makes the price decrease, we must compare P and P':
P = 10 - 4c/3
P' = 10 - 8c/3
To find the value of c that makes P' < P, we must solve the inequality:
P' < P
P' - P < 0-8c/3 + 4c/3 < 0-4c/3 < 0c > 0
Thus, the value of c that makes the price decrease is c > 0.
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PLEASE HELP ME ANSWER ASAP
L = k/f, where k is the variational constant, is the formula for the inverse variation.
Inverse proportionsA mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.
Using the variables length of violin 'l' and frequency of vibration 'f'
If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:
l α 1/f
l = k/f
Hence the formula for the inverse variation is l = k/f where k is the constant of variation.
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Halfway through the season, the Florida State Seminoles football team had the highest average final score. What was the Florida State
Seminoles' average score if their final scores were 33, 41, 33, 45, and 43?
Help me plsss
What is the value of the expression below when y = 4 and z = 4 , 6y - 3z ? Please answer !!!!!!!!! Will mark Brianliest !!!!!!!!!!
Answer:
12
Step-by-step explanation:
6y - 3z
6(4) - 3(4)
24 - 12
12
Hope this helps plz mark me as Brainliest
do you ride horses??
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
i have a friesian horse named butters he is a male!
6) −3 + 3k = −27
solve
Answer:
k = -8
Step-by-step explanation:
−3 + 3k = −27
⇔ -3 + 3k +3 = -27 +3
⇔ 3k = -24
⇔ k = -8
Answer:
Step-by-step explanation:
6) −3 + 3k = −27
k= -10
Two very small spheres are initially neutral and separated by a distance of 0.50m. Suppose that 3.0 x 1013 electrons are removed from one sphere and placed on the other.
A.What is the magnitude of the electrostatic force that acts on each sphere? B.Is the force attractive or repulsive? Why?
The magnitude of the electrostatic force that acts on each sphere are: 1.6×10⁻⁹N. The electrostatic force is repulsive.
The electrostatic force is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the charges. Hence, if two charges of like signs are brought close to each other, the force between them is repulsive and if two charges of opposite signs are brought close to each other, the force between them is attractive.
Given that two very small spheres are initially neutral and separated by a distance of 0.50m. Suppose that 3.0 x 10¹³ electrons are removed from one sphere and placed on the other.A charge of - 3.0 × 10¹³ electrons is transferred from one sphere to the other. Hence, one sphere becomes negatively charged while the other one becomes positively charged. The magnitude of the charge on each sphere can be determined as follows:
We know that the elementary charge on one electron = 1.6 × 10⁻¹⁹ C. Therefore, the charge on 3.0 × 10¹³ electrons = 3.0 × 10¹³ × 1.6 × 10⁻¹⁹ C= 4.8 × 10⁻⁶ C.
The magnitude of the electrostatic force that acts on each sphere is given by Coulomb's law as:
F = k × (q1 × q2) / r²Here,k = Coulomb's constant = 9 × 10⁹ Nm²/C²q1 = charge on sphere 1 = 4.8 × 10⁻⁶ Cq2 = charge on sphere 2 = 4.8 × 10⁻⁶ Cr = separation between the spheres = 0.50 m
Substituting these values in the Coulomb's law expression, we get:
F = 9 × 10⁹ × (4.8 × 10⁻⁶)² / (0.50)²= 1.6 × 10⁻⁹ N.
Thus, the magnitude of the electrostatic force that acts on each sphere is 1.6 × 10⁻⁹ N. Since both the spheres have the same charge (one positive and the other negative), the force between them is repulsive.
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