The result when (-2/3m + 4) is added to (5/6m - 1/2) is 4 - 1/3m.
Hence, the correct answer is option A: -1/6m + 7/2.
To find the result when (-2/3m + 4) is added to (5/6m - 1/2), we need to combine like terms.
First, let's simplify the expression -2/3m + 4:
This can be rewritten as (4 - 2/3m).
Next, let's simplify the expression 5/6m - 1/2:
This can be rewritten as (5/6m - 3/6m).
Now, let's add the two expressions together:
(4 - 2/3m) + (5/6m - 3/6m)
Combining the constants and the terms with "m," we get:
4 + 5/6m - 2/3m - 3/6m
To simplify further, we need to find a common denominator for the fractions:
4 + 5/6m - (2/3m + 3/6m)
The common denominator for the fractions is 6:
4 + 5/6m - (4/6m + 3/6m)
Now, let's combine the like terms:
4 + 5/6m - 7/6m
Finally, we can simplify the expression:
4 - 2/6m
Simplifying further, we have:
4 - 1/3m.
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Estimate the sum of the weights of Frailyn 10.2 pounds +611/12 pounds. Which statements are true about the estimate CHECK ALL THAT APPLY
Determine the equation of the parabola that opens to the right, has focus (13,-6),
and a focal diameter of 28.
The equation of the parabola is[tex](y + 6)^2 = 4(x - 13)[/tex], where the vertex is (13, -6) and the distance between the directrix and focus is 14.
To determine the equation of the parabola, we need to use the standard form for a parabola with a horizontal axis:
[tex](x - h)^2 = 4p(y - k)[/tex]
Where (h, k) represents the vertex of the parabola, and p is the distance from the vertex to the focus (and also from the vertex to the directrix).
Given that the parabola opens to the right, the vertex will be on the left side. Let's assume the vertex is (h, k).
We know that the focus of the parabola is at (13, -6), so the distance from the vertex to the focus is p = 13 - h.
We are also given that the focal diameter is 28, which means the distance between the directrix and the focus is twice the distance from the vertex to the focus.
Therefore, the distance from the vertex to the directrix is d = 28/2 = 14.
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Draw a graph of y=log_1/3 (x) and its inverse on the same pair of axis.
The graph of y = log1/3(x) is a decreasing curve that passes through the points (1, 0) and (3, -1). The horizontal asymptote is y = 0, and the vertical asymptote is x = 0.
The inverse of y = log1/3(x) is x = 3^y, which is equivalent to y = log3(x). The graph of y = log3(x) is an increasing curve that passes through the points (1, 0) and (3, 1). The horizontal asymptote is y = 0, and the vertical asymptote is x = 0.
When both graphs are plotted on the same pair of axis, they intersect at the point (1, 0) and (3, -1) and (3, 1).
Step tariffs 0-6 ke 7-15 ke 16-30 ke 31-60 ke Above 61 ke Basic charge per month 2016/2017 Prices (R) per 6,91 15,95 17,00 19, 04 21,58 22,00 % increase 8% 9% 11% 11,5% 12,5% 12% 2017/2018 Prices (R) per 7,46 17,39 Use the table above to answer the questions that follow 2.1.1 Define the basic charge in the given context. 2.1.2 Show how the tariff of R18,87 during 2017/2018 was calculated. 18,87 21,23 24, 28 24, 64 2.1.3 Mr Morake's municipal bill showed R201,27, for water usage at the end of August 2018. He stated that the basic charge was not included on the water bill. Verify if this statement is correct. (2) (2)
2.1.1: The basic charge in the given context refers to a fixed monthly fee that is charged by the municipality for the provision of water services, regardless of the amount of water consumed by the user.
2.1.2: To calculate the tariff for a particular consumption level during 2017/2018, you need to find the relevant consumption tier and then apply the corresponding rate. For example, if the consumption level is 10,000 litres per month, then the relevant tier is 7-15 kilolitres, and the rate for this tier is R15.95 per kilolitre. Therefore, the cost of water for this consumption level is:
10 kilolitres x R15.95/kilolitre = R159.50
To this cost, the basic charge needs to be added. According to the table, the basic charge for 2017/2018 is R7.46 per month. Therefore, the total cost of water and basic charge for this consumption level is:
R159.50 + R7.46 = R166.96
Therefore, the tariff for a consumption level of 10,000 litres per month during 2017/2018 is R166.96.
2.1.3: To verify if Mr Morake's statement is correct, we need to check if the basic charge was included in the calculation of his water bill. Assuming that Mr Morake's water usage for the month of August 2018 fell within the 7-15 kilolitre tier, we can calculate his bill as follows:
Water usage: 10 kilolitres
Cost of water: 10 kilolitres x R17.39/kilolitre = R173.90
Based on the above calculation, it appears that the basic charge was included in Mr Morake's water bill, as his total bill of R201.27 exceeds the cost of water alone. Therefore, it seems that Mr Morake's statement is incorrect, and the basic charge was indeed included in his water bill.
Written in simple form
Answer:
a = 8, b = 2
Step-by-step explanation:
[tex]\sqrt[3]{x^{10} }[/tex] ( substitute x = - 2
= [tex]\sqrt[3]{(-2)^{10} }[/tex]
= [tex]\sqrt[3]{1024}[/tex]
= [tex]\sqrt[3]{2^{10} }[/tex]
= [tex]\sqrt[3]{2^{9 (2)} }[/tex]
= 2³ [tex]\sqrt[3]{2}[/tex]
= 8[tex]\sqrt[3]{2}[/tex] ← in the form a[tex]\sqrt[3]{b}[/tex]
with a = 8 and b = 2
pls help will mark brainleist
Answer:
x = 48°
Step-by-step explanation:
[tex]x=(90-42)^{0} =48^{0}[/tex]
Hope this helps
★ The sum of the angles in a triangle is always 180° ...
➺ 42° + x + 90° = 180°➺ 42° + 90° + x = 180°➺ 132° + x = 180°➺ x = 180° - 132° ➺ x = 48°________________________________
1.2
Mr Mohalati has Mr Prepaid account with one of the banks
Africa. He uses the account to pay water bills. TABLE 2 shows deposit
fees applicable on his account in 2023.
TABLE 2: Mr Prepaid ACCOUNT COSTS AT ABA BANK FOR DEPOSITS
TRANSACTION
Notes and coin deposit
COSTS
R80 + R2,25 per R100 (for notes) +R5 per R100 (for coins)
or part thereof the amount deposited.
[Adapted by aaminer from information supplied by various banks
Use the information from TABLE 2 to answer the questions that follow.
1.2.1 Determine the minimum amount one will pay when making a deposit of notes and coins
3
Please turn over
The minimum amount one will pay making a deposit of notes and coins is R7.25.
To determine the minimum amount one will pay when making a deposit of notes and coins, we need to consider the costs mentioned in Table 2.
According to Table 2, the cost for notes deposit is R2.25 per R100 (or part thereof) deposited, and the cost for coins deposit is R5 per R100 (or part thereof) deposited.
To calculate the minimum amount, we need to determine the lowest possible value for both the notes and coins deposit costs.
For notes deposit:
The minimum value would be R2.25, as it is the cost for depositing less than R100 worth of notes.
For coins deposit:
The minimum value would be R5, as it is the cost for depositing less than R100 worth of coins.
To calculate the total minimum amount, we sum up the costs for notes and coins deposits:
Minimum amount = R2.25 (notes deposit cost) + R5 (coins deposit cost)
Minimum amount = R7.25
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Select the correct answer.
What is the value of this expression when n approaches infinity?
24 - 3 - 2/4 + 40
3n
n
+
E
15
3n²
The limit when n approaches infinity for the given expression is the one in option D, 21.
What is the value of the expression when n tends to infinity?Here we want to take the following limit of n when it tends to infinity in the following rational expression:
[tex]\lim_{n \to \infty} 24 - 3 - \frac{24}{2n} + \frac{40}{n} + \frac{15}{3n^2}[/tex]
Notice that in all the terms where n appears, it is on the denominator. Thus, when n tends slowly to infinity, the denominator will be way larger than the numerator, and thus, all the fractions will tend to zero, then we will get:
[tex]\lim_{n \to \infty} 24 - 3 - \frac{24}{2n} + \frac{40}{n} + \frac{15}{3n^2} = 24 - 3 = 21[/tex]
The correct option is the last one, D.
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The figure shows a circle with center
P
, a diameter
¯¯¯¯¯¯
B
D
, and inscribed
△
B
C
D
.
P
C
=
10
.
Let
m
∠
C
B
D
=
(
x
)
°
and
m
∠
B
C
D
=
(
x
+
54
)
°
.
From the given information, we have:
PC = 10 (length of segment PC)
∠CBD = x°
∠BCD = x + 54°
We can determine the relationship between angles ∠CBD and ∠BCD by recognizing that they are inscribed angles intercepting the same arc CD. In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. Therefore, we have:
∠BCD = 1/2(arc CD)
Since ∠BCD = x + 54° and arc CD is the diameter, which is 180°, we can set up the following equation:
x + 54 = 1/2(180)
Simplifying the equation:
x + 54 = 90
x = 90 - 54
x = 36
So, the measure of ∠CBD (m∠CBD) is 36°.
What is the simplest
Answer:
(c) x³·∛x
Step-by-step explanation:
You want the simplified form of ∛(x¹⁰).
Cube rootsThe first part of the problem tells you how to get there. After you have that expression, you need to bring the x⁹ term from under the radical.
[tex]\sqrt[3]{x^{10}}=\sqrt[3]{x^9\cdot x}=\sqrt[3]{x^9}\cdot\sqrt[3]{x}=\boxed{x^3\cdot\sqrt[3]{x}}\qquad\text{matches choice C}[/tex]
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A simulated game of chess is programmed between two computers. The game is supposed to be biased in favor of player B winning 4 out of 5 times. Which is the most suspicious set of outcomes of 30 games played between the two computers?
A.
AABABBBABBBBBBBBABBBABBBBBBBBA
B.
ABBABBAABBBBBABBBBBBBBBBBBBABB
C.
ABBABABABABBABABABABABABABABAA
D.
ABBABBBABBBBBBBBABBBABBBBBBBBB
The most suspicious set of outcomes of 30 games played between the two computers would be option C: ABBABABABABBABABABABABABABABAA.
In a fair game where player B is supposed to win 4 out of 5 times, we would expect player B to win approximately 24 out of 30 games. However, option C shows player B winning only 6 out of 30 games, which deviates significantly from the expected outcome.
This set of outcomes suggests a strong bias towards player A winning, as player B's wins are significantly lower than expected.
It is highly unlikely to observe such a low success rate for player B if the game was truly biased in favor of player B winning 4 out of 5 times.
Option C raises suspicions of an unfair advantage given to player A, potentially indicating some manipulation or incorrect implementation in the programming of the game.
Further investigation would be warranted to determine the cause of this biased outcome and to ensure fair play between the two computers in future games.
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Select the interval(s) where the function is increasing:
f(x) = x ^ 4 - 5x ^ 2 - 3
(- 9.3, - 3)
(- ∞,- 1.5)
(0, 1.5)
(-1.5, 0)
(1.5, ∞)
(-∞, ∞)
(-9.3, ∞)
Explain the meaning of the scale 1:1000 in words
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite
direction. The number b varies directly with the number a. For example b = 2 when a = -2
-22. Which equation
represents this direct variation between a and b?
b=-a
-b=-a
b-a=0
b(-a) = 0
Mark this and return
Next
Submit
The equation that represents the direct variation between a and b in this scenario is: b = -a.
The correct option is (A).
We have,
The number b varies directly with the number a.
This equation states that b is equal to the negative value of a, which reflects the condition that b is located in the opposite direction from 0 compared to a and varies directly with a.
So, the equation cab be stated as b = -a.
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twenty-nine percent of all light emitting diode displays are manufactured by samsung. what is the probability that in a collection of two independent purchases, at lease one is a sumsung?
Answer:
The probability that at least one of two independent purchases is a Samsung display can be calculated using the complement rule:
P(at least one Samsung) = 1 - P(neither is a Samsung)
The probability that neither of the two purchases is a Samsung display is:
P(neither is a Samsung) = (1 - 0.29) x (1 - 0.29) = 0.51
Therefore, the probability that at least one of the two purchases is a Samsung display is:
P(at least one Samsung) = 1 - 0.51 = 0.49
The probability that in a collection of two independent purchases, at least one is a Samsung is 0.49.
Does 17 divide each of these numbers?
a)68 b) 84 c) 357 d) 1001
Hello !
68/17 = 4
=> yes for 68
84/17 = 4.941...
=> no for 84
357/17 = 21
=> yes for 357
1001/17 = 58.882...
=> no for 1001
Wooden poles produced for electricity networks in rural areas have lengths that are normally distributed. 2% of the poles are rejected because they are considered too short, and 5% are rejected because they are too long.a. Find the mean and standard deviation of these poles if the acceptable range is between
6.3 m and 7.5 m.b. In a randomly selected sample of 20 poles, find the probability of finding 2 rejected poles.
Answer:
a. Let X be the length of a wooden pole produced for electricity networks in rural areas. The probability of a pole being rejected because it is too short is 0.02, and the probability of a pole being rejected because it is too long is 0.05. The acceptable range is between 6.3 m and 7.5 m. We can find the mean and standard deviation of X as follows:
First, we need to find the z-score corresponding to the lower bound of the acceptable range:
z1 = (6.3 - μ) / σ
Similarly, we need to find the z-score corresponding to the upper bound of the acceptable range:
z2 = (7.5 - μ) / σ
Using a standard normal table, we can find the values of z1 and z2 that correspond to the probabilities of 0.02 and 0.95, respectively:
z1 = -2.05
z2 = 1.64
Solving for μ and σ, we get:
z1 = (6.3 - μ) / σ => μ = 6.3 + 2.05σ
z2 = (7.5 - μ) / σ => σ = (7.5 - 6.3) / 1.64 = 0.74
Therefore, the mean and standard deviation of X are:
μ = 6.3 + 2.05(0.74) = 7.6 m
σ = 0.74 m
b. Let Y be the number of rejected poles in a sample of 20 poles. Y follows a binomial distribution with parameters n = 20 and p = 0.02 + 0.05 = 0.07. The probability of finding 2 rejected poles in a sample of 20 poles is:
P(Y = 2) = (20 choose 2) * 0.07^2 * 0.93^18 = 0.242
The probability of finding 2 rejected poles in a sample of 20 poles is 0.242.
PLS HELP ASAP I NEED IT PLS
Step-by-step explanation:
The equation for this function is y=2x
So 32*2=64
36/2=18
2*x=2x
y/2=y/2
2x*2=4x
(x+3)*2=2x+6
Plot the points A(- 1, - 1); B(9, 2) * C(2,- 6) on the coordinate axes below. State the coordinates of point D such that A, B, C, and D would form a parallelogram .
A cone-shaped paperweight is 5 inches tall, and the base has a circumference of about 12.56 inches. What is the area of a vertical cross section through the center of the base of the paperweight? Use 3.14 for π .
The area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.
To find the area of a vertical cross section through the center of the base of the cone-shaped paperweight, we need to determine the radius of the base first.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is about 12.56 inches, so we can set up the equation:
12.56 = 2πr
To solve for r, we divide both sides of the equation by 2π:
r = 12.56 / (2π)
Now we can calculate the radius:
r ≈ 12.56 / (2 × 3.14)
r ≈ 12.56 / 6.28
r ≈ 2 inches
The radius of the base is approximately 2 inches.
Since the vertical cross section passes through the center of the base, the shape of the cross section is a circle. The formula for the area of a circle is A = [tex]πr^2[/tex], where A is the area and r is the radius.
Now we can calculate the area of the cross section:
A = [tex]πr^2[/tex]
A ≈ 3.14 × [tex](2^2)[/tex]
A ≈ 3.14 × 4
A ≈ 12.56 square inches
Therefore, the area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.
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solve the following proportion
Answer: 4.5 or A
Step-by-step explanation:
1) Find LCM of 9 and 6, which is 18.
2) Multiply x/9 by 2. (2x/18)
3) Multiply 3/6 by 3. (9/18)
4) Divide by 2 (numberator on both sides)
x = 4.5
Help plssssssss 3+4x2
Answer:
The expression 3+4x2 can be simplified using the order of operations, which is a set of rules used to determine the sequence in which operations are performed in an expression. According to the order of operations, we first perform any calculations inside parentheses, then we perform any multiplications or divisions (from left to right), and finally we perform any additions or subtractions (from left to right).
There are no parentheses in this expression, so we move on to the next step, which is to perform any multiplications or divisions. In this case, we have 4x2, which equals 8. So, we can replace 4x2 with 8, and the expression becomes:
3+8
Finally, we perform the addition, and get the final result:
11
Therefore, 3+4x2 is equal to 11.
Step-by-step explanation:
A wheelchair ramp is 4.2m long. It rises 0.7m what is its angle of inclination to the nearest degree? Solve step by step
Sure, I can help you solve that math problem step by step.
First, we need to find the length of the hypotenuse of the ramp using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides (a^2 + b^2 = c^2).
So, using that formula, we can calculate the length of the ramp's hypotenuse: c^2 = 4.2^2 + 0.7^2
c^2 = 17.64 + 0.49
c^2 = 18.13
c = sqrt(18.13)
c = 4.26m
Now that we have the length of the hypotenuse, we can use the inverse trigonometric function of sine to find the angle of inclination. The sine of an angle is equal to the opposite side (in this case, the rise of the ramp, which is 0.7m) over the hypotenuse (4.26m).
So, sin(theta) = opposite/hypotenuse
sin(theta) = 0.7/4.26
sin(theta) = 0.1643
Now, we need to find theta by taking the inverse sine of 0.1643 (or sin(theta)).
theta = sin^-1(0.1643)
theta = 9.47 degrees
So the angle of inclination of the ramp to the nearest degree is 9 degrees.
the median of a given data set is also the
5 The population of a country was 13.1 million. (a) Nine hundred thousand of the population were at least 2 metres tall. How many were less than 2 metres tall?
If cards are sold at the rate of 3 for 10c,what will be the costof 3-dozen such cards?
Answer:
120c
Step-by-step explanation:
3 for 10c 1 for 10/3c 3*12 for 10/3 *36 =12*10=120c is the cost of 3 dozen of such cards
If tan (theta)=-2.1, what is the value of theta to the nearest whole degree?
Answer:
-65°
Step-by-step explanation:
You want the angle whose tangent is -2.1.
ArctangentThe inverse tangent function is used to find the angle when the tangent is known. On your calculator, the key for this will likely be labeled tan⁻¹. You need to make sure the calculator mode is set to degrees.
The value of θ is about -65°.
__
Additional comment
The principal branch of the arctangent function extends from -90° to +90°. The tangent function is periodic with period 180°, so adding any integer multiple of 180° to -65° will give you another angle whose tangent is -2.1. One such angle is 115°.
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Show a number line that solves the solution to the inequality x - 3 <\ 1
Answer:
x ≤ 4
Step-by-step explanation:
To solve the inequality x - 3 ≤ 1, we need to isolate x.
Remember that this is a linear inequality, and linear inequalities are solved the same way as a linear equation - the objective is to leave the variable alone on one side (usually the left-hand side or LHS) to find its value −
x - 3 ≤ 1
x ≤ 4
Therefore, x ≤ 4
Which of these expressions is equivalent to 2/0.4? (Iready)
Answer:
5
-----
0.4 | 2
- 0
2.0
- 1.6
-----
4
15 pies a m regla de 3
Answer:
5m
Step-by-step explanation:
regla de 3:
1m = 3ft
15 pies ÷ 3 = 5m