The function (fog)(x) is 4x² - x - 3.
Define functionIn mathematics, a function is a rule that maps each element from a set (called the domain) to a unique element in another set (called the range or codomain).
In other words, a function is a mathematical object that takes one or more inputs, performs a specified operation on them, and produces an output. The input values of a function are called its arguments, and the output value is called the function value.
Starting with g(x):
g(x) = -4x² + x + 5
Now substituting g(x) into f(x):
f(g(x)) = -(g(x)) + 2
= -[-4x² + x + 5] + 2 (substituting g(x) into f(x))
= 4x² - x - 3
Therefore, (fog)(x) = 4x² - x - 3.
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4 Mr Thapelo employed five more cleaners to make the cleaning work faster. He claims that the additional salary he has to pay on the cleaners are ten times the salary of a messenger. Verify his claim by showing all the necessary calculations whether his claim is valid or not
Answer: Read One Piece and Check Explanation.
Step-by-step explanation: Yes, Mr Thapelo's claim is valid.
Let's assume that the salary of the messenger is $1,000.
Therefore, the salary of the five additional cleaners should be 10 x $1,000 = $10,000.
What is 468,839 rounded to the nearest hundred thousand?
Answer:
500,000
Step-by-step explanation:
Answer:
500,000
hope this is right
06. A shop sells 200 chocolate, vanilla and strawberry ice creams in a day. Forty-two of
the loe creams sold are vanilla, and a quarter are strawberry. What percentage are
chocolate?
[2mks] show full working out
Answer:
If 200 is four qoaters, then 1 quater is 200/4 is 50. so 50 ice creams is strawberry. One quater in procantage is 25%.
after that you count how many ice crams are vanilia
\(\frac{42}{200}\) after you divide it you get 0.21 which is 21%
After you just deduct 25+21 from 100
you get
100-46=54
the answer is 54%
i hope this is right
use eulers method with step size 0.5 to compute the approximate y values y1 y2 y3 and y4 of the solution of the intitial value problem y'=y 2x y(3)=0
Answer:
\(y_1=\boxed{-3}\)
\(y_2=\boxed{-8}\)
\(y_3=\boxed{-16}\)
\(y_4=\boxed{-28.5}\)
Step-by-step explanation:
Given:
\(y'=y-2x, \;\;y(3)=0\)\(h=0.5\)Use Euler’s method with h = 0.5 to find approximate values for the solution of the initial value problem:
\(y'=y-2x, \;\;y(3)=0\)
at x = 3.5, 4, 4.5, 5.
Therefore:
\(f(x,y)=y-2x, \quad x_0=3 \;\;\text{and}\; \;y_0=0\)
Euler's Method
\(\boxed{y_{n+1}=y_n+hf(x_n,y_n)}\)
\(\begin{aligned}\implies y_1&=y_0+hf(x_0,y_0)\\&=0+(0.5)f(3,0)\\&=0+0.5[0-2(3)]\\&=0+0.5(-6)\\&=-3\end{aligned}\)
\(\begin{aligned}\implies y_2&=y_1+hf(x_1,y_1)\\&=-3+(0.5)f(3.5,-3)\\&=-3+0.5[-3-2(3.5)]\\&=-3+0.5(-10)\\&=-3-5\\&=-8\end{aligned}\)
\(\begin{aligned}\implies y_3&=y_2+hf(x_2,y_2)\\&=-8+(0.5)f(4,-8)\\&=-8+0.5[-8-2(4)]\\&=-8+0.5(-16)\\&=-8-8\\&=-16\end{aligned}\)
\(\begin{aligned}\implies y_4&=y_3+hf(x_3,y_3)\\&=-16+(0.5)f(4.5,-16)\\&=-16+0.5[-16-2(4.5)]\\&=-16+0.5(-25)\\&=-16-12.5\\&=-28.5\end{aligned}\)
\(\begin{array}{|c|c|c|}\cline{1-3} \text{Step}\;(n) & x_n&y_n\\\cline{1-3} 0&3&0\\\cline{1-3} 1&3.5&-3\\\cline{1-3} 2&4&-8\\\cline{1-3} 3&4.5&-16\\\cline{1-3} 4&5&-28.5\\\cline{1-3} \end{array}\)
Find the quotient of z₁ by z2. Express your answer in
trigonometric
form.
² - 3 (0 (4) + (*))
Z₁ cos
+/sin
Z₂
²2 = 7 (cos(377)+
COS
8
O A. 7 (cos (577) + i sin (5/77))
8
B.
21(cos(577)+isin (577))
8
OC. 21 cos
21(cos(-7)+ i sin(-77))
O D. 7 (cos(-7) + + sin(-7))
i
+/sin
37T
8
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.
Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.
We have:
z₁ = 7(cos(577°) + i sin(577°))
Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.
From the given information, we have:
z₂ = 21(cos(-7°) + i sin(-77°))
To find the quotient, we divide z₁ by z₂:
z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]
Substituting the given values, we have:
z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]
= (7/21) * [cos(584°) + i sin(584°)]
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.
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if y is directly porportional to x^2 and the difference in the values of y when x=1 and x=3 is 32, find the value of y when x=-2
Answer:
Step-by-step explanation:
y=kx²
y₁=k(1)²=k
y₃=k(3)²=9k
y₁-y₃=k-9k=32
-8k=32
k=-4
y=-4x²
y₋₂=-4(-2)²=-16
-4
C
--5
Find the side lengths and perimeter of triangle JKL. If necessary, round your answers to the nearest hundredth.
The approximate distance between J and K is
The approximate distance between K and Lis
units.
✓units.
The approximate distance between L and J is
✓units.
If you join all three points, then the perimeter of the triangle created is approximately
C
Reset
Next
✓units.
Answer:
Step-by-step explanation:
i dont understand
A cafeteria purchases milk from one of three providers each week, depending on what other items need to be purchased. The probability of shopping at each store and the cost of one gallon of milk are shown in the table below. Probability and Milk Cost by Store Store Probability Milk Cost per Gallon A 30% $3.00 B 10% $3.50 C 60% $2.75 The cafeteria should budget $ on average for one gallon of milk.
Answer:
The cafeteria should budget $2.90 on average for one gallon of milk.
Step-by-step explanation:
The cafeteria should budget $ 2.90 on average for one gallon of milk.
Percentage What is percentage?Percentage, a comparative figure denoting one hundredth of any quantity. One percent (symbolised as 1%) is equal to one tenth of something; hence, 100 percent denotes the full thing, and 200 percent defines twice the amount that is stated. percentage
How to calculate percentage?Divide one number by the other and multiply the result by 100 to determine the percentage difference between the two values.
Calculation for the price of one gallon of milk:Cafeteria purchases 30% of milk from A at cost $3.00 for one gallon.= Calculate 30% of 3.00,
= 3×(30/100)
= 0.9
Cafeteria purchases 10% of milk from B at cost $3.50 for one gallon.
Calculate 10% of 3.50,
= 3.50×(10/100)
= 0.35
And,cafeteria purchases 60% of milk from C at cost $2.75 for one gallon.
Calculate 60% of 2.75,
= 2.75×(60/100)
= 1.65
Average cost for one gallon of milk.
= 0.9 + 0.35 + 1.65
= 2.90
Therefore,the cost for on an average one gallon of milk is $2.90.
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A wire 22 cm long has a mass of 374 g. What is the mass of 13 cm of this wire?
Answer:
221 g
The up pinned pic is of inverse variation typed answer.. If u want word problem type answer here are the steps (EVEN IF THE STEPS ARE DIFFERENT ANSWERS REMAIN SAME)
Step-by-step explanation:
Mass of wire from 22cm = 374g
Mass of wire from 1 cm = 374÷22 = 17g
Mass of wire from 13 cm = 13×17 = 221 g
Write the name (not the equation) of each of the following:
The names of the functions in the attached figure are:
Cubic functionAbsolute value functionSquare root function.Rational function.Quadratic functionHow to name the functions?Functions can be named by their parent functions.
This is so because functions derive their properties from their parent functions.
There are several parent functions, some of them are:
Linear equationExponential equationQuadratic equationRational equationLogarithmic equationSquare root equationCubic equationCube root equationUsing the above as a guide, the names of the functions in the attached figure are:
Cubic functionAbsolute value functionSquare root function.Rational function.Quadratic functionRead more about parent functions at:
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Help me on question 3 pls I’ll Karl you as brainliest
Can you please help me
Answer:
the first answer is 4/9x 2/1 i believe or 4/9x 1/2.
the second answer is 8/9 or 4/18
I hope this helped
9,261.95 x 0.003= ?
Plzz help
Answer:
27.78585
Step-by-step explanation:
Recall that with base-ten blocks: 1 long 10 units, 1 flat 10 longs, and 1 block 10 flats. What is the fewest number of multibase blocks that can be used to represent the corresponding numeral in the given base?
a. 20 longs in base seven
b. 10 longs in base three
a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.
b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.
a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.
In base seven, we have the following conversions:
1 long = 1 unit
1 flat = 10 units
1 block = 10 flats
To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.
So, the fewest number of multibase blocks required would be 2 flats.
Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.
b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.
In base three, we have the following conversions:
1 long = 1 unit
1 flat = 3 units
1 block = 3 flats
To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.
So, the fewest number of multibase blocks required would be 3 flats and 1 unit.
Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.
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please answer faster then I will mark you branliest
Answer:
4. The strength of class V is 300
5. Meenakshi bought a TV for Rc 46,000
Step-by-step explanation:
4. To round to the nearest hundred, check the number in the 'tens'. If its five or greater, round up, and if its lower than 5, round down. In this case it was 7, so we rounded up to 300.
5. To round to the nearest thousand, check the number in the 'hundreds'. If its five or greater, round up, and if its lower than 5, round down. In this case it was 3, so we rounded down to 46,000.
Which of the following rules describes the function graphed below
Answer:
Output = (0.5)(Input) + 1.5
Step-by-step explanation:
input = 1 , output = (0.5)(1) + 1.5 = 2
input = 3 , output = (0.5)(3) + 1.5 = 3
input = 5 , output = (0.5)(5) + 1.5 = 4
input = -1 , output = (0.5)(-1) + 1.5 = 1
hope it helps mark as brainliest pls
DONT IGNORE PLEASE!! What is the measure of angle c
A. 94°
B. 86°
C. 18°
D. 274°
Answer:
B
Step-by-step explanation:
the sum of the 3 angles in a triangle is 180° , so
∠ c + 56° + 38° = 180°
∠ c + 94° = 180° ( subtract 94° from both sides )
∠ c = 86°
A container in the shape of a cube has a capacity of 8 litres. Find the height
the container in cm.
Answer:
b
Step-by-step explanation:
n
A rectangular garden is to be constructed using a rock wall as one side of the garden and wire fencing for the other three sides. Given that there are 30 meters of fencing available, determine the dimensions that would create the garden of maximum area. What is the maximum possible area?
The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters
What is measurement?
Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.
Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.
Since we have 30 meters of fencing available, the total length of wire fencing used is:
L + 2W = 30 - W
Simplifying this equation, we get:
L = 30 - 3W
The area of the garden is:
A = LW
Substituting the expression for L from the previous equation, we get:
A = W(30 - 3W)
Expanding the expression, we get:
A = 30W - 3W²
To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:
dA/dW = 30 - 6W = 0
Solving for W, we get:
W = 5
Substituting this value back into the expression for L, we get:
L = 15
Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:
A = 5(15) = 75 square meters
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The table shows the results of a survey in which 10th-grade students were asked how many siblings (brothers and/or sisters) they have. A 2-column table has 4 rows. The first column is labeled Number of siblings with entries 0, 1, 2, 3. The second column is labeled number of students with entries 4, 18, 10, 8. What is the experimental probability that a 10th-grade student chosen at random has at least one, but no more than two, siblings? Round to the nearest whole percent. 65% 70% 75% 80%
Answer:
70%
Step-by-step explanation:
Given
Number of Siblings: || 0 || 1 || 2 || 3
Number of Students: || 4 || 18 || 10 || 8
Required
Determine the probability of a student having at least one but not more than 2 siblings
First, we have to determine the total number of 10th grade students
\(Total = 4 + 18 + 10 + 8\)
\(Total = 40\)
The probability of a student having at least one but not more than 2 siblings = P(1) + P(2)
Solving for P(1)
P(1) = number of students with 1 sibling / total number of students
From the given parameters, we have that:
Number of students with 1 sibling = 18
So:
\(P(1) = \frac{18}{40}\)
Solving for P(2)
P(2) = number of students with 2 siblings / total number of students
From the given parameters, we have that:
Number of students with 2 siblings = 10
So:
\(P(2) = \frac{10}{40}\)
\(P(1) + P(2) = \frac{18}{40} + \frac{10}{40}\)
Take LCM
\(P(1) + P(2) = \frac{18 + 10}{40}\)
\(P(1) + P(2) = \frac{28}{40}\)
Divide numerator and denominator by 4
\(P(1) + P(2) = \frac{7}{10}\)
\(P(1) + P(2) = 0.7\)
Convert to percentage
\(P(1) + P(2) = 70\%\)
Hence, the required probability is 70%
Answer:
Step-by-step explanation:
bB
An arcade charges $3.00 for entry per person and $2.00 per game played. Write an equation that represents the total cost in relation to however many games are played?
The side of a triangle are in the ratio 4:4:3 what kind of triangle is it (b) calculate the smallest angle of the triangle to the nearest degree
The smallest angle of the equilateral triangle is 60 degrees
If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.
To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.
For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:
Smallest angle \(= \frac{180}{3} = 60\)\) degrees.
Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).
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Guys my main account is gone i dont know why. Am I baned?
Answer:
Try contacting the Help center located at the bottom part of the home page of this site. It is recoverable as long as no violation committed
Standard form of this number - two hundred nineteen million , seven hundred fifty-one thousand , eight hundred eighty two
Assume that there is a 150 year old law in the statutes of your state which makes kissing in a public graveyard a crime punishable by a fine of up to $1,000 and imprisonment in the county jail for up to six months. (a sentence following conviction can include a fine in any amount up to that limit and / or imprisonment of no time up to that limit - all in the judge's discretion). a couple were caught kissing in the local public cemetery, and they are being prosecuted for the crime in your courtroom.
a. Choose whether you, the judge hearing the case, are guided by the legal philosophy of "Natural Law", "Positive Law", or "Legal Realism".
b. State in your response which philosophy you are following, then decide the case, briefly stating your reasoning from the perspective of the legal philosophy followed.
Answer: Natural law.
Step-by-step explanation:
Natural law this is a theory which is based on ethics and philosophy which states that human beings possess intrinsic values which guide our reasoning and behaviors. Natural law stands to maintain that these rules of right and wrong are inborn in people and are not created by the society or court judges. An example of Natural law is that it is bad to kill someone, and it’s is right to punish whoever kills someone.
in the example cited above it is morally wrong to kiss or furnicate in a cemetery ground and as such falls under the natural law cause our sense of judgment should come into play there.
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the expressions to their limit values.
Answer:
see photo
Step-by-step explanation:
took the test
1. Given the following information about a hypothesis test of comparing the two variances based on independent random samples, what is the critical value of the test statistic at a significance level of .05? Assume that the samples are obtained from normally distributed populations having equal variances.
H0: A = B
H1: A > B
X ¯ 1 = 12
X ¯ 2 = 9
s1 = 4
s2 = 2
n1 = 13
n2 = 10
A. Reject H0 if Z > 1.96
B. Reject H0 if Z > 1.645
C. Reject H0 if t > 2.08
D. Reject H0 if t > 1.782
E. Reject H0 if t > 1.721
2. Given the following information about a hypothesis test of the difference between two means based on independent random samples, what is the standard deviation of the difference between the two means? Assume that the samples are obtained from normally distributed populations having equal variances.
H0: A = B
H1: A > B
X ¯ 1 = 12
X ¯ 2 = 9
s1= 5
s2 = 3
n1 =13
n2 =10
A. 1.792
B. 1.679
C. 2.823
D. 3.210
E. 1.478
Answer:
1. E. Reject H0 if t > 1.721
2. B. 1.679
Step-by-step explanation:
This would be a hypothesis test for the difference between two means. In the way that the alternative hypothesis.
The critical value depends on the significance level, the test type (one-tail or two-tailed) and the degrees of freedom.
This is a t-test type, so the statistic is t and not z. In the way that the alternative hypothesis, where only matter if the mean A is significantly bigger than mean B, this is a one-tail test.
The degrees of freedom can be calculated as:
\(df=n_1+n_2-2=13+10-2=21\)
Then, for a one-tail t-test, with significance level of 0.05 and 21 degrees of freedom, the critical value is t=1.721.
The standard deviation of the difference between the two means can be calculated as:
\(s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{5^2}{13}+\dfrac{3^2}{10}}\\\\\\s_{M_d}=\sqrt{1.923+0.9}=\sqrt{2.823}=1.6802\)
The Singh family ordered a large pizza with a diameter of 20 inches for dinner. If one of the members of the family ate one eighth of the pizza, how many square inches of pizza are remaining? Use 3.14 for π.
274.75 square inches
39.25 square inches
314 square inches
157 square inches
274.75 square inches of pizza are remaining. Option A is the correct option.
What is π in math?
The ratio of a circle's diameter to its circumference, or "pi," is a mathematical constant that is roughly equal to 3.14159 (/pa/; also written as "pi"). Numerous mathematical and physics formulas contain the number. It is an irrational number, meaning that although fractions like 22/7 are frequently used to approximate it, it cannot be expressed exactly as a ratio of two integers.
Given that, the diameter of large pizza is 20 inches.
The radius of a circular shape is half of the diameter.
The radius of the pizza is (20 inches)/2 = 10 inches.
Area of a circular shape is ∏r² .
The area of the pizza is 3.14×10² = 314 in²
The total part of the pizza is considered as 1.
One-eighth of the pizza is eaten, and the remaining portion is (1-1/8) = 7/8.
The area of remaining pizza is
314 in² × (7/8)
= 274.75 square inches
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Compare and 1.6. Use <, >, or =.
A. 5/3 = 1.6
B. 5/3 < 1.6
c. 5/3 > 1.5
Step-by-step explanation:
\( \frac{5}{3} = 1 \frac{2}{3} = 1.67\)
Since
\(1.67 > 1.6 \: and \: > 1.5\)
C is the answer
8x18÷4+15 use pemdas right answers only please
Answer:
51
Step-by-step explanation:
PEMDAS means parenthesis (there are none), exponents (there are none), multiplication. So you multiply 8x18 to get 144. Then you have division, so 144/4 is 36. Finally, you add this number to 15 to get 51 as your final answer.
By PEMDAS, the solution of the expression 8x18÷4+15 is 51.
What is PEMDAS?The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.
Given:
An expression,
8x18÷4+15.
In order to solve the problem by PEMDAS:
First, solve the multiplication operation,
144÷4+15
Now, solving division operations,
36 + 15
Applying addition operation,
51
Therefore, 51 is the solution to the expression.
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