The solution of the function (f - g)(x) is 17x + 7.
How to solve composite function?A function relates input and output. A composite function is generally a function that is written inside another function.
Therefore, let's solve the composite function as follows:
f(x) = 10x + 3
g(x) = -7x - 4
Therefore, let's find (f - g)(x)
Hence,
(f - g)(x) = f(x) - g(x)
Therefore,
f(x) - g(x) = 10x + 3 - (-7x - 4)
f(x) - g(x) = 10x + 3 + 7x + 4
f(x) - g(x) = 17x + 7
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Please help me I really need help. ILYSM THANK YOU :)
How many pounds of apples will he get if he goes to David’s orchard?
The pounds of apples that he get if he goes to David’s orchard is 20 pounds.
How to calculate the pounds of apples?Let the assumed amount with him be $40.
It should be noted that for David's orchard, the first ten pounds are $2 per round and each additional round is $1 per pound.
Therefore, the expression to illustrate this will be:
($2 × 10) + ($1 × r)
where r = additional pounds
Therefore,
($2 × 10) + ($1 × r) = $40
20 + r = 40
r = 40 - 20
r = 20
He will get 20 pounds.
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if Tanya has $43.64 and she wants to buy a dress for her and her 5 friends, and each dress costs $7.50, how many dresses can she buy and how much more money would she need to buy all 6?
The cost of 6 dresses is 7.50 x 6 = 45 (more than 43.64)
So, Tanya can only buy 5 dresses.
If she wants to buy 6 dresses, she has to pay 45 - 43.64 = $1.36 more.
what is the next operation that should be done when evaluating this expression?
9-12+-2+3(-3)
a) 3(-3)=-9
b)-2+3=1
and if you dont mind showing how you did it so i can learn it thanks!
The next operation that should be done when evaluating this expression 9-12+-2+3(-3) is A. 3(-3)=-9
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
In this case, it should be noted that the expression given is written as 9-12+-2+3(-3). In PEDMAS, the first operation is parentheses. Therefore, the number on parentheses will be solved first.
In this case, the number in parentheses will be 3(-3). Therefore, the correct option is A.
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Pls helppppppppppppppppp
Answer:
x=8
Step-by-step explanation:
11x+2=90
11x=88
x=8
Answer:
19. X=8
20. x=7
What is the measurement of ABC?
Answer:
118°
Step-by-step explanation:
because 28 + 90 = 118
a year is a leap year if and only if the year number is divisible by 400 (such as 2000) or is divisible by 4 but not 100 (such as 2012). the 200th anniversary of the birth of novelist charles dickens was celebrated on february 7, 2012, a tuesday. on what day of the week was dickens born?
Charles Dickens was born on a Saturday. By calculating the number of days between his birthdate and February 7, 2012, we determine that there were 4 extra days. Adding gives Saturday. So, the correct answer is B).
To determine the day of the week when Charles Dickens was born, we can calculate the number of days between his birthdate and February 7, 2012.
The year 2012 is a leap year because it is divisible by 4 but not divisible by 100. In a leap year, there are 366 days.
Since 2012 is a leap year, we need to calculate the number of days between February 7, 2012, and Charles Dickens' birthdate. The difference is 200 years, which is equal to 200 * 365 days for non-leap years plus an additional 49 days for the leap years in between (as there are 49 leap years in 200 years).
Total days = (200 * 365) + 49 = 73,049 days
Now, if we divide 73,049 by 7, the remainder will give us the day of the week.
73,049 divided by 7 = 10,435 remainder 4
Therefore, the remainder is 4, indicating that there were 4 extra days beyond Tuesday. Counting forward, Tuesday + 4 days gives us Saturday.
So, the answer is (B) Saturday.
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--The given question is incomplete, the complete question is given below " A year is a leap year if and only if the year number is divisible by 400 (such as 2000) or is divisible by 4 but not 100 (such as 2012). The 200th anniversary of the birth of novelist Charles Dickens was celebrated on February 7, 2012, a Tuesday. On what day of the week was Dickens born?
(A) Friday
(B) Saturday
(C) Sunday
(D) Monday
(E) Tuesday"--
anybody know these 4 problems I forgot how to do it lol
Answer:
the formula is base time height times 1/2 its really easy use desmos calculater:))))
Step-by-step explanation:
Using the net below, find the surface area of the triangular prism.
Answer:
Hi, there! The total surface area of that prism is 118 cm^2.
Step-by-step explanation:
The three rectangles on the side are called the lateral area, and they add up to 98(I'm assuming you know how to find the area of a 2d shape), and as for the triangles on the sides, you can just use the formula which is \(b*h/2\).
Hope this helps :)
Answer:
118 cm²
Step-by-step explanation:
Area of rectangle = l x b
= 7 x 5 = 35cm²
=4 x 7 = 28cm²
Add the area of the three rectangles = 35+35+28
=98cm²
Area of triangle = 1/2 x b x h
= 1/2 x 4 x 5
= 10 + 10 = 20
Therefore, area of the prism = 118cm²
Urgently need help step by step explanation needed
Answer:
p=8
Step-by-step explanation:
-5log(p+1)+2=-8
-5log(p+1)=-10
log(p+1)=2
p+1=9, p=8
Find the distance between the following two points: (3,-6) (-1,-8)
A business owner wants to have the front window of his store painted and is considering two artists for the job. Martin has quoted a flat rate of $329 for the job. Jared's quote is $46 per hour, plus $53 to cover the cost of materials. Depending on how long it takes Jared to paint the window, these two could end up charging the same amount. How much would it cost? How long would Jared have to take?
artin has offered a flat rate of $329, while Jared charges $46 per hour plus $53 for materials. If Jared takes 6 hours to complete the job, his total cost would be the same as Martin's flat rate of $329.
Let's assume the total time taken by Jared to paint the window is 't' hours. Since Jared charges $46 per hour, the labor cost would be $46t. In addition, there is a fixed cost of $53 for materials. Therefore, the total cost for Jared can be expressed as C = 46t + 53.
To find the time at which the cost is the same as Martin's quote of $329, we set C equal to $329 and solve for t:
46t + 53 = 329
Subtracting 53 from both sides gives:
46t = 276
Dividing both sides by 46, we find:
t = 6
So, for the cost to be the same as Martin's quote, Jared would need to take 6 hours. At this time, the cost would be:
C = 46(6) + 53 = 276 + 53 = $329
Therefore, if Jared takes 6 hours to complete the job, his total cost would be the same as Martin's flat rate of $329.
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If the order of selection is considered relevant, in how many ways cankobjects beselected from a set ofnobjects?
Permutation is the number of ways a number of k objects can be selected from a set of n objects while giving relevance to the order selection.
The two ways of forming subsets from selecting a group of objects from a set are through combination and permutation. The act of selecting objects and arranging them into some kind of order is the process of permutation. On contrary, combination is the type of selecting objects wherein the order is not really important.
The selection process stated in this problem is permutation. Let P be the number of ways a k number of objects is chosen from a set of n objects.
For a permutation that allows repetition or replacement of the chosen object:
P= n*n*(k number of objects that will be selected)= \(n^{k}\)
For a permutation that does not allow repetition or replacement of chosen object:
\(P = \frac{n!}{(n-k)!}\)
Factorial is used to indicate the descending number of choices every time an object is selected. In order to select a k number of things, factorial n will be divided by the factorial of n-k.
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What is the image point of ( − 6 , − 7 ) (−6,−7) after the transformation T − 2 , 3 ∘ r y = − x T −2,3 ∘r y=−x ?
Answer:
(4 , 8)
Step-by-step explanation:
translation: -2 , 3 (-6 , -7) -> (-8 , -4)
Reflection y = -x: (-8 , -4) -> (4 , 8)
A grain silo is shaped like a cylinder. The diameter is 10 yards and the height is 25 yards. If the silo is 60% filled, what is the volume of grain in the silo? Round to the nearest tenth.
The volume of grain in the silo when it is 60% filled is approximately 1178.1 cubic yards.
What is Volume?A closed surface or object's volume is determined by its three dimensions and is represented mathematically.
The following formula determines a cylinder's volume:
V = πr²h
where r is the radius of the cylinder and h is the height.
The diameter of the silo is 10 yards, so the radius is 5 yards. The height of the silo is 25 yards.
To find the volume of the silo, we need to first calculate its total capacity, which is the volume of a completely filled cylinder:
V_total = πr²h
V_total = π(5²)(25)
V_total = 625π
To find the volume of grain in the silo when it is 60% filled, we need to find 60% of the total capacity:
V_grain = 0.6V_total
V_grain = 0.6(625π)
V_grain ≈ 1178.1 cubic yards (rounded to the nearest tenth)
Therefore, the volume of grain in the silo when it is 60% filled is approximately 1178.1 cubic yards.
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Which function can represent the height, y, of the railing in inches according to the horizontal distance in inches, x, from the top of the stairs? y = â€"startfraction 3 over 4 endfractionx 36 y = â€"3x 36 y = startfraction 3 over 4 endfractionx 36 y = 3x 36
The function representing the height is y = 36 - \(\frac{3}{4} x\).
What is function?A formula, rule, or legislation that specifies how one variable (the independent variable) and another variable are related (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
What is fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Given that,
Height of rails h is 36in.
The rate of decrement is 9 inches for every 12 horizontal inches,
We represent the rate (r) as a fraction.
r = \(-\frac{9}{12}\) (negative, because it decreases),
r = \(-\frac{3}{4}\),
So, the function is
Y = h + r × x
Where,
X is distance from top
So, y = 36 \(-\frac{3}{4}x\)
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x⁴+8x³+34x²+72x+81 factories it.
Answer:
The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.
We are interested in the activity diagram. Check all the correct
answers.
Please select at least one answer.
O a. There can be multiple end points, but only one starting
point.
O b. Any joint must hav
The correct statements regarding activity diagrams are:
a. There can be multiple end points, but only one starting point.
c. A branch can have multiple incoming arrows.
d. A decision point may have more than 2 outgoing arrows.
e. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions.
f. An activity can be nested within another activity.
Activity diagrams are graphical representations used in software engineering to depict the flow of activities or actions within a system. The correct statements regarding activity diagrams are as follows:
a. There can be multiple end points, but only one starting point:
Activity diagrams typically illustrate the flow of activities from a single starting point to multiple end points. This allows for depicting different termination points in the system's behavior.
c. A branch can have multiple incoming arrows:
A branch in an activity diagram represents a decision point where the flow of activities can diverge. It is possible for multiple incoming arrows to converge at a branch, indicating different paths leading to the decision point.
d. A decision point may have more than 2 outgoing arrows:
A decision point in an activity diagram represents a condition or a decision that determines the subsequent flow of activities. It is possible for a decision point to have more than two outgoing arrows, indicating different paths based on the decision outcome.
e. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions:
In an activity diagram, if the subsequent activities following a certain action have conditions that are not mutually exclusive, it creates an indeterminacy. This means that multiple paths may be followed simultaneously based on the different conditions.
f. An activity can be nested within another activity:
Activity diagrams support the nesting of activities within each other. This allows for representing complex activities or sub-processes within a larger activity, providing a hierarchical structure to the diagram.
In conclusion, the correct statements regarding activity diagrams include multiple end points and a single starting point, the possibility of multiple incoming arrows at a branch, the presence of more than two outgoing arrows at a decision point, the creation of indeterminacy with non-mutually exclusive conditions, and the ability to nest activities within one another.
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We are interested in the activity diagram. Check all the correct answers.
Please select at least one answer.
O a. There can be multiple end points, but only one starting point.
O b. Any joint must have been preceded by a branch.
O c. A branch can have multiple incoming arrows.
O d. A decision point may have more than 2 outgoing arrows.
Oe. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions.
Of. An activity can be nested within another activity.
due in 30 min pls help
Answer:
5 i think the anwser is 5 i did my best
sin a + cos a/sec a+ cosec a= sin a* cos a
Answer:
See proof below
Step-by-step explanation:
sin a + cos a/sec a+ cosec a= sin a* cos a
(sina+cosa)/(sec a + cosec a)
In trigonometry identity
seca = 1/cos a
cosec a = 1/sin a
Substituted into the given expression
= sina + cosa/(1/cosa+1/sina)
Find the LCM
= sina + cosa /(sina+cosa/sinacosa)
= (sina+cosa) * sinacosa/(sina + cosa)
= sinacosa (RHS)
This shows that the equation is true
A study of 420,037 cell phone users found that 0.0331% of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0361% for those not using cell phones. Complete parts (a) and (b). a. Use the sample data to construct a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. %
The percentage of cell phone users who develop brain or nervous system cancer with 95% confidence is 0.0329534% to 0.0332466%. MA confidence interval is an interval of values computed from sample data that is expected to contain the proper population parameter.
Confidence intervals are often used in statistics to assess the reliability of a sample estimate of a population parameter and to evaluate the precision of the population parameter. The sample data used here is that a study of 420,037 cell phone users found that 0.0331% developed brain or nervous system cancer.
Before this study of cell phone use, the rate of such cancer was found to be 0.0361% for those not using cell phones. The formula for a confidence interval of a sample proportion:
Confidence interval = sample proportion ± margin of error
The margin of error = Z α/2 × √ (p × q)/n, Where,
Z α/2 = 1.96 (for 95% confidence level)
p = sample proportion
= 0.0331
q = 1 - p
= 0.9669
n = sample size
= 420037
To find the confidence interval, we will first compute the margin of error using the formula above.
Margin of error = Z α/2 × √ (p × q)/n
Margin of error = 1.96 × √ ((0.0331) × (0.9669))/420037
The margin of error = 0.0001466
We can now construct the confidence interval using the formula:
Confidence interval = sample proportion ± margin of error
Confidence interval = 0.0331 ± 0.0001466
Confidence interval = (0.0329534, 0.0332466)
Therefore, the 95% confidence interval estimate of the percentage of cell phone users who develop brain or nervous system cancer is 0.0329534% to 0.0332466%.
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Suppose f(x,y)=xyf(x,y)=xy, P=(0,−3)P=(0,−3) and v=3i+1jv=3i+1j.
Find the directional derivative of ff at PP in the direction of vv.
(Duf)(P)=
Find the maximum rate of change of ff at PP.
Find the (unit) direction vector ww in which the maximum rate of change occurs at PP.
w=
The directional derivative of f at P in the direction of v is 3. The maximum rate of change of f at P is 3, which occurs in the direction of the vector w = (3/√10)i + (1/√10)j.
The directional derivative of a function f at a point P in the direction of a vector v is given by the dot product of the gradient of f at P and the unit vector in the direction of v. In this case, the gradient of f is given by (∂f/∂x, ∂f/∂y) = (y, x), so the gradient at P is (−3, 0). The unit vector in the direction of v is (3/√10, 1/√10). Taking the dot product of the gradient and the unit vector gives (−3)(3/√10) + (0)(1/√10) = −9/√10 = −3/√10. Therefore, the directional derivative of f at P in the direction of v is 3.
To find the maximum rate of change of f at P, we need to find the magnitude of the gradient of f at P. The magnitude of the gradient is given by √(∂f/∂x)^2 + (∂f/∂y)^2 = √(y^2 + x^2). Substituting P into the expression gives √((-3)^2 + 0^2) = 3. Therefore, the maximum rate of change of f at P is 3.
To find the unit direction vector w in which the maximum rate of change occurs at P, we divide the gradient vector at P by its magnitude. The gradient at P is (−3, 0), and its magnitude is 3. Dividing each component by 3 gives the unit vector (−1, 0). Thus, the unit direction vector w in which the maximum rate of change occurs at P is w = (−1, 0).
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A cosine function has a period of 4, a maximum value of 20, and a minimum value of 0. The function is a not a reflection of its parent function over the x-axis.
Which function could be the function described?
Answer:
Step-by-step explanation:
You'll need to find a way to share the graph or graphs associated with this problem.
The period is 4. The relationship between period and b (the coefficient of the independent variable of the cosine function) is (period) =(2π.b). Given that the period here is 4,
2π 2π
4 = ---------, and so b = ------- = π/2.
4
So now our y = a*cos (bx + c) becomes
π
y = 10*cos (------x + 0 + 10
2
The horizontal center line of this cosine curve is y = 10. The maximum value of the curve is 20, which is 10 + 10, and the minimum value is 0, which is 10 - 10.
The function that describes the given situation is \(\rm y = 10\;cos\left(\dfrac{\pi}{2}x\right) + 10\) and this can be determined by using the properties of the trigonometric function.
Given :
A cosine function has a period of 4, a maximum value of 20, and a minimum value of 0. The function is not a reflection of its parent function over the x-axis.The following steps can be used in order to determine the function could be the function described:
Step 1 - According to the given data, the cosine function has a period of 4.
Step 2 - Now, the independent variable of the cosine function is given by:
\(\rm 4b = 2\pi\)
\(\rm b =\dfrac{\pi}{2}\)
Step 3 - The maximum value of the cosine function is 1 and the minimum value of the cosine function is -1.
Step 4 - From the above steps, the function that described the given situation is given by:
\(\rm y = 10\;cos\left(\dfrac{\pi}{2}x\right) + 10\)
Therefore, the correct option is C).
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Solve the right triangle, Please Do not Roundup. NEED HELP ASAP PLEASE.
The angles and length of the right triangle are as follows:
WX = 10√141 units
m∠X = 30°
m∠V = 60°
How to find the side of a right angle triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right angle triangle is 180 degrees.
Trigonometric ratios can be used to find the side and angles of the right triangle as follows;
Therefore,
Using Pythagoras's theorem,
WX² = (20√47)² - (10√47)²
WX² = 400(47) - 100(47)
WX² = 18800 - 4700
WX = √14100
WX = 10√141
Let's find the angles
sin m∠X = opposite / hypotenuse
sin m∠X = 10√47 / 20√47
sin m∠X = 1 / 2
m∠X = sin⁻¹ 0.5
m∠X = 30 degrees
Therefore,
m∠V = 180 - 90 - 30
m∠V = 60 degrees
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Ray has tea. He has 2.671 liters of tea he pours 0.47 liters in a glass. how many liters did he pour? Solve.
On solving the given problem by help of mathematical operations, we got - After Ray poured 0.47L, he was left with 2.201L.
What does the term "mathematical operations" mean?The term "operation" in mathematics refers to the process of calculating a value using operands and a math operator. For the given operands or numbers, the math operator's symbol has predetermined rules that must be followed.
What are the five operations in mathematics?In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Total amount of tea Ray has - 2.671L
Amount of tea Ray poured - 0.47
Therefore,
amount he was left with was = 2.671- 0.47 = 2.201L
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PLEASE HELP I'M MARKING BRAINLIEST!!!!!!
Answer:
download Gauthnath and see answer
which of the following compares the overall difference between two or more independent samples? a. kruskal-wallis one-way ANOVA b. the sign test c. wilcoxon rank test d. mann-whitney U test
The Kruskal-wallis one-way ANOVA compares the overall difference between two or more independent samples. So, the correct option is option a. kruskal-wallis one-way ANOVA
The answer is option A, the Kruskal-Wallis one-way ANOVA compares the overall difference between two or more independent samples.
The Sign test and Wilcoxon rank test are non-parametric tests used for comparing paired samples, while the Mann-Whitney U test is used for comparing two independent samples.
This test is used to compare the overall difference between two or more independent samples when the assumptions of a regular one-way ANOVA are not met.
The Kruskal-Wallis test is applicable when the data violate the assumptions of normality and/or equal variances required by parametric ANOVA tests.
Instead of comparing means, it compares the ranks of the data values within each group to assess if there are significant differences between the groups.
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complete the square to rewrite the following equation in standard form
By completing the square, the equation in standard form is (x - 2)² + (y + 4)² = 4².
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.From the information provided below, we have the following equation of a circle:
x² - 4x + y² + 8y = -4
x² - 4x + (-4/2)² + y² + 8y + (8/2)² = -4 + (-4/2)² + (8/2)²
x² - 4x + 4 + y² + 8y + 16 = -4 + 4 + 16
(x - 2)² + (y + 4)² = 16
(x - 2)² + (y + 4)² = 4²
Therefore, the center (h, k) is (2, -4) and the radius is equal to 4 units.
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Complete Question:
Complete the square to rewrite the following equation in standard form. x² - 4x + y² + 8y = -4.
Which answer choice below is not a correct way to show the answer to a division problem?
A) 913 ÷ 29 = 31 r 14
B) 913 ÷ 29 = 31 14/29
C) 913 ÷ 29 = 31.14
D) 913 ÷ 29 = 31
Answer:
option D
Step-by-step explanation:
it is the incomplete answer
the circle graph shows how a family budgets its annual income. if the total annual income is $90,000 what amount is budgeted for clothing?
Answer:
$11700
Step-by-step explanation:
comment if u need the explanantion ;D
Which equation best models the data shown on the scatter-plot below?
The scatterplot is an illustration of a linear regression.
The equation that best models the scatter plot is y = 4x+ 35
How to determine the equation of the scatterplot?The equation of a linear regression is represented as:
y = mx + b
Where:
m represents the slope
b represents the y-intercept
From the graph, we have the following points on the line of best fit (see attachment)
(x,y) = (10,75) and (20,105)
The equation is then calculated as:
\(y = (\frac{y_2 - y_1}{x_2 - x_1})(x -x_1) + y_1\)
This gives
\(y = (\frac{105 - 75}{20- 10})(x -10) + 75\)
Evaluate
\(y = 4(x -10) + 75\)
Open the bracket
\(y = 4x -40 + 75\)
Simplify
\(y = 4x+ 35\)
Hence, the equation that best models the scatter plot is y = 4x+ 35
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