Function Composition exists when two functions f(x) and g(x) result in another function h(x), such that h(x) = f(g(x)). For function composition h(x) = f(g(x)), the value of a exist -4.
What is function Composition?
Function Composition exists when two functions f(x) and g(x) result in another function h(x), such that h(x) = f(g(x)). In other words, put the outcome of one function into the other one.
Here, h(x) = f(g(x))
which means, h(x) = f(x³+ a)
[tex]$h(x) = \sqrt{x^3+a+2}[/tex]
[tex]$\sqrt{x^3-2} = \sqrt{x^3+a+2}[/tex]
To estimate the value of a, we separate equal terms:
1) Both are squared, so we can "eliminate" the square;
2) x³ = x³
3) -2 = a+2
a = -4
For function composition h(x) = f(g(x)), the value of a exist -4.
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x - 2y = 3
5x + 3y = 2
The lines whose equations are shown intersect at which point?
The point of intersection of the two lines is at (1,-1)
System of equationThe given system of expression is shown below
x - 2y = 3
5x + 3y = 2
The solution to the system of equation is the point of intersection
From equation 1
x = 3 + 2y
Substitute into 2
5(3+2y) + 3y = 2
15 +10y + 3y = 2
13y = -13
y = -1
Substitute y = -1 into 3
x = 3 + 2y
x = 3+(-2)
x = 1
Hence the point of intersection of the two lines is at (1,-1)
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there are 6 girls and 8 boys in Mr. Stevenson's class the ratio of girls to boys in the class can be expressed as the simplified ratio ?/4 what is the missing number ?
Answer: 3
Step-by-step explanation:
The missing number in the simplified ratio ?/4 is 3.
Here, we have to find the missing number in the simplified ratio ?/4, we need to determine the ratio of girls to boys in Mr. Stevenson's class.
Given that there are 6 girls and 8 boys in the class, the ratio of girls to boys can be expressed as:
Number of girls : Number of boys = 6 : 8
To simplify the ratio, we can divide both the number of girls and the number of boys by their greatest common divisor (GCD).
In this case, the GCD of 6 and 8 is 2.
Dividing both 6 and 8 by 2, we get:
Number of girls : Number of boys = 6/2 : 8/2 = 3 : 4
So, the simplified ratio of girls to boys is 3/4.
Therefore, the missing number in the simplified ratio ?/4 is 3.
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. [Multiples / Factors / Primes] *
What is the highest
common factor (HCF)
of 24 and 45?
If BD = 16 yd and the area of rhombus ABCD is 72 yd^2, what is AC?
Formula for finding area of rhombus: [tex]\frac{d1 * d2}{2}[/tex]
d₁ = 16 yd
Area = 72 yd²
Rhombus Area =>
[tex]\frac{16 * d2}{2} = 72[/tex]
16*d₂ = 144
d₂ = 9
AC = 9 yd
Hope it helps!
3. A square garden plot has an area of 24 ft^2. Find the length of each side in simplest radical form. Calculate the length of each side to the nearest tenth of a foot
The length of each side of the square garden plot in simplest radical form and to the nearest tenth of a foot is 2√6 and 4.9 ft
Area of a squareArea of square = Length ²
Area of the square garden plot = 24 ft²Area of square = Length ²
24 = length ²
find the square root of both sides√24 = √length²
√24 = length
length = 4.898979485566356196394568149411782783
Approximately,
length = 4.9 ft
In radical form
length = √24
= 2√6
Therefore, the length of each side of the square garden plot in simplest radical form and to the nearest tenth of a foot is 2√6 and 4.9 ft
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Estimate the product of 0. 235 and 13. 467 to the nearest hundredth.
Answer:
3.16
Step-by-step explanation:
An estimate is usually made to 1 or 2 significant digits. Here, we want an estimate accurate to hundredths, which will be 3 significant digits.
EstimateWe can round the numbers to some reasonable values, then look at the effect of the rounding error.
0.235 × 13.467 = (0.25 -0.015) × (13.5 -0.033)
= 0.25(13.5) -0.25(0.033) -0.015(13.5) +0.015(0.033)
= 3.375 -0.00825 -0.2025 + (something small)
≈ 3.375 -0.008 -0.203 = 3.375 -0.211 = 3.164
0.235 × 13.467 ≈ 3.16
Mental mathNote that the values we have can make use of mental math methods.
0.25 = 1/4 = (1/2)(1/2)
0.015 = 0.01(1 +1/2)
That is, dividing numbers by 2 mentally is usually not terribly difficult. (Here, it is made more difficult by the odd digits involved.)
0.25 × 13.5 = (1/2)(13.5/2) = 1/2(6.75) = 3.375
0.015 × 13.5 = 0.135 +0.135/2 = 0.135 +0.0675 = 0.2025
or, recognizing that 1.35 = 1.5 -.15, ...
0.015 × 13.5 = (0.01)(1.5) × (10)(1.5-.15) = 1.5²×(.1 -.01) = .225 -.0225
__
Additional comment
A calculator gives the actual product as 3.164745, so our estimate is accurate to hundredths.
Find the standard deviation for the set of data. {15,17,23,5,21,19,26,4,14} a. 7.17 b. 7.39 c. 7.1 d. 6.65
The standard deviation exists as the positive square root of the variance.
So, the standard deviation = 6.819.
How to estimate the standard deviation?Given data set: 15, 17, 23, 5, 21, 19, 26, 4, 14
To calculate the mean of the data.
We know that mean exists as the average of the data values and exists estimated as:
Mean [tex]$=\frac{15+17+23+5+21+19+26+4+14}{9}[/tex]
Mean [tex]$=\frac{144}{9}[/tex]
Mean = 16
To estimate the difference of each data point from the mean as:
Deviation:
15 - 16 = -1
17 - 16 = 1
23 - 16 = 7
5 - 16 = -11
21 - 16 = 5
19 - 16 = 3
26 - 16 = 10
4 - 16 = -12
14 - 16 = -2
Now we have to square the above deviations we obtain:
1 , 1, 14, 121, 25, 9, 100, 144, 4
To estimate the variance of the above sets:
variance [tex]$=\frac{1+ 1+14+ 121+25+ 9+ 100+ 144+ 4}{9}[/tex]
Variance [tex]$=\frac{419}{9}[/tex]
Variance = 46.5
The standard deviation exists as the positive square root of the variance.
so, the standard deviation [tex]$\sqrt{46.5} =6.819[/tex] .
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Deion misses 4% of the free throws he attempts in a seaon. how many total free throws did he attempt if he missed 17
He has thrown 425 free throws if he missed 17
How to determine the total number of free throws?The given parameters are:
Proportion of free throw missed, p = 4%
Number of free throw missed, n = 17
Let the total number of throws be N.
So we have
n = p * N
Substitute the known values in the above equation
17 = 4% * N
Divide both sides by 4%
N = 425
Hence, he has thrown 425 free throws if he missed 17
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this is my last ever question on brainly.com
please help
A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
What is a line plot?A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
What is a mean?In Mathematics, a mean is also referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
Mathematically, the distance between the means of both classes A and B is given by:
Distance = Mean of class A - Mean of class B
Distance = 12 - 4
Distance = 8.
The mean absolute deviation (MAD) for class A is given by:
MAD A = 1/9[2(9 - 12) + (10 - 12) + (11 - 12) + (12 - 12) + (13 - 12) + (14 - 12) + 2(15 - 12)]
MAD A = 1/9[2(3) + (2) + (1) + 0 + (1) + (2) + (1) + 2(3)]
MAD A = 1/9[6 + 2 + 1 + 1 + 2 + 1 + 6]
MAD A = 1/9 × [18]
MAD A = 18/9
MAD A = 2.
Also, the mean absolute deviation (MAD) for class B is given by:
MAD B = 1/9[2(1 - 4) + (2 - 4) + (3 - 4) + (4 - 4) + (5 - 4) + (6 - 4) + 2(7 - 4)]
MAD B = 1/9[2(3) + 2(2) + (1) + (0) + (1) + (2) + 2(3)]
MAD B = 1/9[6 + 4 + 1 + 0 + 1 + 2 + 6]
MAD B = 1/9 × [18]
MAD B = 18/9
MAD B = 2.
Therefore, distance between the means = four (4) times the MAD.
Distance = Means × MAD
8 = 4 × 2.
In conclusion, we can infer and logically deduce that there is no overlap and the distance between the means of both classes A and B is between one (1) times the MAD and five (5) times the MAD.
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Find the value of Theta in these diagrams (a and b)
a. θ = 36. 9°
b. θ = 114. 2°
How to determine the value of theta
a. We use the cosine identity
cos θ = adjacent/hypotenuse
Adjacent = 4cm
Hypotenuse = 5cm
cos θ = 4/ 5
cos θ = 0. 8
Now, we have the inverse of the cosine value
θ = cos^-1 (0. 8)
θ = 36. 9°
b. We use the tangent identity
tan a = opposite / adjacent
tan a = 3. 8/1. 7
tan a = 2. 23
a = tan^-1 ( 2. 23)
a = 65. 8
We have;
a + θ = 180 °; angles on a straight line
θ = 180 - 65. 9
θ = 114. 2°
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In a study on the placebo effect on 100 students, 64 were found to perform better on tests after taking a fake pill to improve concentration. What is the experimental probability the placebo pill induced better concentration on the student exams?
The experimental probability the placebo pill induced better concentration on the student exams is 0.64
The question has to do with probability.
What is probability?Probability is the likelihood of an event occurring.
The probability of an event A is given by
P(A) = number of occurrences of event A/total number of occurrences of all events.
What is the experimental probability the placebo pill induced better concentration on the student exams?Given that in the study on the placebo effect on 100 students, 64 were found to perform better on tests after taking a fake pill to improve concentration.
The event A = students performing better.
Since 64 students performed better, the number of occurrences of event A = 64.
Since there were 100 students, the total number of occurrences = 100.
So, P(A) = P(students perform better)
= number of occurrences of event A/total number of occurrences of all events.
= 64/100
= 0.64
So, the experimental probability the placebo pill induced better concentration on the student exams is 0.64
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1) A 20-foot ladder is placed against a building. If the top of the ladder will lean against the building 4sqrt(7) - f feet high, how far away from the base of the building is the bottom of the ladder located? Include a sketch that shows all known information and clearly shows what you need to findShow all work and give the exact answer
Answer:
12√2.
Step-by-step explanation:
You can do this by the Pythagoras theorem:
20^2 = x^2 + (4sqrt7)^2 where x is the distance required.
x^2 = 20^2 - (4sqrt7)^2
= 400 - 112
= 288
x = √288
= √144 *√2
= 12√2.
What are the step to the Quadratic Formula?
The steps to solve a quadratic formula include:
Combine all of the like terms and move them to one side of the equationFactor the expressionSet each set of parenthesis equal to zero as separate equationsSolve each "zeroed" equation independentlyWhat is a quadratic equation?In algebra, a quadratic equation is a equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.
A quadratic equation is an equation that could be written as ax² + bx + c = 0
when a 0. The factoring method is illustrated:
To solve a quadratic equation by factoring, put all terms on one side of the equal sign, leaving zero on the other side.
Set each factor equal to zero.
Solve each of these equations.
Check by inserting your answer in the original equation.
Example 1
Solve x² – 6 x = 16.
Following the steps,
x² – 6 x = 16 becomes x² – 8x + 2x – 16 = 0
Factor.
( x – 8)( x + 2) = 0
Therefore, x = 8 and -2.
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Evaluate the expression using a calculator:
The value of the expression is 0.0265. Using exponents and power rules, the required value is calculated.
What are the exponent and power rules?The important exponent and power rules are:
a⁻ⁿ = 1/aⁿ; negative exponent(ab)ⁿ = aⁿ × bⁿ; power of a product ruleaⁿ × aˣ = aⁿ⁺ˣ; multiplication ruleaⁿ/aˣ = aⁿ⁻ˣ; division rule[tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]; fractional exponentCalculation:The given expression is [tex]126^{-3/4}[/tex]
Using calculator: [tex]126^{-3/4}[/tex] = 0.0265
Applying the exponent rule for evaluating the given expression:
[tex]126^{-3/4}[/tex]
Applying the negative power rule;
I.e., a⁻ⁿ = 1/aⁿ
⇒ [tex]126^{-3/4}=\frac{1}{126^{3/4}}[/tex]
Applying fractional exponent rule;
I.e., [tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]
⇒ [tex]\frac{1}{126^{3/4}}=\frac{1}{\sqrt[4]{126^3} }[/tex]
⇒ 1/[tex]\sqrt[4]{2000376}[/tex]
⇒ 1/37.6077
⇒ 0.0265
Therefore, the value of the given expression is 0.0265.
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Need help!!!!!!! Please help me out
Answer:
x = 10°
Step-by-step explanation:
If the two lines are parallel then the two marked angles will be equal.
8x = 2x + 60
Subtract 2x to combine like terms.
6x = 60
Divide by 6.
x = 10
Write the following expression using exponents -3x7x7x7x7x7x7
Solution -:
[tex] \bold{ \underline{ \underline{Given}}}[/tex]
-3x7x7x7x7x7x7
[tex]\bold{\underline {\underline{lets \: begin}}}[/tex]
We have,,
[tex] -3 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \\ = - 3¹ \times {7}^{6} [/tex]
exponent and shortcut to express a multiplication of number by itself several times explain us how many time we should multiply the number by itself this process of using exponent is called raising to a power where the exponent is the power.Law of exponent -: a ⁰ = 1 a ^ m × a ^ n (a^m)^na^m × b^ mAs like example→ 2⁴
here 2 is base and 4 is power , index or exponent. and 2⁴ is known as Exponential form.
expand and simplify -2(x + 4x^2) + 3(x^2 + 2x)
......................
The data in the table can be entered into a calculator to determine a linear equation of best fit where x represents the number of years with a company and y represents an employee’s salary in dollars.
Based on the data given, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is C. There's a weak negative correlation between the variables.
How to illustrate the information?From the information given, it can be seen that the value of y is increasing with the increase in the value of x.
This implies that the correlation is positive. Also, the change in the values of y with x are scattered a lot.
Therefore, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is that there's a weak negative correlation between the variables
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What is the multiplicity of f(x) = -2x3(x + 2)2?
The manager of spiffy lube auto lubrication shop is trying to revise his policy on ordering grease gun cartridges. currently he orders 110 cartridges per week, but he runs out of cartridges 1 out of 4 weeks. he knows that, on average, the shop uses 95 cartridges per week. he was also willing to assume that the demand for cartridges is normally distributed. a. compute the standard deviation of the distribution?
Using the normal distribution, it is found that the standard deviation is of 26.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, we have that the mean is of [tex]\mu = 95[/tex], while X = 110 has a p-value of 0.75, hence X = 110, Z = 0.575, and then we solve for [tex]\sigma[/tex] to find the standard deviation.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.575 = \frac{110 - 95}{\sigma}[/tex]
[tex]0.575\sigma = 15[/tex]
[tex]\sigma = \frac{15}{0.575}[/tex]
[tex]\sigma = 26[/tex]
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Write down the next two numbers in each of the following sequences. 40 POINTS
a) 0.04,0.1,0.16, __ , __
b)3,9,27 , __,__
c)0.3,1/3,11/30,__,__
Answer:
Below in bold.
Step-by-step explanation:
a) 0.04, 0.1, 0.16
You add 0.06 to get the next term:
The next 2 are: 0.22, 0.28.
b) 3, 9, 27
You multiply by 3 to get next term
Next 2 are: 81, 243.
c) 0.3, 1/3, 11/30
1/3 - 0.3 = 1/30
11/30 - 1/3 = 1/30
So common difference = 1/30
The next 2 terms are 12/30 and 13/30
= 2/5 , 13/30.
PLS HELP>>>>solving functions
Answer:
The first option:
[tex]x^2-5x+9[/tex]
Step-by-step explanation:
Trust me I am right.
If you need work please ask!
Have a nice day!
Find a so that line CD will have the given slope: C(3, -3), D(-3,a); m= -4/3
Work Shown:
m = (y2 - y1)/(x2 - x1)
-4/3 = (a - (-3))/(-3 - 3)
-4/3 = (a+3)/(-6)
-4*(-6) = 3(a+3)
24 = 3a+9
3a+9 = 24
3a = 24-9
3a = 15
a = 15/3
a = 5
the titanic had about half as many plates as they did pieces of silverware . About how many plates did they have ?
Answer:
about 1800 im sorry if im wrong
Step-by-step explanation:
Use 3.14 for pi. ROUND FINAL ANSWER TO TENTHS!
2461,8
hope this helps!! just use the formulas and substitute
solve the equation r = 1(x-1) for x in terms of r
After some algebraic handling, the algebraic expression for x in terms of r is x = 1 / r + 1 .
How to clear a variable within an algebraic formula
In this question we must make use of algebra properties to clear a variable within a formula only formed by algebraic form, there are no trascendent functions herein. Clearing variables consists in leaving such variables alone in one side of the equivalence. Now we proceed to present the procedure in detail:
r = 1 / (x - 1) Givenr = (x - 1)⁻¹ Definition of divisionx - 1 = r⁻¹ Compatibility with multiplication / Existence of multiplicative inverse / Associative, commutative and modulative properties.x = 1 / r + 1 Definition of division / Compatibility with addition / Existence of additive inverse / Commutative and modulative properties / ResultRemarkThe statement presents a typing omission, correct form is shown below:
Solve the equation r = 1 / (x - 1) for x in terms of r.
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A graph titled Speed as a Function of Time with horizontal axis time (seconds) and vertical axis speed (meters per second). A straight orange line labeled A starts at 0 seconds 4 meters per second and runs to 6 seconds 7 meters. A straight blue line labeled B starts at 0 seconds 4 meters and upward to 6 seconds 4 meters. A straight green line starts at 0 seconds 4 meters and runs to 4 seconds 0 meters.
Use the graph of speed versus time to answer the questions about acceleration.
Which of the cars is speeding up?
Which of the cars is slowing down?
Which of the cars is maintaining a constant speed?
From the attached speed versus time graph, it can be seen that the orange or first or car is speeding up. The third or green car is slowing down, and the blue or second car is maintaining a constant speed.
Speed Analysis from the Graph
The graph in the attachment shows the linear increase in speed of the first car over time. Therefore, we can say that it is accelerating at a certain rate.
The graph shows how the speed of the third car is decreasing with time. This demonstrates that the green vehicle is de-accelerating.
The graph shows a straight line for the second car. It displays that the speed does not alter as seconds or minutes pass. We might infer that the blue car is continuing to travel at its current pace as a result.
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Answer:
A C B
Step-by-step explanation:
Which of the cars is speeding up?
A
Which of the cars is slowing down?
C
Which of the cars is maintaining a constant speed?
B
Solve -6x + 3 ≥ 21.
OA. x2 3
OB. x≤-3
OC. x≥-3
OD. x≤3
Answer:
B
Step-by-step explanation:
- 6x + 3 ≥ 21 ( subtract 3 from both sides )
- 6x ≥ 18
divide both sides by - 6, reversing the symbol as a result of dividing by a negative quantity.
x ≤ - 3
If the two lines below are perpendicular and the slope of the red line is -
what is the slope of the green line?
O A.
A.
OB. -3
314
O D.
D. -
-10
10
15
Answer:
-(10/7)
Step-by-step explanation:
See attached graphic. The slope of the Green Line is cut off in the problem photo, but can be calculated from the graph to find the slope of the Red Line. The answer options are on drugs; pick the one that looks closest.
Answer:
-4/3
Step-by-step explanation:
Use the diagram to complete the following tasks.
Given: S' is the midpoint of QT.
Finish the following statement: AQRSA_
Identify the congruent Zs.
Justify your answer.
R
S
This exercise is about a proof in Euclidian geometry. See the explanation below.
What is Euclidian Geometry?The study of solid and flat objects using the axioms and theorems developed by the Greek mathematician Euclid is known as Euclidean geometry (c. 300 bce).
What is the statement that completes the above proof?Given that S is the midpoint of [tex]\overline{QT}[/tex]:
Hence QS = TS ......................1
It is right to indicate that
PQ = TV ........................2
And ∠RSQ is vertically opposite to ∠TSV
Hence
∠RSQ = ∠TSV.........................3
Given 1, 2, and 3,
Δ QRS ≅ ΔVTS
Therefore,
Δ QRS ≅ ΔVTS
and ∠ RSQ can be termed to be congruent to ∠TSV.
What does it mean for an angel to be congruent?It is to be noted that the measure of an angle is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees.
The angles of a regular polygon will always be congruent, regardless of its size or scale.
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