Answers
replace the numbers inside () for x
f(4) = -4(4)-3 = -16 -3 = -19
G(-4) = 2(-4)^2 -3(-4) = 44
Related Questions
Earns 8.50 an hour . Works 45 hours.
Answers
What is the smallest positive integer with exactly 14 positive divisors?
Answers
The smallest positive integer with exactly 14 positive divisors is 24. The number is found by considering its prime factorization and adding 1 to each exponent, then multiplying the results together. Another prime factor raised to the power of 5 can be included to have exactly 14 divisors.
Explanation:The smallest positive integer with exactly 14 positive divisors is 24.
To find this, we need to consider the prime factorization of the number. Let's express 24 as a product of prime factors: 24 = 2^3 * 3^1.
The number of divisors is found by adding 1 to each exponent in the prime factorization and multiplying them together: (3+1)(1+1) = 4 * 2 = 8. However, we need exactly 14 divisors, so we can multiply 24 by another prime factor raised to the power of 5: 24 * 5^4 = 24 * 625 = 15,000.
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The smallest positive integer with exactly 14 positive divisors is 192. We derived this by using the prime factorization method and finding suitable combinations to get exactly 14 divisors.
To find the smallest positive integer with exactly 14 positive divisors, we need to understand the number of divisors formula. For an integer n = p1e* p2e² * ... * p^ke^k, the number of divisors is given by (e1 + 1)(e² + 1) ... (e^k + 1).
To have exactly 14 divisors, we need (e1 + 1)(e² + 1) ... (e^k + 1) = 14. The factorizations of 14 are 14 = 14 * 1, 7 * 2, or 2 * 7. Let's use the smallest primes to minimize our number:
14 = 14 * 1: This means n = p113. Using the smallest prime number, we have n = 213 = 8192, which is too large.
14 = 7 * 2: This means n = p16 * p21. Using the smallest primes, we get n = 26 * 3 = 64 * 3 = 192.
14 = 2 * 7: This means n = p11 * p26. Using the smallest primes, we get n = 2 * 36 = 2 * 729 = 1458.
Comparing these solutions, the smallest positive integer is n = 192, which has exactly 14 positive divisors.
State what additional information is required in order to know that the triangles are congruent for the reason given.
Answers
Amanda apent 2$ more than Barry on school supplies together they spent
34 How much money did each spend
Answers
[tex]2x + 2 = 34 \\ x = 16[/tex]
so amanda spent 18 and Barry 16
hope this helps you(:
if not plz let me know(:
One box of crackers costs $1.75. The crackers are advertised as “3 boxes for $5.25.” Which proportion can be used to represent the cost of the crackers?
Answers
What is the least common multiple of 3, 4a, 5b, and 6ab?
Answers
Final answer:
The least common multiple (LCM) of 3, 4a, 5b, and 6ab is 60ab, calculated by prime factorizing each term and identifying the highest power of each prime factor.
Explanation:
The least common multiple (LCM) of 3, 4a, 5b, and 6ab is calculated by finding the LCM of the individual components.
Prime factorize each term: 3 = 3, 4a = 2*2*a, 5b = 5*b, 6ab = 2*3*a*b.
Identify the highest power of each prime factor: LCM = 2*2*3*5*a*b = 60ab.
A company makes storage tanks in the shape of a cylinder of height H and radius R. The standard model the company sells has a height of 20 cm in the radius of 20 cm. Customers may also request tanks that have a smaller radius. For each centimeter a tank’s radius decreases, however it’s height must increase by 5 cm.
The volume of a cylinder Jeckel storage tank is represented by the formula V= 3.14 (radius)^2 (height). X represent the number of centimeters by which the radius is decreased due to a customer’s request. Write a function V(x) to represent the volume of a tank a customer a request as a function of X.
Answers
We are given the formula for volume V:
V = 3.14 r^2 h
where r is radius and h is height
The standard height and radius is both 20 cm each, therefore we can write it as:
V = 3.14 (20)^2 (20)
It is stated that the radius can be modified, for every 1 cm change in tanks radius, the height must increase by 5 cm, therefore:
V = 3.14 (20 – x)^2 (20 + 5x)
or in general form:
V = 3.14 (r – x)^2 (h + 5x)
48.5 out of 50 as a percentage
Answers
48.5 out of 50 as a percentage, is 97%.
48.5 out of 50 as a percentage can be calculated by dividing 48.5 by 50 and then multiplying by 100 to get the percentage.
Divide 48.5 by 50: 48.5 / 50 = 0.97
Multiply by 100 to get the percentage: 0.97 * 100 = 97%
A sample of n = 25 individuals is selected from a population with µ = 60 and sigma = 10 and a treatment is administered to the sample. after treatment, the sample mean is m = 63. what is the value of cohen's d for this sample?
Answers
The information regarding the sampling shows that the value of cohen's d for this sample is 0.3.
How to calculate the sampleFrom the information given, the sample of n = 25 individuals is selected from a population with µ = 60 and sigma = 10 and a treatment is administered to the sample. after treatment, and the sample mean is m = 63.
Therefore, the value of cohen's d for this sample will be:
= (M - µ) / 10
= (63 - 60) / 10
= 0.3
In conclusion, the correct option is 0.3.
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Final answer:
Cohen's d for the given sample is 0.3, calculated by subtracting the population mean from the sample mean and dividing by the population standard deviation.
Explanation:
The student's question is regarding the calculation of Cohen's d for a sample after treatment. Cohen's d is a measure of effect size used to indicate the standardized difference between two means. In this case, the following formula can be used: Cohen's d = (M - μ) / σ, where M is the sample mean after treatment, μ is the population mean, and σ is the population standard deviation.
Given that M = 63, μ = 60, and σ = 10, the calculation of Cohen's d is as follows:
Cohen's d = (63 - 60) / 10 = 3 / 10 = 0.3.
Therefore, the value of Cohen's d for this sample is 0.3, which is considered a small effect size according to Cohen's standards.
Fill in the blanks to write an equation in slope-intercept form representing the function shown in the table.
Answers
10-4 6
-------- = ---- = 3
3-1 2
So the slope is 3. y=3x+1
A spinner is divided into 4 equal sections the probability of landing on A is 1/4 Norma spins the spinner 16 times how many times can she expect the spinner to land on A
Answers
1/4 = 0.25
So 0.25 * 16 = 4
≈ 4 times
Final answer:
Norma can expect the spinner to land on section A 4 times after spinning it 16 times, based on the probability of [tex]\frac{1}{4}[/tex].
Explanation:
The question asks about the expected number of times Norma can anticipate the spinner to land on section A after spinning it 16 times, given that the probability of landing on A is [tex]\frac{1}{4}[/tex]. To find this, we use the concept of expected value, which in this context is the probability of an event happening multiplied by the number of trials. Since the probability of landing on A is [tex]\frac{1}{4}[/tex] and there are 16 spins, the expected number of times landing on A is calculated as [tex]\frac{1}{4}[/tex] multiplied by 16.
Expected number of landings on A = Probability of landing on A × Number of spins = [tex]\frac{1}{4}[/tex] × 16 = 4.
Therefore, Norma can expect the spinner to land on section A four times after spinning it 16 times.
A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 12 mm and it wants to know how the area A(x) of a wafer changes when the side length x changes. Find A'(12)
Answers
The value of the derivatives is A'(12) = 24.
We have,
To find the derivative of the area function A(x) with respect to x, we can differentiate the equation for the area of a square:
A(x) = x^2
Using the power rule, we differentiate A(x) with respect to x:
A'(x) = 2x
To find A'(12), we substitute x = 12 into the derivative equation:
A'(12) = 2 * 12 = 24
Therefore,
The value of the derivatives is A'(12) = 24.
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Final answer:
To find A'(12), the rate at which the area A(x) changes when the side length x changes, take the derivative of A(x), which is 2x, and evaluate it at x = 12. The derivative of A(x) is 2x, so A'(12) = 2(12) = 24.
Explanation:
To find the rate at which the area A(x) changes with respect to a change in x, we need to take the derivative of A(x) with respect to x. In this case, A(x) represents the area of a square wafer of silicon with a side length x. The derivative with respect to x is A'(x), which represents the rate of change of the area.
We want to find A'(12), which means we want to find the rate of change of the area when the side length is 12 mm. To do this, we need to take the derivative of A(x) and then evaluate it at x = 12.
Since the side length of the wafer is very close to 12 mm, we can assume x = 12.
Let's find the derivative of A(x):
A(x) = x^2
A'(x) = 2x
Now we can evaluate A'(12):
A'(12) = 2(12) = 24
Merry and pippin were working on a project in carpentry class. they needed to cut 4 lengths of 1 5/8 feet from a board. how long must the board be to allow this?
Answers
13/8×4/1=52/8 feet
We can change it back to proper fraction by dividing 52 by 8.
We get 6 with remainder 4.
6 4/8 =6 1/2 feet
Harper has $15.00 to spend at the grocery store. She is going to buy bags of fruit that cost $4.75 each and one box of crackers that cost $3.50. Model the problem algebraically and determine the maximum number of bags of fruit,b, Harper can buy.
Answers
That means we would have 15 > or = 4.75b + 3.5c.
The best way to solve this would be to divide,
15 ÷ 4.75 = 3.15
Then round down to the nearest whole number.
You should get 3 bags of fruit.
♥ Hope I helped ♥
There are 13 animals in the barn. Some are chickens and some are pig's. There are 40legs in all. How many of each animal are there?
Answers
Answer:
7 pigs6 chickensStep-by-step explanation:
If all were chickens, there would be 26 legs. There are 14 legs more than that. Each pig contributes 2 additional legs, so there must be 14/2 = 7 pigs. The remaining 6 animals are chickens.
___
Check
7×4 + 6×2 = 28 +12 = 40 . . . . total legs
Answer:
easy! 27
Step-by-step explanation:
13- 40 = 27
or 13 + 27 =40
just add up 13 and 27 you'll get 40 in all
edit; btw I'm not the brightest
PLEASE HELP!!! What is the product in simplest form? State any restrictions on the variable. z^2/z+1 times z^2+3z+2/z^2+3z
Answers
Hence, the product is:
[tex]\dfrac{z(z+2)}{z+3}[/tex] such that: z≠ -1,0 and -3.
Step-by-step explanation:We are asked to represent the product in the simplest form along with the restrictions applied to z.
We have to evaluate the expression:
[tex]\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z^2+3z}\\\\=\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z(z+3)}[/tex]
Hence,
z≠ -1,0 and -3.
Since, otherwise the denominator will be equal to zero and hence the product will not be defined.
Now, we know that:
[tex]z^2+3z+2=z^2+2z+z+2\\\\z^2+3z+2=z(z+2)+1(z+2)\\\\z^2+3z+2=(z+1)(z+2)[/tex]
Hence,
[tex]\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z^2+3z}=\dfrac{z^2}{z+1}\times \dfrac{(z+1)(z+2)}{z(z+3)}\\\\=\dfrac{z(z+2)}{z+3}[/tex]
( since z and (z+1) term is cancelled as it was same in numerator and denominator)
Hence, the product is:
[tex]\dfrac{z(z+2)}{z+3}[/tex] such that: z≠ -1,0 and -3.
What are the roots of the equation? 5 x 3+45x2+70x=0
Answers
Final answer:
The roots of the equation 5x³ + 45x² + 70x = 0 are -7 and -2.
Explanation:
This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 5, b = 45, and c = 70. To find the roots of the equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values, we get:
x = (-45 ± √(45² - 4(5)(70))) / (2(5))
Simplifying further gives us:
x = (-45 ± √(2025 - 1400)) / 10
And finally, calculating the square root and applying the ± gives us the two roots:
x = (-45 ± √625) / 10
x = (-45 ± 25) / 10
which can be further simplified to:
x = -7 or x = -2
Which value of x is the solution of the equation
2( x-4) + 7= 3?
1. 1
2.2
3 . 6
4 . 0
Answers
The solution to the equation 2(x - 4) + 7 = 3 is x = 2, after simplifying and solving for x.
Explanation:The student has asked which value of x is the solution of the equation 2(x - 4) + 7 = 3. To find the solution, we first simplify and solve for x:
2(x - 4) + 7 = 32(x - 4) = 3 - 72(x - 4) = -4x - 4 = -2x = -2 + 4x = 2Therefore, the correct solution for x is 2.
A credit card issuer offers an APR of 19.94% and compounds interest monthly. Find the effective interest rate and explain which the card issuer is mostly likely to advertise, its APR or its effective interest rate?
Answers
((1+0.1994/12)^12)-1 = 21.87% effective rate
it would advertise the APR because it is lower
Which linear inequality is represented by the graph?
A.y ≥1/3 x – 4
B.y ≤1/3 x – 4
C.y ≤1/3 x + 4
D.y ≥1/3 x + 4
Answers
Answer:
the answer is actually D
Step-by-step explanation:
got it on edg
Mr. Vella can build a brick wall in 4 days. His apprentice can build the same wall in 6 days. After working alone for 3 days, Mr. Vella became ill and left the job for his apprentice to complete. How many days did it take the apprentice to finish the wall?
Answers
Apprentice will take [tex]1\frac{1}{2}[/tex] days to finish the wall.
What is work?" Work is defined as when force is applied to move an object in the direction of displacement."
According to the question,
Number of days taken by Vella to build a brick = 4 days
Work done by Vella in 1 day = [tex]\frac{1}{4}[/tex]
Work done by Vella in 3 days = [tex]\frac{3}{4}[/tex]
Number of days taken by apprentice to build same brick = 6 days
Total days taken by apprentice to complete 3/4 of work = [tex]\frac{3}{4} of 6[/tex]
= [tex]\frac{3}{4}[/tex] × 6
=[tex]\frac{9}{2}[/tex]
= [tex]4\frac{1}{2}[/tex] days
Number of days apprentice take to finish the wall is = 6 - [tex]4\frac{1}{2}[/tex]
= [tex]1\frac{1}{2}[/tex]
Hence, apprentice will take [tex]1\frac{1}{2}[/tex] days to finish the wall.
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what are the x intercepts for 5/x + 1/3x = 4x/3
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now, the cheap answer will be, let's just get the LCD of all those fractions, hmm let's see is 3x, and multiply all the fractions by the LCD, that way, getting rid of the denominators.
[tex]\bf \cfrac{5}{x}+\cfrac{1}{3}x=\cfrac{4x}{3}\implies \cfrac{5}{x}+\cfrac{x}{3}=\cfrac{4x}{3}\impliedby \times \stackrel{LCD}{3x} \\\\\\ \boxed{3x}\cdot \cfrac{5}{x}+\boxed{3x}\cdot \cfrac{x}{3}=\boxed{3x}\cdot \cfrac{4x}{3}\implies 15+x^2=4x^2\implies 15=3x^2 \\\\\\ \cfrac{15}{3}=x^2\implies 5=x^2\implies \pm\sqrt{5}=x[/tex]
How are these shortcuts (SSS, SAS, ASA, and AAS) similar to or different from those for proving triangle congruence?
Answers
AD¯¯¯¯¯ , BD¯¯¯¯¯ , and CD¯¯¯¯¯ are angle bisectors of the sides of △ABC . BE=12 m and BD=20 m
Answers
Since AD bisects angle A, I think then side DG should be congruent with DG. So then
DG = 16 m
The sum of three consecutive odd integers is 75. find the numbers
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23+27=50
50+25= 75
Did the Native Americans The pilgrims encountered lived in tipis and traveled on horseback?
Answers
Answer:
They were nomadic and moved from place to place.
Step-by-step explanation:
the perimeter of the rectangle shown is 76 cm. it is rotated about line b.
which best describes the resulting three-dimensional figure?
•a cone with a base radius of 26cm
•a cone with a base radius of 14cm
•a cylinder with a base radius of 26cm
•a cylinder with a base radius of 14cm
Answers
If a rectangle is rotated about the line b, then the three-dimensional figure formed is cylinder with a circle base.
One side of the rectangle has lenght of 24 cm. Let the second side has length of x cm. The perimeter of the rectangle is 76 cm, then
24 + x + 24 + x = 76,
2x + 48 = 76,
2x= 76 - 48,
2x= 28,
x = 14 cm.
Then the three-dimensional figure is a cylinder with a base radius of 14 cm.
Answer: correct choice is D
Answer: •a cylinder with a base radius of 14cm
Step-by-step explanation:
From the given picture it can be seen that the side of rectangle is adjacent to line B is the longer side.
If the rectangle is rotated about line b, then it will create a cylinder such that
the radius of the cylinder= smaller(width) side of the rectangle
The measure of the longer side (length) of rectangle= 24 cm
Perimeter of rectangle=[tex]2[length+width][/tex]
[tex]\\\Rightarrow\ 76=2[24+w]\\\Rightarrow\ 24+w=38\\\Rightarrow\ w=14[/tex]
hence, the measure of smaller side is 14 cm.
Therefore, the base radius =14 cm
The data set below shows the number of cars parked in the restaurant parking lot during the lunch hour each day for two weeks: 8 7 14 10 13 27 11 10 14 7 12 9 14 9 Which of the following statements is true based on the data set? There is one outlier that indicates an unusually small number of cars were in the parking lot that day. There are two outliers that indicate an unusually small number of cars were in the parking lot those two days. There is one outlier that indicates an unusually large number of cars were in the parking lot that day. There are two outliers that indicate an unusually large number of cars were in the parking lot those two days.
Answers
Answer:
The data set for two weeks that shows the number of cars parked in the restaurant parking lot during the lunch hour each day is given as:
8 7 14 10 13 27 11 10 14 7 12 9 14 9
The statements that hold true according to the data is:
There is one outlier that indicates an unusually large number of cars were in the parking lot that day( i.e. 27 in one day which is the highest among all the days).Based on the data set, the true statement is: C. There is one outlier that indicates an unusually large number of cars were in the parking lot that day.
What is an outlier?An outlier can be defined as a data value that is either unusually small or large when compared to the overall pattern of the numerical values in a data set.
This ultimately implies that, an outlier lies outside most of the other values in a particular data set, and as such makes them different from the other numerical values.
In this scenario, there is only one outlier in this data set, which is 27 and it simply indicates an unusually large number of cars were in the parking lot that day.
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Match the expression with its name. 9x4 – 3x + 4
Answers
Trinomial means that there is 3 monomials.
1st monomial = 9x^4
2nd monomial = -3x
3rd monomial = 4
Therefore, Trinomial is your answer
hope this helps
Answer:
Fourth-degree trinomial
Step-by-step explanation:
9x^4 – 3x + 4 is a trinomial expression because it has three parts: 9x^4, –3x and 4, and is a fourth-degree expression because four is the highest exponent applied to the variable x (the other exponents are one and zero).
Which linear inequality is represented by the graph?
y > 2x + 2
y ≥ x + 1
y > 2x + 1
y ≥ x + 2
Answers
Step 1
Find the slope of the line
Let
[tex]A(0,1)\\B(2,5)[/tex]
the slope is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{5-1}{2-0}[/tex]
[tex]m=\frac{4}{2}[/tex]
[tex]m=2[/tex]
Find the equation of the line
we know that
the equation of the line into slope-intercept form is
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
in this problem we have
[tex]m=2[/tex]
[tex]b=1[/tex] ------> the y-intercept is the point A
substitute
[tex]y=2x+1[/tex]
Step 2
Find the equation of the inequality
we know that
the solution is the shaded area above the dotted line
so
above dotted line---------> represent the symbol ([tex]>[/tex])
the inequality is
[tex]y>2x+1[/tex]
therefore
the answer is
[tex]y>2x+1[/tex]
The correct option is [tex]\boxed{\bf option (c)}[/tex] i.e., [tex]\boxed{y>2x+1}[/tex].
Further explanation:
The linear equation of the line is [tex]y=mx+b[/tex] where, [tex]m[/tex] is the slope of the line and [tex]c[/tex] is the [tex]y[/tex]-intercept of the line.
Suppose the line passes through the two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex].
Therefore, the slope of the line can be calculated as follows:
[tex]\boxed{m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]
The symbol [tex]>[/tex] represents the solution set lies above the dotted line and the symbol [tex]<[/tex] represents the solution set below the dotted line.
Given:
The linear inequalities are given as follows:
[tex]\boxed{\begin{aligned}y&>2x+2\\ y&\geq x+1\\ y&>2x+1\\ y&\geq x+2\end{aligned}}[/tex]
Calculation:
First we will find the equation of the line.
The line cuts the [tex]y[/tex]-axis on the coordinate [tex](0,1)[/tex] as shown in the Figure 1 (attached in the end).
Therefore, the [tex]y[/tex]-intercept is [tex]1[/tex].
Kindly refer the Figure attached to the question.
From the figure 1 (attached in the end) we can see that the line passes through the points [tex](-2,-3)\text{ and }(1,3)[/tex].
The slope of the line can be calculated as follows:
[tex]\begin{aligned}m&=\dfrac{3-(-3)}{1-(-2)}\\&=\dfrac{6}{3}\\&=2\end{aligned}[/tex]
Therefore, the value of [tex]m[/tex] is [tex]m=2[/tex] and the value of [tex]b[/tex] is [tex]b=1[/tex].
Substitute [tex]2[/tex] for [tex]m[/tex] and [tex]1[/tex] for [tex]b[/tex] in the equation of the line [tex]y=mx+b[/tex].
Second we will find the equation of the inequality.
The shaded region is shown in Figure 1 above the dotted line .
Therefore, the solution set of the line lie above the dotted line and it will represented by the symbol [tex]>[/tex].
Thus, the inequality [tex]y>2x+1[/tex] satisfies the given graph.
Therefore, the correct option is [tex]\boxed{\bf option (c)}[/tex] i.e., [tex]\boxed{y>2x+1}[/tex].
Learn more:
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Linear inequalities
Keywords: Linear equations, linear inequality, equation, line, slope, intercept, dotted line , coordinate, shaded region, solutions set, graph, curve.