The function is given as,
[tex]h(x)=7x^2-4x-15[/tex]The objective is to determine the value h(20).
This can be obtained by substituting 20 for 'x' in the given expression,
[tex]\begin{gathered} h(20)=7(20)^2-4(20)-15 \\ h(20)=7(400)-80-15 \\ h(20)=2800-95 \\ h(20)=2705 \end{gathered}[/tex]Thus, the value of the given function h(20) is 2705.
A model of a 51 foot long airplane is 25 in long how is is a tire that is 1/6 tinch
The length of the tire on the airplane given the length of the tire on the model is 17 / 50 foot.
What is the length of the tire?The first step is to determine the scale of the model. In order to determine the scale, divide the length of the airplane by the length of the plane in the model.
Scale of the model = length of the airplane / length of the model
51 / 25 = 1 inch represents 2 1/25 foot
The next step is to multiply the scale determined in the previous step by the length of the tire.
Length of the tire on the airplane = scale x length of the tire in the model
1 / 6 x 2 1/25
1/6 x 51 / 25 = 17 / 50 foot
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The boxplot shown below results from the heights (cm) of males listed in a data set. What do the numbers in that boxplot tell us?
Given:
The boxplot is given.
To fill in the blanks:
Explanation:
As we know,
The minimum value is represented by the line at the far left end of the diagram.
So, the minimum height is 153cm.
The first quartile on the left side is represented by the line between the minimum value ad the median.
So, the first quartile is 166.6cm.
The second quartile (or median) is represented by the line at the centre of the box.
So, the second quartile is 173.2cm.
The third quartile on the right side is represented by the line between the maximum value ad the median.
So, the third quartile is 180.1cm.
The maximum value is represented by the line at the far right end of the diagram.
So, the maximum height is 193cm.
Final answer:
The minimum height is 153cm, the first quartile is 166.6cm, the second quartile is 173.2cm, the third quartile is 180.1cm, and the maximum height is 193cm.
a wood cutter measures a piece of wood to be 830 grams.There are 1000 grams in a kilogram and a kilogram is equal to about 2.2 pounds.Whats is the mass of the wood in pounds
The mass of the wood in pounds is 1.826 pounds.
How to calculate the value?From the information, the wood cutter measures a piece of wood to be 830 grams and there are 1000 grams in a kilogram and a kilogram is equal to about 2.2 pound.
Therefore,the mass will be represented as x
This will be:
830 grams = 0.83 kilograms
0.83/1 = x/2.2
Cross multiply
x = 2.2 × 0.83
x = 1.826 pounds.
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Lucky Champ owes $209.10 interest on a 6% loan he took out on his March 17 birthday to upgrade an oven in his Irish restaurant, Lucky's Pub and Grub. The loan is due on August 17. What is the principal? (Use 360 days a year.)
Based on the interest owed on the loan and the date that the loan is due and when Lucky Champ took it, the principal for the loan is $8,200.
How to find the principal?First, find the period of the loan:
= 14 days in March + 30 + 31 + 30 + 31 + 17 days in August
= 153 days
The interest can be found by the formula:
= Principal x Interest rate x Period
The Principal can therefore be found by the formula:
= Interest owed x Number of days in year / Number of days x 100 / 6
= 209.10 x 360 / 153 x 100 / 6
= $8,200
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What is the x values that satisfies the linear equations on the graph?
In the linear equations shown on the coordinate grid, the values of x that satisfies both equations is 2 (option b).
The graph of both equations intersect at the point where x equals 2.
What is the slope and y-intercept?
y=7x+2
Options:
Blank # 1
Blank # 2
Answer:
Step-by-step explanation:
18098
Form a polynomial whose zeros and degree are given.Zeros: -4, multiplicity 2; -3, multiplicity 1; degree 3O x3 + 8x2 + 40x + 48O x3 - 11x2 + 24x - 48O x3 + 11x2 + 40x + 48O x3 - 11x2 + 40% - 48
the probability that DeAndre missed at least 1 day of school in a given week is
Probability that Deandre missed at least 1 day is;
[tex]Pr(x\ge1)=Pr(1)+Pr(2)+Pr(3)+Pr(4)+Pr(5)[/tex]Write out the values of each probability and sum them
[tex]\begin{gathered} Pr(x\ge1)=0.25+0.18+0.34+0.12+0.04 \\ =0.93 \end{gathered}[/tex]Hence,
The probability that Deandre missed at least 1 day is 0.93
The length of each side of a square is extended 5 in. The area of the resulting square is 64 in,2 Find the length of a side of the
original square.
Answer: i donno
Step-by-step explanation:
ask Professor Ahmad Shaoki
How do you find the square root of -6 by imaginary numbers
To find the square root of a negative number use the next:
[tex]\sqrt{-1}=i[/tex]For -6:
You can write -6 as the product of 6 and -1:
[tex]\sqrt{\left(6\right)*\left(-1\right)}[/tex]The square root of a product is the same as the product of the square root if each of the factors:
[tex]=\sqrt{6}*\sqrt{-1}[/tex]As the square root of 6 is not a exact number (it has many decimals) you leave the square root of 6 as it is. The square root of -1 is i; then, the square root of -6 is:
[tex]\begin{gathered} =\sqrt{6}*i \\ =\sqrt{6}i \end{gathered}[/tex]Then, the square root of -6 is: (√6)iRewrite the equation by completing the square. x^{2}-6x-16 = 0
Answer:
Step-by-step explanation:
x^2 - 6x - 16 = x^2 - 6x + 9 - 9 - 16 = (x - 3)^2 - 25
Theoretical Probabilities. Use the theoretical method to determine the probability ofthe following outcomes and events. State any assumptions that you make. Drawing a red card (heart or diamond) from a standard deck of cards
Recall that the theoretical probability that an event occurring is given by the following quotient:
[tex]\frac{\text{favorable cases}}{total\text{ cases}}.[/tex]We know that there are 26 red cards in a standard deck, therefore:
[tex]P(\text{Drawing a red car)=}\frac{26}{52}=0.5.[/tex]Answer: 0.5.
Give the degree of the polynomial.
-v^8u^9 + 6x - 16u^6x^2v^6 - 5
Answer: nonic
Step-by-step explanation:
If t = (- pi)/3 find the terminal point P(x,y) on the unit circle
Find the corresponding possitive angle by adding to the angle t 2pi:
[tex]-\frac{\pi}{3}+2\pi=\frac{-\pi+6\pi}{3}=\frac{5\pi}{3}[/tex]Identify the coordiantes using a unit circle:
Then, for angle t=-pi/3 the coordinates are:x=1/2y=-√3 /2Write the equation of the line when the slope is 1/5 and the y-intercept is 13.
Given:
• Slope, m = 1/5
,• y-intercept = 13
Let's write the equation of the line.
To write the equation of the line, apply the slope-intercept equation of a line:
[tex]y=mx+b[/tex]Where:
m is the slope
b is the y-intercept.
Thus, we have:
m = 1/5
b = 13
Plug in the values in the equation:
[tex]y=\frac{1}{5}x+13[/tex]Therefore, the equation of the line is:
[tex]y=\frac{1}{5}x+13[/tex]Neptune is about how many times as far from the Sun as Mars is fronthe Sun?Neptune = 2,600, 000,000MarS= 143,000,000Solution:
Determine whether or not the digits below are divisible by: 2,3,4,5,6,8,9,or, 10 a. 897 b. 12,000 c. 8190 d. 327
You have the following numbrs:
897
12,000
8190
327
In order to determine if the previous numbers are divisibles for numbers between 2 and 10, you take into account the following points:
- If last two digits are divisible by a number, and the part of the number without the last units is divisible too, you can consider that the complete number is divisible too.
- If the last digit is 0, then the number is divisible by 2 and 5 and 10.
- If the number is even, it is dividible by 2.
- In case a number ends in varios zeros you can consider if the digits before the zeros are divisible by a specific number.
- 897 is divisible by 3, because 97 is divisible by 3 and 800 too.
- 12,000 is divisible by 2, 3, 4, 5, 6, 8 and 10, because it is an even number, ends in 0 and the first digits are divisible by 3, 4, 6.
- 8190 is divisible by 2, 3, 5, 6, and 10, becaues it is even, ends in 0 and the number of last two digits is divisible by 3 and 6 and 8100 too.
- 327 is divisible by 3, because number of last two digits is divisible by 3 and 300 too.
There are 9,321 leaves on a tree. Explain why the digit 3 stays the same when9,321 is rounded to the nearest hundred.
To round the nearest hundred the digit in the hundred column and test digit in the tens column.
To round the nearest hundred the digit in the hundred column is rounding digit and the digit in the tens column is test digit.
We find the rounding digit in hundred column is 3. Then we look out the test digit 2 to the right of the 3 in the tens column. Because 2<5 we round down and leave the 3 in the hundred column. Then replace the two rightmost digits with 0's.
The 9,321 rounded to the nearest hundred is 9,300.
Which of the following equations shows the correct way to apply the Associative Property of Addition? (1 point)0 6x (2 + 3) = 6 x 2) + 3O 9+8 = 8+9O 6+2 = 4+4O 3+ (4+5) = (3+4) +5
This property indicates that when there are or more digits in these operations, the result does not depends on the way the terms are grouped. Therefore:
[tex]\begin{gathered} 3+(4+5)=(3+4)+5 \\ 3+9=7+5 \\ 12=12 \end{gathered}[/tex]therefore, the answer is the last option 3+ (4+5) = (3+4) +5
Which choice could be used in proving that the given triangles are similar? A) PO 6 DE 4 II B) PO 4 EF 9 PO 4 DE 6 D) PR 6 DE 6 allo
Find the slope of the line that contains the two points.ROUND YOUR ANSWER TO TWO DECIMAL PLACES.
The slope of a line is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1,y1) and (x2,y2) are the coordinates of the given points. Replace the given values and solve for m:
[tex]m=\frac{8-(-4)}{-6-0}=\frac{8+4}{-6}=\frac{12}{-6}=-2[/tex]The slope of the line that contains the two given points is -2.
Miguel is judging an essay contest. He has to select the best, second best, and third best. If there are 6 essays entered, how many ways could he choose the top essays?
There are 120 ways to choose the top essays.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
There are 6 essays entered.
And, He has to select the best, second best, and third best.
Now,
Since, There are 6 essays entered.
Hence, The number of ways to choose the top essays = [tex]^{6} P_{3}[/tex]
= 6! / 3!
= 6×5×4
= 120
Thus, The number of ways = 120
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a gallon of ice cream costs $4.76. How much does it cost per quart? There are 4 qts per gallon.
There are 4 quarts in a gallon so the price of one gallon that they have given us has to be split into four so $4.76/4 =$1. 19/quart
Solve the inequality below to determine and state the smallest possible value of x in the solution set. - 7(x + 4) + 3x < 8x - 2(2x - 2)
given the inequality :
- 7(x + 4) + 3x < 8x - 2(2x - 2)
so,
-7x - 28 + 3x < 8x - 4x + 4
combine like terms:
-7x + 3x - 8x + 4x < 28 + 4
-8x < 32
Divide both sides by -8
Do not forget to flip the inequality sign
so,
x > -4
so, The solution is the interval ( -4 , ∞ )
On the number line the solution will be :
The smallest possible interger of x = -3
Determine if the 2 lines are parallel, perpendicular, or neither based on their slope-intercept equations.
Equations of lines G & H;
Line G: y=-6x + 14
Line H: y=6x-14
O Perpendicular
O Not Enough Information
O Parallel
O Neither
POSS
10 11
12 13 14 15
Answer:
perpendicular because the slopes are opposite
Step-by-step explanation:
1. Knowledge: Use your Factoring Flowchart or Concept Map to factor the following Quadratic Polynomials. Copy down the question and show any necessary steps if it is a multi-step factoring process (not just a single-step solution). Question F to I
Solution
We are asked to factorize the following questions
Question F:
[tex]\begin{gathered} 4+6x+2x^2 \\ \text{ 2 is common among the terms, so we can factorize it out} \\ \\ 2(2+3x+x^2) \\ \text{ The term }3x\text{ can also be written as }2x+x.\text{ And the terms }2x\text{ and }x\text{ multiply to get }2x^2 \\ \text{ Thus, we have,} \\ \\ 2(2+3x+x^2)=2(2+2x+x+x^2) \\ \text{ In this new expression, }2\text{ is common to }2+2x\text{ while }x\text{ is common to }x+x^2 \\ \text{ Thus, we can factorize them out} \\ \\ 2(2+2x+x+x^2)=2(2(1+x)+x(1+x)) \\ \text{ Lastly, }(1+x)\text{ is common to }2(1+x)\text{ and }x(1+x) \\ \\ 2(2(1+x)+x(1+x))=2((2+x)(1+x)) \\ \\ \therefore4+6x+2x^2=2(2+x)(1+x) \end{gathered}[/tex]Question G:
[tex]\begin{gathered} 3x^2-1x-10 \\ \text{ The term }-1x\text{ can also be written as }-6x+5x\text{ and the terms }-6x\text{ and }5x\text{ multiply to get} \\ -30x^2.\text{ Thus, we have,} \\ \\ 3x^2-1x-10=3x^2-6x+5x-10 \\ 3x\text{ is common to }(3x^2-6x)\text{ and }5\text{ is common to \lparen}5x-10) \\ \text{ Thus, we can factor them out} \\ \\ 3x^2-6x+5x-10=3x(x-2)+5(x-2) \\ (x-2)\text{ is common to both terms, so we can factor again} \\ \\ 3x(x-2)+5(x-2)=(x-2)(3x+5) \\ \\ \therefore3x^2-1x-10=(x-2)(3x+5) \end{gathered}[/tex]Final Answer
The answers to questions F and G are:
[tex]\begin{gathered} 4+6x+2x^2=2(2+x)(1+x) \\ \\ 3x^2-1x-10=(x-2)(3x+5) \end{gathered}[/tex]
Suppose a mutual fund yielded a return of 14% last year. Its CAPM beta (β) is 1.2. The risk-free rate was 5% last year and the stock market return was 10% last year. What is the alpha (α) of the mutual fund?
The Jensen's Alpha of the mutual fund is given as follows:
α = 3.
Jensen's AlphaThe Jensen's Alpha of a mutual fund is calculated according to the rule presented as follows:
α = [Rp - (Rf + Bp x (Rm - Rf))]
The parameters of the problem are defined as follows:
Rp is the expected portfolio return.Rf is the risk free rate.Bp is the beta of the portfolio.Rm is the expected market return.Hence, in the context of this problem, the values of the parameters are given as follows:
Rp = 14, Rf = 5, Bp = 1.2, Rm = 10.
Hence the Jensen's Alpha of the mutual fund is given as follows:
α = [Rp - (Rf + Bp x (Rm - Rf))]
α = [14 - (5 + 1.2 x (10 - 5))]
α = 3.
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the mean salary offered to students who are graduating from coastal state university this year is $24,215, with a standard deviation of $3712. A random sample of 80 coastal state students graduating this year has been selected. What is the probability that the mean salary offer for these 80 students is $24,250 or more?
Given that the mean and standard deviation of the population are $24,215 and $3712 respectively,
[tex]\begin{gathered} \mu=24215 \\ \sigma=3712 \end{gathered}[/tex]The sample size taken is 80,
[tex]n=80[/tex]Consider that the salary of students in the sample is assumed to follow Normal Distribution with mean and standard deviation as follows,
[tex]\begin{gathered} \mu_x=\mu\Rightarrow\mu_x=24215 \\ \sigma_x=\frac{\sigma}{\sqrt[]{n}}=\frac{3712}{\sqrt[]{80}}\approx415 \end{gathered}[/tex]So the probability that the mean salary (X) is $24250 or more, is calculated as,
[tex]\begin{gathered} P(X\ge24250)=P(z\ge\frac{24250-24215}{415}) \\ P(X\ge24250)=P(z\ge0.084) \\ P(X\ge24250)=P(z\ge0)-P(0From the Standard Normal Distribution Table,[tex]\begin{gathered} \emptyset(0.08)=0.0319 \\ \emptyset(0.09)=0.0359 \end{gathered}[/tex]So the approximate value for z=0.084 is,
[tex]\emptyset(0.084)=\frac{0.0319+0.0359}{2}=0.0339[/tex]Substitute the value in the expression,
[tex]\begin{gathered} P(X\ge24250)=0.5-0.0339 \\ P(X\ge24250)=0.4661 \end{gathered}[/tex]Thus, there is a 0.4661 probability that the mean salary offer for these 80 students is $24,250 or more.
a computer program is in Shannon's computer carries out a single mathematical operation in 1.5 * 10 over 6 seconds how much time would the program take to complete 2.5 * 10/3 mathematical operations
Question:
Solution:
This computer program carries out a single mathematical operation in
[tex]1.5x10^{-6}\text{ seconds}[/tex]then, to complete 2.5 x 10^3 mathematical operations the program will take a time of:
[tex](1.5x10^{-6})(2.5x10^3)=3.75x10^{-3}[/tex]thus, the correct answer is:
[tex]3.75x10^{-3}[/tex]If 1 is added to a number and the sum is tripled, the result is 5 more than the number. Find the number
Answer;
[tex]n=1[/tex]Explanation;
Here, we want to get a number
Since the number is not known at the moment, we can start by identifying the number with an a;phabet
Let us call this n
If 1 is added to the number
mathematical representation;
[tex]1+n[/tex]And the sum is tripled;
[tex]3(1+n)[/tex]The result is 5 more than the number
5 more than the number is simply;
[tex]5+n[/tex]So, we equate this to what we had initially as follows;
[tex]5+n=3(1+n)[/tex]We can now solve this equation for n
[tex]\begin{gathered} 5+n=3+3n \\ 5-3=3n-n \\ 2n=2 \\ n=\frac{2}{2} \\ n=1 \end{gathered}[/tex]