Reason:
We look for two values that
a) multiply to 12b) add to 8Using trial and error, you should find those two values are 2 and 6
2 times 6 = 122 plus 6 = 8This is how we arrive at (x+2)(x+6)
Use the FOIL rule to expand that out and you should get x^2+8x+12 to confirm the answer.
Neville purchases a guitar for $78.44. He has a coupon for 20% off the price. How much does Neville pay for the guitar after using the coupon?
Answer: 62.752
Step-by-step explanation: 78.44$ - 20% = 62.752
suppose that an allergist wishes to test the hypothesis that at least 30% of the public is allergic to some cheese products. explain how the allergist could commit a. a type i error; b. a type ii error.
Through hypothesis testing, it can be explained that Type I error occurs when the allergist determines that the percentage of the population who are allergic to some cheese products is at least 30% when it is actually less than 30%. Similarly, Type II error occurs when the allergist assumes that the percentage of the population who are allergic to certain cheese products is less than 30% when it is actually at least 30%
There are two possible outcomes for hypothesis testing, which leads to two different sorts of conclusion-related errors. This is due to the possibility that the estimated value of the measure and the inference made about the population measure from the samples could diverge.
Let's say an allergist wants to investigate the claim that at least 30% of the population has a cheese allergy.
Let p represent the actual percentage of the population that were allergic to certain cheese products.
The following is how the hypotheses are put forth:
[tex]H_{0}:p < 0.3\\H_{a}:p\geq 0.3[/tex]
The two types of errors that can be committed by the allergist can be described as below:
(a) Type I error:
When the null hypothesis is assumed to be true when it is actually false, type I error arises.
When an allergist determines that the percentage of the population who are allergic to some cheese products is at least 30% when it is actually less than 30%, type I mistake has been committed.
(b) Type II error:
When the null hypothesis is unsuccessfully rejected even when it is false, type II error has occurred.
When an allergist assumes that the percentage of the population who are allergic to certain cheese products is less than 30% when it is actually at least 30%, type II error has occurred.
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Lydia invests $1,100 in an account that earns interest at an annual rate of 5.5% compounded monthly.What is Lydia's return on investment after 2 years?
The rule of the compounded interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A is the new amount
P is the initial amount
r is the interest rate in decimal
n is the number of periods per year
t is the number of years
Since the initial amount is $1100, then
P = 1100
Since the interest rate is 5.5%, then
[tex]r=\frac{5.5}{100}=0.055[/tex]r = 0.055
Since the interest is compounded monthly, then
n = 12
Since the time is 2 years, then
t = 2
Substitute them in the rule above to find A
[tex]\begin{gathered} A=1100(1+\frac{0.055}{12})^{12\times2} \\ A=1100(1+\frac{11}{2400})^{24} \\ A=1227.597324 \end{gathered}[/tex]Lydia's return after 2 years is $1227.60 to the nearest cent
Write the equation of a line that goes through point (4, 0) and has an undefined slope
Answer:
x = 4
Step-by-step explanation:
You want the equation of a line that goes through point (4, 0) and has an undefined slope.
Undefined slopeThe slope of a line is the ratio of "rise" to "run." When the "run" is zero, the ratio involves division by zero, which results in the value "undefined." That is, a line with undefined slope has a "run" of zero, meaning it is a vertical line.
The equation for a vertical line is ...
x = c . . . . . where c is some constant
We want the line to go through a point that has x-coordinate = 4, so that constant must be 4.
The equation is x = 4.
The measure of an angle is four times the measure of its supplementary angle. What is the measure of each angle?
Answer: 1 angle is 144° and the other angle is 36°
Step-by-step explanation:
To find the smaller angle you would do:
1. x+4x=180
2. 5x=180
3. x=36
Then for the larger angle it would be 36×4=144
Write an expression to
describe the sequence below. Use n to represent the position of a term
in the sequence, where n = 1 for the first term.
5, 6, 7, 8, ...
Answer:
n + 4
Step-by-step explanation:
n is being used to describe the position of a term.
We can see that the sequence is increasing linearly by 1.
Since the position of the next term is increasing linearly by 1, all we have to do is look at the first term and subtract 1 from it to get our constant (4).
An equation to think about this better would be
n + C = S
C is the constant we are solving for.
We know n = 1.
S is the number corresponding in the sequence with n.
1 + C = 5
Subtract 1 from both sides to isolate C.
C = 4
1 + 4 = 5 Checks out
n + 4
You don't need to include the equals sign because the problem asks for an expression which doesn't contain an equals sign unlike an equation.
9+3.5g=11-0.5g is what
an = an-1 + 15; a₁ = 8
The explicit formula which correctly represents the progression represented by the recursive formula above is; a(n) = 8 + 15(n - 1).
What is the explicit formula which correctly describes the progression represented by the recursive formula given?It follows from the complete task content that the explicit formula which correctly represents the progression described by the recursive formula; an = an-1 + 15 be determined.
Therefore, by observation of the recursive formula; it follows that the progression is arithmetic with a common difference, d = 15.
Also, since the first term; a₁ = 8, the required explicit formula is;
a(n) = 8 + 15(n - 1).
This follows from the general explicit formula of arithmetic progressions; a(n) = a₁ + (n - 1)d.
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Solve the inequality. Graph the solution. |8x−8|≤24
The solution of the given inequality would be x = 4. the graph of the given inequality is attached below.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
Given the inequality as |8x−8|≤24.
For solving the given expression,
|8x−8|≤24
We can consider the expression as;
8x−8 = 24
8x = 24 + 8
8x = 32
x = 32/8
x = 4
Hence, the solution of the given inequality would be x = 4.
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Bellrose Bank charges a monthly maintenance fee of $17 and a check-writing fee of $0.05 per
check. Last year, Patricia wrote 445 checks from her account at Bellrose. What was the total of all
fees she paid on that account last year?
The amount Patricia paid as fees on on the account last year was $226.25
What makes up the total cost for Patricia?
Patricia pays a fixed monthly maintenance fee of $17 for every month last year, which means that the total annual maintenance fee last year is the monthly maintenance fee multiplied by 12 months, whereas, the annual check-writing fee is the check-writing fee per check multiplied by the number of checks issued last year.
total annual maintenance fee=monthly maintenance fee *12
monthly maintenance fee=$17
total annual maintenance fee=$17*12
total annual maintenance fee=$204.00
annual check-writing fee= check-writing fee per check*number of checks
annual check-writing fee=$0.05*445
annual check-writing fee=$22.25
total fees paid by Patricia last year=$204.00+$22.25
total fees paid by Patricia last year=$226.25
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standard to intercept form
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{2}{3} x + 9[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given equation is :
[tex]\qquad\displaystyle \tt \rightarrow \: 8x + 12y = 108[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 12y = 108 - 8x[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{108}{12} - \frac{8}{12} x[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{2}{3} x + 9[/tex]
That's the required equation, with slope (m) = -2/3 and y - intercept = 9
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Write an equation of the parabola shown. (0,4) (-5, 1.5)
the general formula of a parabola is
[tex]y=ax^2+bx+c[/tex]we can replace the the points to find a,b and c
First (0,4)
[tex]\begin{gathered} 4=a(0)^2+b(0)+c \\ 4=0+0+c \\ c=4 \end{gathered}[/tex]Then (-5,1.5) and c=4
[tex]1.5=a(-5)^2+b(-5)+4[/tex]Compare, choose , or = 20% of 25 25% of 16
Answer: 20% of 25 is more than 25% of 16 if that is the question
I hope that is the question-
20% of 25 > 25% of 16
11-(15g-13)=-6
what does G stand for
Answer:
g = 2
Step-by-step explanation:
11- (15g - 13) = - 6 ( subtract 11 from both sides )
- (15g - 13) = - 17 ( multiply both sides by - 1 )
15g - 13 = 17 ( add 13 to both sides )
15g = 30 ( divide both sides by 15 )
g = 2
Consider these two graphs. Does each represent a function? Why or why not?
Answer:
The first one is a function but the second one is not.
Step-by-step explanation:
Using the vertical line test, we can check if the graphs are a function or not. Every vertical line can only touch a graph once in order for the function to pass the Vertical Line Test. If a graph passes the Vertical Line Test, it's the graph of a function. The first one has no points intersecting each other if you draw a vertical line for each point. However, if you draw vertical lines for the second graph, the points vertically intersect each other, making it not a function.
Nelson has half of his investments in stock paying a 6% dividend and the other half in a stock paying 9% interest. if his total annual interest is $660 how much does he have invested?
Given:
percent of dividend = 6%
percent of interest = 9%
Total annual interest = $ 660
Let the amount invested in both stocks be x and y.
Annual interest on 6% dividend gives:
[tex]\begin{gathered} =\text{ }\frac{6}{100}\text{ }\times\text{ x} \\ =\text{ 0.06x} \end{gathered}[/tex]Annual interest on 9% interest rate:
[tex]\begin{gathered} =\text{ }\frac{9}{100\text{ }}\times\text{ y} \\ =\text{ 0.09y} \end{gathered}[/tex]The total annual interest is $ 660. We can write:
[tex]0.06x\text{ + 0.09y =660}[/tex]We are given that Nelson divided his investment in half. This implies:
[tex]x\text{ = y}[/tex]Substituting, we have:
[tex]\begin{gathered} 0.06x\text{ + 0.09x = 660} \\ 0.15x\text{ = 660} \end{gathered}[/tex]Divide both sides by 0.15:
[tex]\begin{gathered} \frac{0.15x}{0.15}\text{ = }\frac{660}{0.15} \\ x\text{ = 4400} \end{gathered}[/tex]Hence, the amount Nelson has invested:
[tex]\begin{gathered} x\text{ = y = 4400} \\ \text{Amount invested = 4400 + 4400} \\ =\text{ 8800} \end{gathered}[/tex]Answer:
Nelson has $4400 invested in each investment
Joe mows a lawn, for which he charges $30, and does some one-time cleanup work, for which he is paid $60. How many times will he have to mow the law before he makes a total of $300
He has mowed the law before he makes a total of Dollar 300, The number of times he has to mow a lawn is 10
Joe mows a lawn, for which he charges = $ 30
Some one-time cleanup work, for which he is paid = $ 60
According to the question:
He has to mow the lawn before he makes a total of Dollar300
Number of times he has to mow a lawn = 300 / 30
The number of times he has to mow a lawn = is 10
He has mowed the law before he makes a total of Dollar 300, 10 times.
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The diagram below is divided into equal parts.Which ratio compares the number of shaded to the total number of sections
Ratio compares the number of shaded to the total number of sections is 1/2
Given- diagram
Find- ratio of shaded sections to total number of section
Shaded sections =4
total sections =8
Hence, Shaded sections: total sections.
= 4: 8
=4/8
=1/2
Hence,
1/2
A solid's cross section is a plane figure formed when the solid intersects another plane. As a result, the cross section of an object is an infinitesimal "slice" of a solid, and it can vary depending on how the slicing plane is oriented.
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I NEED HELP WITH MY HOMEWORK
Chester made 9 sales and Vickie made 16 sales this week
Base salary of Vickie = $70
Vickie's commission per sale = $24
Base salary of Chester = $142
Chester's commission per sale = $9
Both people earned the same amount this week. Let x represent the number of sales made by Vickie, then sales made by Chester is x+7
Formulating the equation we get:
Base salary of Vickie + Vickie's commission per sale*Number of sales = Base salary of Chester + Chester's commission per sale*Number of sales
= 70 + 24x = 142 + 9(x+7)
70+24x = 142+9x+63
70+24x = 205+9x
15x = 135
x = 9
Chester sales = 9
Vickies sales = 9+7 = 16
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Using the graph what percentage of college graduates believe their education was useful for helping them grow personally and intellectually, but not useful for helping them develop specific skills and knowledge for the workplace?Write your answer as a percentage
62 + 35 = 97
62 represents the people who think the education helped them grow personally
35 represents the people who somewhat believe it helps them develope specific skills in the work place.
93 in total were interviewed for the "helping them grow personally" question
84 in total for the question that talkings about helping the people develop specific skills and knowlege
93 + 84 = 177
If 97 of those people believe the college degree was useful personally and somewhat useful for learning specific skills, we have to find what is 97 of 177 as a percentage.
[tex]\frac{97}{177}\times100=54.802259887[/tex]54.802259887 rounded is 54.8%
Which means 54.8% of college graduates believe their education was useful for helping them grow personally but not useful for developing specific skills.
The ordered pair (a,b) satisfies the inequality y
A. If you subtract 6 from b, it will be less than or equal to a.
B. If you add 6 to a, it will be greater than b.
C. a is greater than b.
D. If you add 6 to a, it will be less than b.
The false statement about the statement is (a) If you subtract 6 from b, it will be less than or equal to a.
How to determine the true statement?From the question, the inequality is given as
y > x - 6
The ordered pair is given as
(a, b)
The above ordered pair implies that
(x, y) = (a, b)
So, we have
x = a and y = b
This means that
b > a - 6
Subtract 6 from both sides
b - 6 > a - 6 - 6
Evaluate
b - 6 > a - 12
Using the above as a guide, we cannot determine the direct relationship between variables a and b.
However, it is false that b is less than a
Hence, the false statement is (a)
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Complete question
The ordered pair (a,b) satisfies the inequality y > x - 6
Which statement is NOT true?
A. If you subtract 6 from b, it will be less than or equal to a.
B. If you add 6 to a, it will be greater than b.
C. a is greater than b.
D. If you add 6 to a, it will be less than b.
Divide.
3/4÷2 1/2
Responses
3/10
1 1/2
1 7/8
3 1/3
The answer is 3/10
Explanation:
= 3/4 x 2/5
= 3/4 x 2/5
= 3/2 x 1/5
= 3 x 1 / 2 x 5
= 3 / 2 x 5
= 3/10
When driving up a certain hill, you rise 15 feet for every 1000 feet you drive forward. What is the slope of the rode?
slope of the rode is 0.015.
What is slope of line ?
Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.
The point with coordinate having same slope as with given coordinates can be plotted on the same line.
Here, it is given that :
When driving up a certain hill, we rise 15 feet for every 1000 feet that is :
for 15 feet up = 1000 feet forward
Now,
slope = upward distance / horizontal distance covered
slope = 15/1000
slope = 0.015
slope is a unitless quantity.
Therefore, slope of the rode is 0.015.
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-26, 174, 374, 574, …
Find the explicit and recursive formula.
The explicit formula and the recursive formula are aₙ₋₁ + 200 and the rest is mentioned below.
What does explicit and recursive formula mean?A formula can be either recursive or explicit. The main difference between Recursive and Explicit is that Recursive formula gives the value of a specific term based on the previous term while Explicit formula gives the value of a specific term based on the position.
Given : a₁ = -26, a₂ = 174, a₃ = 374, a₄= 574
The common difference that is d can be found out by
thus d = a₂ - a₁ = 174 -(- 26 ) = 174 + 26 = 200
And this is same for all the numbers of this particular sequence.
Thus aₙ = aₙ₋₁ + d
= aₙ₋₁ + 200
Recursive formula : aₙ₋₁ + d
That is the following sequence will have a common difference of 200 and the next 5th, 6th, 7th and nth term is going to be .
774 , 974 ... etc
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May someone please help me out with this
Answer:
y=-1/4x-6
Step-by-step explanation:
it hit -6 on the y axis
And it is jumpin by 4 going down
So -4 is the x axis
What is the diameter of a circle whose area is 28.3 cm^2
I don't understand this question can someone help me with the answer
The approximate diameter of the circle is 5.77 cm
Given that :
area of circle = 28.3 cm²
How is Area of circle is calculated ?
Area of circle is calculated using formula :
A= πr²
where "π" represents 3.14 and r is radius. So now, according to given information,
Where Pi = 3.14
Hence,
A= πr²
Substitution the value of A in above formula :
28.3 = πr²
28.3 = 3.14r²
r² =28.3/3.14
r² =8.323
√r²=√8.323
r = 2.885
r = 2.885 cm Approximately.
d = 2r
d = 5.77 Approximately.
Therefore, the diameter of the circle is 5.77 cm
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1.) Tony deposited $743.22 to his checking account on July 1st. He then wrote a
check for $312.29 and another check for $36.70. The bank charged a
monthly service of $6.26. He now has $410.98 in the bank. How much did
Tony have in the bank at the end of June?
34
A. $387.97
B. $23.01
C. $798.95
D. $394.23
Answer:
23.01
Step-by-step explanation:
743.22-312.29-36.7-6.26
=387.97
410.98-387.97
=23.01
a perfect square is an integer that is the square of an integer. suppose that m and n are positive integers such that mn > 15. if 15mn is a perfect square, what is the least possible value of mn ?
Least possible value of m and n are 6 and 10.
Given a perfect square is an integer that is also square of an integer.
The given m and n are positive integers such that mn > 15.
To find out the least possible value of mn;
As given 15mn is a perfect square.
[tex]\sqrt{15mn}[/tex] is to be an integer.
[tex]\sqrt{15mn} = \sqrt{5*3*m*n}[/tex]
Now, insert m = 3, n = 5;
⇒ [tex]\sqrt{5*3*m*n} = \sqrt{5^2* 3^2} = 15[/tex]
but it is mn < 15.
So, assume m = 3 * 2, n = 5 * 2;
⇒ [tex]\sqrt{5*3*m*n} = \sqrt{5*3*3*2*5*2} = \sqrt{5^2*3^2*2^2} = 30[/tex]
30 it is an integer.
As we solved that the least possible value of m and n are 6 and 10.
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he value of a baseball player's rookie card began to increase once the player retired. When he retired in 1999 his card was worth $7.81. The value has increased by $1.28 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2005? Question content area bottom Part 1 Express the relationship with an equation.
The value of the card in 2005 is $15.49.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
When he retired in 1999 his card was worth $7.81 but the value has increased by $1.28 each year since then.
Therefore, the value of the card in 2005 will be:
y = 7.81 + 1.28x
where x = number of years
From 1999 to 2005 is 6 years. This will be:
= 7.81 + 1.28x
= 7.81 + 1.28(6)
= 7.81 + 7.68
= 15.49
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What is the degree of the polynomial 12x^2+8x-9
Answer:f(x)=x8−8x6+19x4−12x3+14x2−8x+9=x8−8x6+16x4+3x4−12x3+12x2+2x2−8x+8+1
which allows us to rewrite f(x) as
f(x)=x4(x2−4)2+3x2(x−2)2+2(x−2)2+1
The first three terms are clearly non-negative, and each reaches their minimum of 0 at x=2 (the first term also has a minimum at x=−2). Thus, the minimum of f(x) must be 1.
This can't really be generalized. (I mean, you can apply the approach generally, but it won't generally give you such a convenient result.) I'm not sure I would have looked for this decomposition of f(x) except for the presence of the question.
Step-by-step explanation: