Answer:
En álgebra, el teorema del factor es un teorema que vincula factores y ceros de un polinomio. Es un caso especial del teorema del resto polinómico.
Step-by-step explanation:
If log 5 = p and log 2=q then log 200 can be written in terms of p and q as?
Work Shown:
log(200) = log(2^3*5^2)
log(200) = log(2^3) + log(5^2)
log(200) = 3*log(2) + 2*log(5)
log(200) = 3*q + 2*p
log(200) = 2p + 3q
The log rules I used were
log(A*B) = log(A)+log(B)
log(A^B) = B*log(A)
The equivalent expression of log(200) is 2p + 3q
The logarithmic expression is given as:
[tex]\mathbf{log 200}[/tex]
Rewrite as:
[tex]\mathbf{log(200) = log (25 \times 8)}[/tex]
Express as exponents
[tex]\mathbf{log(200) = log (5^2 \times 2^3)}[/tex]
Split
[tex]\mathbf{log(200) = log (5^2) +log(2^3)}[/tex]
Apply law of logarithms
[tex]\mathbf{log(200) = 2log (5) +3log(2)}[/tex]
From the question;
log(5) = p and log(2) = q
So, we have:
[tex]\mathbf{log(200) = 2p +3q}[/tex]
Hence, the equivalent expression of log(200) is 2p + 3q
Read more about logarithmic expressions at:
https://brainly.com/question/9665281
Which will provide the largest yield on an annuity after 30 years with 6% annual interest, compounded monthly? Annuity A: Deposit $2400 per year. Annuity B: Deposit $600 per quarter. Annuity C: Deposit $72,000 one lump sum.
Answer:
Annuity C: Deposit $72,000 one lump sum
Step-by-step explanation:
The yield is improved when the money is on deposit for a longer period.
If the $2400 annual deposit is made at the first of the year, then it will yield more than $600 deposits made at the first of each quarter.
If the $72,000 deposit is made at the beginning of the period, the entire amount is earning interest for the entire period.
Annuity C will provide the largest yield.
Emily worked only 4/5 of her normal 40-hr work week. If she makes $18 per hour, how much money did she earn for the week? Use the equation
Answer:
576 for the week
Step-by-step explanation:
First determine how many hours she worked
4/5 * 40 = 32 hours
32 hours times the hourly rate of 18
32*18 =576
Any help would be greatly appreciated
Answer:
[tex]\boxed{\sf \ \ \ 49a^8b^6c^2 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex](-7a^4b^3c)^2=(-1)^27^2a^{4*2}b^{3*2}c^2=49a^8b^6c^2[/tex]
as
[tex](-1)^2=1[/tex]
A researcher used the technique with 9 students and observed that they had a mean of 10.8 hours with a standard deviation of 1.5. A level of significance of 0.05 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{10.8-11}{\frac{1.5}{\sqrt{9}}}=-0.4[/tex]
The degrees of freedom are given by:
[tex]df=n-1=9-1=8[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(8)}<-0.4)=0.350[/tex]
Since the p value is higher than the the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from the traditional methods.
Step-by-step explanation:
Assuming this first part of the problem obtained from the web: "Using traditional methods, it takes 11.0 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed"
Information given
[tex]\bar X=10.8[/tex] represent the mean height for the sample
[tex]s=1.5[/tex] represent the sample standard deviation
[tex]n=9[/tex] sample size
[tex]\mu_o =11[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to check if the true mean for this case is equal to 11 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 11[/tex]
Alternative hypothesis:[tex]\mu \neq 11[/tex]
The statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{10.8-11}{\frac{1.5}{\sqrt{9}}}=-0.4[/tex]
The degrees of freedom are given by:
[tex]df=n-1=9-1=8[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(8)}<-0.4)=0.350[/tex]
Since the p value is higher than the the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from the traditional methods.
If 1 euro is 1.07 dollars and 1 pound is 1.25 dollars how many euro is to the pound
Step-by-step explanation:
1.07×1.25
=1.3375 euros
Explain how to translate the statement into an equation. Use n for the variable. Thirteen less than a number is four EXPLAIN:
start here
Answer:
13-n=4
Subtract both sides by 13
-n=-9
n=9
Step-by-step explanation:
13 less means - and a number means n that you don’t know. is means = sign. And so we get the answer that I gave you. Thank you
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is the following.
y 0 1 2 3
p(y) 0.50 0.25 0.20 0.05
A) Compute E(Y).
B) Suppose an individual with Y violations incurs a surcharge of $110Y2. Calculate the expected amount of the surcharg.
Answer:
A. The E(Y) is 0.80
B. The expected amount of the surcharges is $165
Step-by-step explanation:
A. In order to calculate the E(Y), we would have to calculate the following formula:
E(Y)=∑yp(y)
E(Y)=(0*0.5)+(1*0.25)+(2*0.20)+(3*0.05)
E(Y)=0+0.25+0.40+0.15
E(Y)=0.80
B. In order to calculate the expected amount of the surcharges we would have to calculate the following formula:
E($110Y∧2)=110E(Y∧2)
=110∑y∧2p(y)
=110((0∧2*0.5)+(1∧2*0.25)+(2∧2*0.20)+(3∧2*0.05))
110(0+0.25+0.80+0.45)
=$165
A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola yequals25minusxsquared. What are the dimensions of the rectangle with the maximum area? What is the area?
Answer:
The answer is "[tex]\bold{\frac{32}{3}}\\[/tex]"
Step-by-step explanation:
The rectangle should also be symmetrical to it because of the symmetry to the y-axis The pole of the y-axis. Its lower two vertices are (-x,0). it means that
and (-x,0), and (x,0). Therefore the base measurement of the rectangle is 2x. The top vertices on the parabola are as follows:
The calculation of the height of the rectangle also is clearly 16-x^2, (-x,16,-x^2) and (x,16,-x^2).
The area of the rectangle:
[tex]A(x)=(2x)(16-x^2)\\\\A(x)=32x-2x^3[/tex]
The local extremes of this function are where the first derivative is 0:
[tex]A'(x)=32-6x^2\\\\32-6x^2=0\\\\x= \pm\sqrt{\frac{32}{6}}\\\\x= \pm\frac{4\sqrt{3}}{3}\\\\[/tex]
Simply ignore the negative root because we need a positive length calculation
It wants a maximum, this we want to see if the second derivative's profit at the end is negative.
[tex]A''\frac{4\sqrt{3}}{3} = -12\frac{4\sqrt{3}}{3}<0\\\\2.\frac{4\sqrt{3}}{3}= \frac{8\sqrt{3}}{3}\\\\\vertical \ dimension\\\\16-(\frac{4\sqrt{3}}{3})^2= \frac{32}{3}[/tex]
The checking accounts of USF Credit Union are categorized by age of account and balance in account. We are going to select an account at random from this group of 2000 accounts.What is the conditional probability that the account has a balance at least $500, given that it is at least 3 years old, that is P(>=$500 | >=3 years)?
a. 1/2
b. 1/10
c. 1/4
d. None of these
Missing details to question is attached
Answer:
c) [tex] \frac{1}{4} [/tex]
Step-by-step explanation:
S
Required:
Find the probability that the account has a balance at least $500, given that it is at least 3 years old.
Which means: P(≥$500 | ≥3 years)
To find the probability, use the formula below:
P(≥$500 | ≥3 years) = (No. of accounts with balance≥ 500 and age ≥3 years) / (No. of accounts with age≥3 years)
Where from th given information:
Number of accounts with balance≥ 500 and age ≥3 years = 200
Number of accounts with age≥3 years = 600 + 200 = 800
Therefore,
P(≥$500 | ≥3 years) [tex] = \frac{200}{800} = \frac{1}{4} [/tex]
The probability that the account has a balance at least $500, given that it is at least 3 years old = [tex] \frac{1}{4} [/tex]
Which is the better buy? Store A: $250 of 20% off Or Store B $280 at 25% off
Show your work
Answer:
Store A
Step-by-step explanation:
So. What we are going to want to do here is start off by having two stores obviously. And we have the sales that they have. If the discount is 20% rhat means the new price will be 80% of 250. So we take 250 x .8 = 200
If the discount is 25%, that means the new price will be 75% of what it was before hand. So we take 280 x .75 = 210. So the better price is at Store a
What is the common difference of the sequence 20, 17, 14, 11, 8.... ?
Answer:
-3
Step-by-step explanation:
every sequence goes down by -3
Answer:
take away 3. the common difference is 3
Step-by-step explanation:
take away 3
Dylan paid a plumber $120 for 4 hours of labor. How much does the plumber charge per hour of labor? A. $15 per hour B. $30 per hour C. $116 per hour D. $480 per hour stay safe!
Answer:
Brainleist :)
Step-by-step explanation:
120 dollars for 4 hours of labor
120/4 dollars for 1 hour of labor
B) 30 dollars for 1 hour of labor
answe:
B) 30 dollars for 1 hour of labor
Step-by-step explanation:
120 dollars for 4 hours of labor
120/4 dollars for 1 hour of labor
important messagee:
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Which are true of the function f(x)=49(1/7)?select three options. A)The domain is the set of all real numbers. B) the range is the set of all real numbers. C) the domain is x >0. D)the range is y>0. E)as increases by 1, each y value is one -seventh of the previous y-value.
Answer:
A,D and E
Step-by-step explanation:
We are given that a function
[tex]f(x)=49(\frac{1}{7})^x[/tex]
The given function is exponential function .
The exponential function is defined for all real values of x.
Therefore, domain of f=Set of all real numbers
Substitute x=0
[tex]y=f(0)=49>0[/tex]
Range of f is greater than 0.
x=1
[tex]y(1)=\frac{49}{7}[/tex]
x=2
[tex]y=49(\frac{1}{7})^2=\frac{1}{7}y(1)[/tex]
As x increases by 1, each value of y is one-seventh of the previous y-value.
Therefore, option A,D and E are true.
Answer:
A D E
Step-by-step explanation:
Edge2020 quiz
Solve for x in the equation x squared minus 4 x minus 9 = 29. x = 2 plus-or-minus StartRoot 42 EndRoot x = 2 plus-or-minus StartRoot 33 EndRoot x = 2 plus-or-minus StartRoot 34 EndRoot x = 4 plus-or-minus StartRoot 42 EndRoot
Answer:
[tex]x=2$\pm$\sqrt{42}[/tex]
Step-by-step explanation:
The given equation is:
[tex]x^{2} -4x-9=29\\\Rightarrow x^{2} -4x-9-29=0\\\Rightarrow x^{2} -4x-38=0[/tex]
Formula:
A quadratic equation [tex]ax^{2} +bx+c=0[/tex] has the following roots:
[tex]x=\dfrac{-b+\sqrt D}{2a}\ and\\x=\dfrac{-b-\sqrt D}{2a}[/tex]
Where [tex]D= b^{2} -4ac[/tex]
Comparing the equation with [tex]ax^{2} +bx+c=0[/tex]
a = 1
b = -4
c= -38
Calculating D,
[tex]D= (-4)^{2} -4(1)(-38)\\\Rightarrow D = 16+152 = 168[/tex]
Now, finding the roots:
[tex]x=\dfrac{-(-4)+\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4+2\sqrt {42}}{2}\\\Rightarrow x=2+\sqrt {42}\\and\\x=\dfrac{-(-4)-\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4-2\sqrt {42}}{2}\\\Rightarrow x=2-\sqrt {42}[/tex]
So, the solution is:
[tex]x=2$\pm$\sqrt{42}[/tex]
Answer is A or the first one
PLEASE I NEED HELP ASAP
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
A 11 gram sample of a substance that's
used to treat thyroid disorders has a k-
value of 0.1247.
Enter the correct answer.
N = Noekt
DONE
No = initial mass (at time t = 0)
ĐOO
t?
N = mass at time t.
k = a positive constant that depends on
the substance itself and on the units
used to measure time
t = time, in days
Answer: 55.6 days
Step-by-step explanation:
[tex]P=P_oe^{kt}\\\\\bullet \quad P=\dfrac{1}{2}P_0\\\bullet \quad k=-0.1247\\\bullet \quad t = unknown\\\\\\\dfrac{1}{2}P_o=P_oe^{-0.1247t}\\\\\\\dfrac{1}{2}=e^{-0.1247t}\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=-0.1247t\\\\\\\dfrac{ln\dfrac{1}{2}}{-0.1247}= t\\\\\\\large\boxed{55.6=t}[/tex]
Please answer this correctly without making mistakes
Answer:
7
Step-by-step explanation:
hh
ht
th
tt
so it's a 1/4 chance
1/4 * 28 = 7
Answer:
7
Step-by-step explanation:
The probability of both coins landing on heads is:
1/2 × 1/2 = 1/4
Multiply by 28.
1/4 × 28
= 7
4. The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Answer:
5in³Step-by-step explanation:
The question is in complete. Here is the complete question.
"The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Base of triangle = 1in
height of triangle = 5in"
Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\
B = Base area
H = Height of the pyramid
Base area B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]
b = base of the triangle
h = height of the triangle
B = [tex]\frac{1}{2} * 5 * 1\\[/tex]
[tex]B = 2.5in^{2}[/tex]
Since H = 6inches
Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]
[tex]V = 2.5*2\\V =5in^{3}[/tex]
The graphs below have the same shape. What is the equation of the blue
graph?
Answer: b
Explanation:
The -2 outside of the parentheses means it’s at y=-2 and the -4 inside the parentheses means it’s at x= 4 because it’s always the opposite
Solve the following and
make sure to write your
answer in scientific
notation.
(1.5 x 105)(5 x 103)
Answer:
7.5* 10^8
Step-by-step explanation:
(1.5 x 10^5)(5 x 10^3)
Multiply the numbers
1.5*5=7.5
Add the exponents
10 ^(5+3) = 10^8
Put back together
7.5* 10^8
This is in scientific notation
represent 5 20 30 25 10 on a pie chart
Answer :
I have solved for the points.
Explanation :
Just get a protractor and plot out the angles into a circle. Starting with the largest angle.
given a 60 month car loan at 4.71%, explain how much your monthly payments would be for a $18,400 car and what your TOTAL COST would be given that interest.
Answer:
$23161.10
Step-by-step explanation:
Assuming this is compounded annually, we use our simple interest rate formula: A = P(1 + r)^t
Step 1: Convert months to years
60 months/12 month/year = 5 years
Step 2: Plug in known variables
A = 18400(1 + 0.0471)^5
Step 3: Solve
When you plug step 2 into your calc you should get 23161.1 as your answer. I am assuming that this isn't compounded quarterly or monthly, but just yearly.
Evaluate f(x) = x2 + 1 for f(-1)
Answer: -1
Step-by-step explanation:
to calculate f(-1), you know that x = -1. so all you have to do is substitute:
f(-1) = (-1)2 + 1
f(-1) = -2 + 1
f(-1) = -1
Answer:
0
Step-by-step explanation:
For the dilation, DO, K = (10, 0) → (5, 0), the scale factor is equal to _____.
Answer:
[tex] \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]scale \: factor = \frac{5}{10} = \frac{1}{2} \\ [/tex]
As part of a physics experiment, Ming drops a baseball from the top of a 315-foot building. To the nearest tenth of a second, for how many seconds will the baseball fall? (Hint: Use the formula h = 16t^2, which gives the distance h, in feet, that a free-falling object travels in t seconds.)
Answer: 4.4 seconds
Step-by-step explanation:
h(t) = -16t² + 315
Since we want to find the total time the baseball is in the air, we need to find the time (t) when the ball lands on the ground --> h(t) = 0
0 = -16t² + 315
-315 = -16t²
[tex]\dfrac{315}{16}=t^2\\\\\\\sqrt{\dfrac{315}{16}}=t\\\\\\\dfrac{\sqrt{315}}{4}=t\\\\\\\large\boxed{4.4=t}[/tex]
Answer:
≈ 4.44 sec
Step-by-step explanation:
h= 315 ft
h= 16t²
315 = 16t²
t²=315/16
t=√315/16 ≈ 4.44 sec
If a coin is tossed 5 times, and then a standard six-sided die is rolled 4 times, and finally a group of three cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
Answer: 5,499,187,200
Step-by-step explanation:
A coin is tossed 5 times.
There are two options (heads or tails) so the possible outcomes are: 2⁵
A six-sided die is rolled 4 times.
There are six options so the possible outcomes are: 6⁴
A group of 3 cards are drawn (without replacement).
The first outcome has 52 options, the second has 51 options, and the third has 50 options: 52 x 51 x 50
Now if we want the coin AND the die AND the cards, we have to multiply all of their possible outcomes:
2⁵ x 6⁴ x 52 x 51 x 50
= 32 x 1296 x 132,600
= 5,499,187,200
What is the solution of √1-3x = x+3 ?
Answer:
{-1, -8}
Step-by-step explanation:
Please enclose "1 - 3x" inside parentheses so the reader will know that you want the square root of all of "1 - 3x".
Squaring both sides of the given equation, we get:
1 - 3x = x^2 + 6x + 9, or x^2 + 6x + 8 + 3x, or
x^2 + 9x + 8 = 0. Factoring, we get: (x + 8)(x + 1) = 0, so that the solutions are {-1, -8}.
Answer:
I hope the given equation is :
{-1, -8}
First step to solve this equation to remove square root from the left side. So, take square on each sides of the equation. Therefore,
1 - 3x = (x + 3)²
1 - 3x = (x + 3)*(x + 3) Since a² = a * a
1 - 3x = x² + 3x + 3x + 3² By multiplication.
1 - 3x = x² + 6x + 9 Combine the like terms.
x² + 6x + 9 - 1 + 3x = 0 Subtract 1 and add 3x from each sides of equation
x² + 9x + 8 = 0 Combine the like terms.
Next step is to factor the trinomial to solve the above equation for x.
For that break downn the constant 8 into two multiples so that the addition of the multiples will result the coefficient of x = 9.
So, 8 = 1 * 8
Addition of 1 and 8 will give 9. So, next step is to replace 9x with 1x + 8x. So,
x² + 1x + 8x + 8 = 0
(x² + 1x) + (8x + 8) = 0 Group the terms.
x ( x + 1) + 8 (x + 1 ) = 0 Take out the common factor from each group.
(x +1 ) ( x + 8 ) = 0 Take out the common factor (x + 1).
So, x + 1 = 0 and x + 8 = 0 Set up each factor equal to 0.
Hence, x = -1 and - 8.
Next step is to plug in -1 and -8 in the original equation to cross check the solutions.
For x = -1,
Simplify each sides separately.
2 = 2
2 = 2 is correct. So, x = -1 satisfy the equation.
Hence, x = -1 is the real solution of the given equation.
Similarly let's plug in x = -8 now. So,
Simplify each sides separately.
5 = 2
5 = 2 is not true. So, x = -8 is the extraneous solution.
Therefore, the only solution is x = -1.
Hence, the correct choice is C.
Hope this helps you!
Step-by-step explanation:
mark brainlies plssssssssss
What is the greatest number that can be divided evenly into 78 and 104 without leaving a remainder?
Answer:
26 can be divides evenly into 78 and 104 without leaving a remainder
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
78= 2 × 3 × 13
104= 2 × 2 × 2 × 13
The required number is: 2 × 13= 26
Rhea obtained a CO-OP credit working at a computer store. They have now hired her for a summer job with the store. She makes $8/hour, plus a 5% commission on sales.
Which expression best describes Rhea's total earnings? Explain.
a) E = 8h + 5s b) E = 8h + .50s
c) E = 8h + .005s d) E = 8h + 0.05s
Rhea worked 15 hours last week and made $260 in total. What were her total sales in computers for the week?
Why do you think employers offer commissions to their employees? Do you think there are any potential problems with this form of earnings?
Answer:
d) E = 8h + 0.05s
Her total sales in computers for the week is $2800.
Step-by-step explanation:
Let Rhea's hourly pay =h
She makes $8/hour, therefore sales for h hours =$8h
Let the volume of sales = s
She also earns 5% commission on sales = 5% of s = 0.05s
Therefore, the expression which best describes Rhea's total earnings:
(D) E=8h+0.05s
Rhea worked 15 hours last week and made $260 in total.
h=$15
From the formula
260=8(15)+0.05s
0.05s=260-8(15)
0.05s=140
s=2800
Her total sales in computers for the week is $2800.
Employers offer commissions to their employees to motivate them to seek to make sales rather than just passing time.
In so far as the sales commission do not eat up the profit of the business, there are no potential problems with this form of earnings
Which of the x-values are solutions to the following inequality? 17 > x Choose all answers that apply: (A) x = 7 (B) x = 12 (C) x = 17
Answer:
7 and 12
Step-by-step explanation:
7 and 12 are ok
17 is not
hope this helps
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The inequality is given below.
x < 17
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
More about the inequality link is given below.
https://brainly.com/question/19491153
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