Step-by-step explanation:
Use double and triple angle identities:
sin(2x) + cos(3x)
2 sin x cos x + 4 cos³x − 3 cos x
What is 100 times 10
Answer:
Central graph
Step-by-step explanation:
When a function has a negative rate of change, it means that as the x value increases, the y value decreases. The only graph that does this continuously is the central one. Hope this helps!
The calculated product of the numbers is 1000
The graph with a negative rate to be (c)
How to calculate the product of the numbersFrom the question, we have the following parameters that can be used in our computation:
100 times 10
When represented as an equation, we have
100 times 10 = 100 * 10
Evaluate the products
So, we have the following result
100 times 10 = 1000
Next, we interpret the graph
From the graphs, we have the graph with a negative rate to be (c)
Using the above as a guide, we have the following:
the result is 19/125
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y = 6x - 4
y = -x + 3
Answer:
(1, 2)
Step-by-step explanation:
Subtract the second equation from the first:
(y) -(y) = (6x -4) -(-x +3)
0 = 7x -7 . . . . . simplify
0 = x - 1 . . . . . . divide by 7
1 = x . . . . . . . . . add 1
y = -1 +3 = 2 . . . substitute into the second equation
The solution is (x, y) = (1, 2).
Madison drew Triangle D E F. In her triangle, Measure of angle D is represented as x degrees. The measure of Angle E is half the measure of Angle D. The measure of Angle F is 2 degrees less than twice Measure of angle D. What is Measure of angle F?
A) 36 degrees
B)56 degrees
C)102 degrees
D)147 degrees
Answer:
102 degrees.
Step-By-Step Explanation:
We know that D is x and E is 1/2x and Angle F is 2 less than angle D.
So if we use the sum of 180 and solve for x, we will find angle D.
This is the equation: x+.5x+2x-2=180
solve: 3.5x -2 = 180
+2 +2
3.5x=182
/3.5x /3.5x
X = 52
2(52)-2 = 102 degrees
Thus the answer is 102 degrees
hope this helped:)
Answer:
102º
Step-by-step explanation:
Solving for Unknown Values
Use parallelogram ABCD. What are the values of x and
y?
FERTE
A
4y-3
B
x =
y =
3x-9
42
D
37
C
Answer:x=17 y=10
Step-by-step explanation:
What is the solution to this equation?
5x - x + 12 + 2x - 7 = 10
A. X=
15
6
B. X=
15
7
C.
X =
V01
D. x=
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x=5 (over)/6
Decimal Form:
x=0.8¯3
(Hopefully this helped you solve the problem.)
Write the slope-Intercept form of the equation for the line
Answer:
Equation : y = -0.9x − 1.5
Step-by-step explanation:
Slope is rise over run, 7 over 8
-7/8 = -0.875, round to nearest tenth
-0.875 = -0.9
y- intercept is the point that crosses the y-axis,
the line crosses the y-axis at -1.5
If you spin the spinner 90 times,
how many times should the
number 3 be selected?
Answer:
15
Step-by-step explanation:
1/6 of 90 is 15
The number of times 3 should be selected is 45/2.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We know that;
Number of spins= 90
Number of selected= 3
Now,
If the spinner has 4 equal sections and one of them has a 3, then the probability of landing on 3 is 1/4.
To find the expected number of times that the spinner lands on 3 in 90 spins, we need to multiply 1/4 by 90.
=1/4 * 90
=45/2
Therefore, by algebra the answer will be 45/2.
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what is 4 3/8 - 5 1/2 ?
Answer:-1.125
Step-by-step explanation:
Your friend deposits $6000 in an investment account that earns 7.3% annual interest. Find the balance after 18 years when the interest is compounded quarterly.
Answer: $22,063.2
Step-by-step explanation:
quarterly means that 4 times per year this interest, the balance can be find by the equation:
A = P*(1 + r/4)^(4*t)
Where P is the initial value, r is the rate of increase (7.3% in this case, but remember that you must use the decimal form; 0.073) and t is the number of years:
so we have:
B = $6,000*( (1 + 0.073/4)^(4*18) = $22,063.2
the ratio of savings to expenditure is 2:8 find the savings if the expenditure is 24,000
Answer:
the savings is 6000
Step-by-step explanation:
We are told that the ratio of savings to expenditure is 2: 8, that is, that person saves 2 when he spends 8.
They tell us to find the savings when the cost is 24,000, so we are left with:
24000 * 2/8 = 6000
which means that when 24000 are spent the savings is 6000
Two angles of a triangle measure 78 and 24
Answer: 78
Step-by-step explanation: Remember every triangle ads up to a total of 180 degrees. You just have to make sure that it adds up to 180
You purchased a rare painting for $150 that is increasing in value by 3% annually. How many years will it take until it is doubled in value? Round to the nearest whole year
Answer:
23 years.
Step-by-step explanation:
It is given that the initial price of painting is $150 and its values increasing by 3% annually.
We need to find how many years will it take until it is doubled in value.
The value of painting after t years is given by
[tex]y=150(1+0.03)^t[/tex]
[tex]y=150(1.03)^t[/tex]
The value of painting after double is 300. Substitute y=300.
[tex]300=150(1.03)^t[/tex]
Divide both sides by 150.
[tex]2=(1.03)^t[/tex]
Taking log both sides.
[tex]\log 2=\log (1.03)^t[/tex]
[tex]\log 2=t\log (1.03)[/tex]
[tex]t=\dfrac{\log 2}{\log (1.03)}[/tex]
[tex]t=23.44977[/tex]
[tex]t\approx 23[/tex]
Therefore, the required number of years is 23.
11(11d+3z+8)for d = 10 and z = 12
Answer: 1,694
Step-by-step explanation: 11(11d + 3z + 8) d = 10 and z = 12
121d + 33z + 88
121(10) + 33(12) + 88
1210 + 396 + 88
1,694
Which represents 236 as the sum of a whole number and a fraction? CLEAR CHECK 2+36 3+36 3+56 4+16
Question:
Which represents [tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction?
[tex]2+ \frac{3}{6}[/tex]
[tex]3 + \frac{3}{6}[/tex]
[tex]3+ \frac{5}{6}[/tex]
[tex]4+ \frac{1}{6}[/tex]
Answer:
[tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction is equivalent to [tex]2+ \frac{3}{6}[/tex]
Step-by-step explanation:
Given
Mixed Fraction: [tex]2 \frac{3}{6}[/tex]
Required
Express as the sum of a whole number and fraction.
Given that [tex]2 \frac{3}{6}[/tex] is a mixed fraction; it can be converted to the sum of a whole number and a fraction by following the steps below.
1. Convert the mixed fraction to improper fraction
[tex]2 \frac{3}{6} = \frac{(6 * 2 + 3)}{6}[/tex]
2. Split the numerator
[tex]2 \frac{3}{6} = \frac{((6 * 2) + (3))}{6}[/tex]
3. Split fraction to 2
[tex]2 \frac{3}{6} = \frac{(6 * 2)}{6} +\frac{(3)}{6}[/tex]
Simplify
[tex]2 \frac{3}{6} = \frac{(12)}{6} +\frac{(3)}{6}[/tex]
[tex]2 \frac{3}{6} = 2 + \frac{3}{6}[/tex]
Hence, [tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction is equivalent to [tex]2+ \frac{3}{6}[/tex]
1) Lithium isotope rations are important to medicine, the 6Li/7Li ratio in a standard reference material was measured several times, and the values are: 0.082601, 0.082621, 0.082589, 0.082617, 0.082598. Please use student’s t to find the confidence interval at the 95% confidence level. 2) If one wants the confidence interval to be two thirds of the previous one, how many times should a student repeat? (Assuming the standard deviation is the same as the previous one)?
Answer:
1) [tex]0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588[/tex]
[tex]0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219[/tex]
b) [tex] ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653[/tex]
And we want 2/3 of the margin of error so then would be: [tex] 2/3 ME = 0.00001111[/tex]
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (2)
Replacing we got:
[tex]n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12[/tex]
So the answer for this case would be n=12 rounded up to the nearest integer
Step-by-step explanation:
Information given
0.082601, 0.082621, 0.082589, 0.082617, 0.082598
We can calculate the sample mean and deviation with the following formulas:
[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
[tex]\bar X=0.0826052[/tex] represent the sample mean
[tex]\mu[/tex] population mean
s=0.000013424 represent the sample standard deviation
n=5 represent the sample size
Part 1
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom, given by:
[tex]df=n-1=5-1=4[/tex]
The Confidence level is 0.95 or 95%, and the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value would be using the t distribution with 4 degrees of freedom: [tex]t_{\alpha/2}=2.776[/tex]
Now we have everything in order to replace into formula (1):
[tex]0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588[/tex]
[tex]0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219[/tex]
Part 2
The original margin of error is given by:
[tex] ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653[/tex]
And we want 2/3 of the margin of error so then would be: [tex] 2/3 ME = 0.00001111[/tex]
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (2)
Replacing we got:
[tex]n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12[/tex]
So the answer for this case would be n=12 rounded up to the nearest integer
Simplify the expression by combining like terms.
Write the terms in alphabetical order of the
variables.
6x - 6y + 6z + 18x - 11y + 2z
Answer:
24x - 17y + 8z
Step-by-step explanation:
There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?
(A) Approximately normal with mean $206,274 and standard deviation $3,788
(B) Approximately normal with mean $206,274 and standard deviation $37,881
(C) Approximately normal with mean $206,274 and standard deviation $520
(D) Strongly right-skewed with mean $206,274 and standard deviation $3,788
(E) Strongly right-skewed with mean $206,274 and standard deviation $37,881
Answer:
(A) Approximately normal with mean $206,274 and standard deviation $3,788
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population:
Right skewed
Mean $206,274
Standard deviation $37,881.
Sample:
By the Central Limit Theorem, approximately normal.
Mean $206,274
Standard deviation [tex]s = \frac{37881}{\sqrt{100}} = 3788.1[/tex]
So the correct answer is:
(A) Approximately normal with mean $206,274 and standard deviation $3,788
Approximately normal with mean is $206,274 and standard deviation is $3,788 and this can be determined by applying the central limit theorem.
Given :
There were 5,317 previously owned homes sold in a western city in the year 2000.The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. Simple random samples of size 100.According to the central limit theorem the approximately normal mean is $206274.
Now, to determine the approximately normal standard deviation, use the below formula:
[tex]s =\dfrac{\sigma }{\sqrt{n} }[/tex] ---- (1)
where 's' is the approximately normal standard deviation, 'n' is the sample size, and [tex]\sigma[/tex] is the standard deviation.
Now, put the known values in the equation (1).
[tex]s = \dfrac{37881}{\sqrt{100} }[/tex]
s = 3788.1
[tex]\rm s \approx 3788[/tex]
So, the correct option is A).
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Select all of the following that are quadratic equations. 5 x - 1 = 3 x + 8 5 x - 3 = 0 x2 - 2 x = 4 x + 1 2 x2+ 12 x = 0 x3 - 6 x2 + 8 = 0 9 x2 + 6 x - 3 = 0
Answer:
Answers are below.
Step-by-step explanation:
x2 - 2 x = 4 x + 12
x2+ 12 x = 0
x2 + 8 = 0
9x2 + 6 x - 3 = 0
These are all quadratic equations because they have x2 in all of them.
If this answer is correct, please make me Brainliest!
Answer:
x^2 - 2x = 4x + 1
2x^2 + 12x = 0
9x^2 + 6x - 3 = 0.
Step-by-step explanation:
A quadratic equation will contain a term with an exponent of 2 as the highest exponent.
Which number line shows the solution if 4x - 36 < -12?
One solution was found :
x = 9
Is the point (7,0) located on the x axis
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Yes. As the y value is 0, this point would be on the x axis
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Solve xy^m=yx^3 for m
Answer:
m = 1 + 2log(x)/log(y)
Step-by-step explanation:
Taking logarithms, you have ...
log(x) +m·log(y) = log(y) +3log(x)
m·log(y) = log(y) +2·log(x) . . . . subtract log(x)
m = (log(y) +2·log(x))/log(y) . . . divide by the coefficient of m
m = 1 +2·log(x)/log(y) . . . . . . . simplify a bit*
_____
* The "simplified" form will depend on your preference. Here, I like the integer 1 brought out because most logs are irrational. The result may be very slightly more accurate if we add 1, rather than log(y)/log(y)--depending on your calculator.
A copy machine makes 24 copies per minute. How many copies does it make in 3 minutes and 45 seconds?
copies
Х
?
Answer:
90 copies
Step-by-step explanation:
24*3= 72
1/2*24= 12 for 30 seconds
1/2*6= 6 for 15 seconds
45/15=3
72+18= 90
All equations are identies, but not all identies are equations
True or False
ANSWER: It is false that All equations are identities, but not all identities are equations, as all identities are equations, but only some equations are identities.
HOPE THIS HELP
Write the slope-intercept form of the equation for the line
Answer:
y=3x-1
Step-by-step explanation:
start at (-1,-4) and go up 6 and over 2, thats your slope or m.
the y intercept is -1
Answer: y=3x-1
Step-by-step explanation:
(1,2) and (-1,-4) are on the so we could use then to find the slope.
2-(-4)=6
1-(-1)= 2
6/2=3
We know the y-intercept is -1 because the line passes through (0,-1) which is on the y axis. And the y-intercept is when x is 0.
so the equation will be y = 3x -1
n Hamilton County, Ohio the mean number of days needed to sell a home is days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of homes in a nearby country showed a sample mean of days with a sample standard deviation of days. Conduct a hypothesis test to determine whether the mean number of days until a home is sold is different than the Hamilton county mean of days in the nearby county. Round your answer to four decimal places.
Answer:
There is enough evidence to support the claim that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.
Test statistic t=-1.8974
P-value = 0.0326
Step-by-step explanation:
The question is incomplete:
"In Hamilton County, Ohio the mean number of days needed to sell a home is 86 days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of 40 homes in a nearby county showed a sample mean of 80 days with a sample standard deviation of 20 days. Conduct a hypothesis test to determine whether the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county. Round your answer to four decimal places."
This is a hypothesis test for the population mean.
The claim is that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=86\\\\H_a:\mu< 86[/tex]
The significance level is 0.05.
The sample has a size n=40.
The sample mean is M=80.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=20.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{20}{\sqrt{40}}=3.1623[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{80-86}{3.1623}=\dfrac{-6}{3.1623}=-1.8974[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=40-1=39[/tex]
This test is a left-tailed test, with 39 degrees of freedom and t=-1.8974, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.8974)=0.0326[/tex]
As the P-value (0.0326) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.
In a lottery​ game, the jackpot is won by selecting five different whole numbers from 1 through 37 and getting the same five numbers​ (in any​ order) that are later drawn. In the Pick 5 ​game, you win a straight bet by selecting five digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same five digits in the exact order they are later drawn. The Pick 5 game returns ​$50,000 for a winning​ $1 ticket. Complete parts​ (a) through​ (c) below:a. What is the probability of winning a jackpot in this​ game? ​P(winning a jackpot in this ​game)= ________b. In the Pick 5 ​game, you win a straight bet by selecting five digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same five digits in the exact order they are later drawn. What is the probability of winning this​ game? ​P(winning the Pick 55​game)= ______________c. The Pick 5 game returns ​$50,000 for a winning​ $1 ticket. What should be the return if the lottery organization were to run this game for no​ profit? ​
Answer:
The probability of winning a jackpot is [tex]P = 0.000003[/tex]
The probability of winning the pick 5 game is [tex]P_a = 0.00001[/tex]
The earning of the lottery organisation if the game were to be runed for no profit is [tex]x =[/tex]$10 000
Step-by-step explanation:
From the question
The sample size is n= 37
The number of selection is [tex]r = 5[/tex]
Now the number of way by which these five selection can be made is mathematically represented as
[tex]\left n} \atop {}} \right.C_r = \frac{n!}{(n-r)!r! }[/tex]
Now substituting values
[tex]\left n} \atop {}} \right.C_r = \frac{37!}{(37-5)!5! }[/tex]
[tex]\left n} \atop {}} \right.C_r = 333333.3[/tex]
Now the probability of winning a jackpot from any of the way of selecting 5 whole number from 37 is mathematically evaluated as
[tex]P = \frac{1}{333333.3}[/tex]
[tex]P = 0.000003[/tex]
Now the number of ways of selecting 5 whole number from 0 to 9 with repetition is mathematically evaluated as
[tex]k = 10^5[/tex]
Now the probability of winning the game is
[tex]P_a = \frac{1}{10^5}[/tex]
[tex]P_a = 0.00001[/tex]
We are told that for a $1 ticket that the pick 5 game returns $50 , 000
Generally the expected value is mathematically represented as
[tex]E(X) = x * P(X =x )[/tex]
In this question the expected value is $1
So
[tex]1 = x * 0.00001[/tex]
So [tex]x = \frac{1}{0.00001}[/tex]
[tex]x =[/tex]$10 000
Jessica has to make a trip of 8925 MI. if she travels 425 miles a day how long will the trip take?
Answer:
21 days.
Step-by-step explanation:
You just divide the total number of miles by miles traveled a day.
8925÷425=21
It will takes 21 days.
Answer:21 days
Step-by-step explanation:
Which is greater 16/12 or 9/3
Answer:
[tex] \frac{16}{12} \: \: < \frac{9}{3} [/tex]
9/3 is greater
Step-by-step explanation:
[tex] \frac{16}{12} \: \: \: \: \: \: \: \: \: \: \frac{9}{3} \\ \frac{16}{12} \: \: \: \: \: \: \: \: \: \: \frac{9 \times 4}{3 \times 4} \\ \frac{16}{12} \: \: \: \: \: \: \: \: \: \: \frac{36}{12} \\ \frac{16}{12} \: < \: \frac{36}{12} \\ \\ so \\ \frac{16}{12} < \frac{9}{3} [/tex]
Answer:
the answer is attached to the picture
What would you do to find the area of 5/8 of a circle?
Answer:
5/8 * pi r^2
Step-by-step explanation:
First , you find the full area of the circle
A = pi r^2
Then multiply by the fraction that you want to find
5/8 * pi r^2
Use matrix algebra to show that if A is invertible and D satisfies ADequalsI, then Upper D equals Upper A Superscript negative 1. Choose the correct answer below. A. Left-multiply each side of the equation ADequalsI by Upper A Superscript negative 1 to obtain Upper A Superscript negative 1ADequalsUpper A Superscript negative 1I, IDequalsUpper A Superscript negative 1, and DequalsUpper A Superscript negative 1. B. Add Upper A Superscript negative 1 to both sides of the equation ADequalsI to obtain Upper A Superscript negative 1plusADequalsUpper A Superscript negative 1plusI, IDequalsUpper A Superscript negative 1, and DequalsUpper A Superscript negative 1.
Answer:
D=A^-1
Step-by-step explanation:
Given that A is invertible and matrix D satisfies AD=I
Where I is an identity matrix
D is the inverse of A
Multiply both sides of AD=I by A^-1
A^-1(.AD) =A^-1 I
A^-1 .A=I
Therefore D=A^-1