Given:
The trigonometric expression is,
\(\frac{\sec ^2\theta-1}{\sec ^2\theta}\)Explanation:
Simplify the expression.
\(\begin{gathered} \frac{\sec^2\theta-1}{\sec^2\theta}=\frac{\tan ^2\theta}{\sec ^2\theta}\text{ \lbrack}sec^2\theta+tan^2\theta=1\text{\rbrack} \\ =\frac{\sin^2\theta}{\cos^2\theta}\cdot\frac{1}{\sec ^2\theta} \\ =\frac{\sin^2\theta}{\cos^2\theta}\cdot\cos ^2\theta \\ =\sin ^2\theta \end{gathered}\)So equivalent expression is,
\(\sin ^2\theta\)(x - 3)3 = 27(2x - 1)3
Answer:
24
x= ____
53
Step-by-step explanation:
the right answer
Answer:
x=24/53
Step-by-step explanation:
(x-3)3=27(2x-1)
3x-9=(54x-27)3
3x_9=162x-81
3x-162x=-81+9
-159x=-72
x=-72/-159
x=24/53
Jessica had 207 dollars to spend on 8 books. After
buying them she had 15 dollars. How much did each book cost
207$ - 15$ = 192$
192$ : 8 = 24$
Answer: Each book costed 24$.
ILL GIVE U BRAINLIST OR WHATEVER
The nationwide percentage of Americans who invest in the stock market is usually taken to be 55%. Is this percentage different in Georgia? A survey and analysis among Georgia residents led to a test statistic of 1.75.
(b) What is the p-value to test if the proportion of Georgians who invest in the stock market is different than the nationwide average? (Use 4 decimals.)
Okay, here are the steps to find the p-value:
1) The nationwide proportion of Americans who invest in the stock market is 55% (0.55)
2) The test statistic for Georgia is 1.75
3) To calculate the p-value, we need to know the degrees of freedom (df) and the critical value of the test statistic.
4) The df = 1, since we're comparing a single proportion (Georgia) to a fixed value (national average).
5) The critical value at df = 1 and 95% confidence is 3.84 (for a two-tailed test)
6) Since the test statistic of 1.75 is less than 3.84, we look up 1.75 in tables to find the p-value.
7) For a test statistic of 1.75 and df = 1, the p-value is 0.1860.
So the p-value to test if the proportion of Georgians who invest in the stock market is different than the nationwide average is 0.1860.
Let me know if you have any other questions!
Okay, here are the steps to find the p-value:
1) The nationwide proportion of Americans who invest in the stock market is 55% (0.55)
2) The test statistic for Georgia is 1.75
3) To calculate the p-value, we need to know the degrees of freedom (df) and the critical value of the test statistic.
4) The df = 1, since we're comparing a single proportion (Georgia) to a fixed value (national average).
5) The critical value at df = 1 and 95% confidence is 3.84 (for a two-tailed test)
6) Since the test statistic of 1.75 is less than 3.84, we look up 1.75 in tables to find the p-value.
7) For a test statistic of 1.75 and df = 1, the p-value is 0.1860.
So the p-value to test if the proportion of Georgians who invest in the stock market is different than the nationwide average is 0.1860.
Let me know if you have any other questions!
л IX +6 ІІ 2 someone please help
Given,
\(\frac{x}{5}+6=2\)This can be further solved as, by multiplying with 5 on all the terms,
\(x+30=10\)Thus x can be calculated as
\(undefined\)Help me and there will be an apple at your doorstep. (There might be some shipping issues)
Fill in the blank.
Answer:
9.30 maybe
Step-by-step explanation:
I just did mathz
Answer:
9.30
Step-by-step explanation:
help me on this please
Answer:
14.387
Step-by-step explanation:
an ice cream truck operator tracks total daily sales rounded to nearest dollar for 14 days as shown in the following 1: 201 2:249 3: 285 4:297 5:288 6:262 7:256 8:240 9:210 10:199 11:192 12:215 13:237 14:290 based on a cubic model of the data what is the predicted number of sales on the 15th day
The required predicted sales n the 15th day is given as 244 ice creams.
Given that,
an ice cream truck operator tracks total daily sales rounded to the nearest dollar for 14 days as shown in the following 1: 201 2:249 3: 285 4:297 5:288 6:262 7:256 8:240 9:210 10:199 11:192 12:215 13:237 14:290.
The average of the values is the ratio of the total sum of values to the number of values.
Here,
calculate average sales,
= [201 +249 + 285 + 297 + 288 + 262 + 256 + 240 + 210 + 199 + 192 + 215 + 237 + 290] / 14
= 244
So on the 15 day the sale can be predicted as 244.
Thus, the required predicted sales n the 15th day is given as 244 ice creams.
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Answer: $371
Step-by-step explanation:
use the cubic equation
Vita used the model below to find the sum of two mixed numbers what is the sum?
Answer:
the first mixed number is 1 8/10 which is reduced to 1 and 4/5 and the seconde is 2 and 3/5 added equals 4 and 2/5
Step-by-step explanation:
1 plus 2 equals 3
and 3/5 plus 4/5 equals 7/5
turn it into a mixed number which equals 1 and 2/5 the add 3 and u get 4 and 2/5
Select the correct choice that completes the following statement. A polynomial root of multiplicity 2...?
GIven:
A polynomial has a root of multiplicity 2.
The objective is to choose the correct answer fro mthe options.
The root of a polynomial equation is the point on the x axis where y =0.
Thus, the root of a polynomial touches the x axis and passes throught the x axis.
Hence, option (a) is the correct answer.
5x2x_=90
A-9 B-10. C-80. D-83
six more than x is nine as equation
Answer:
x + 6 = 9
Step-by-step explanation:
6 more means +6. Therefore if 6 more than x is 9, the equation would be
\(x + 6 = 9\)
Answer:
6+x=9
Step-by-step explanation:
Please help.
What is 74+35.6?
Thank you
Answer:
The sum of
74 and 35.6 is 109.6
Step-by-step explanation:
109.6
Now enjoy a free meme thing
Find the equation of the regression line for the data in the table.
X
y
25 6
44 13
46 14
52 10
57 13
Round your answers to the nearest tenth.
x + =
y
Submit
The equation for the regression line from the data is y = -0.98x + 56.8
Given data ,
To find the equation of the regression line, we will use the method of least squares. The regression line is represented by the equation:
y = mx + b
where m is the slope of the line and b is the y-intercept.
We need to calculate the values of m and b. Let's begin by finding the mean values of x and y:
Mean of x (x₁) = (6 + 13 + 14 + 10 + 13) / 5 = 12.2
Mean of y (y₁) = (25 + 44 + 46 + 52 + 57) / 5 = 44.8
Next, we calculate the deviations from the mean for both x and y:
Deviation from the mean of x (Δx) = x - x₁
Deviation from the mean of y (Δy) = y - y₁
Now, we calculate the sum of the products of the deviations from the mean:
Σ(Δx * Δy) = (6 - 12.2) * (25 - 44.8) + (13 - 12.2) * (44 - 44.8) + (14 - 12.2) * (46 - 44.8) + (10 - 12.2) * (52 - 44.8) + (13 - 12.2) * (57 - 44.8)
Σ(Δx * Δy) ≈ -51.6
Next, we calculate the sum of the squared deviations from the mean of x:
Σ(Δx²) = (6 - 12.2)² + (13 - 12.2)² + (14 - 12.2)² + (10 - 12.2)² + (13 - 12.2)²
Σ(Δx²) ≈ 52.8
Now, we can calculate the slope (m) using the formula:
m = Σ(Δx * Δy) / Σ(Δx²)
m ≈ -51.6 / 52.8 ≈ -0.98
Finally, we can calculate the y-intercept (b) using the formula:
b = y₁ - m * x₁
b ≈ 44.8 - (-0.98) * 12.2 ≈ 56.8
Hence , the equation of the regression line for the given data is:
y = -0.98x + 56.8
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Dustin bought 2/3 pounds of peaches for $3.00.what was the price he paid per pound of peches
Answer:
3
Step-by-step explanation:
if 2/3 was 3/3 then it would be divided into 3 there for 3
Samantha opened a savings account and deposited $8192. The account earns 10% in interest annually. She makes no further deposits and does not withdraw any money. In t years, she has $25,710 in this account. Write an equation in terms of t that models the situation.
The equation in terms of t that models the situation is given by
\(8192(1+\frac{0.01}{12} )^{12t} = 25710\).
We know that the interest on a loan or deposit that is accrued on both the initial principal and the total interest from prior periods is known as compound interest and it can be calculated as
\(A = P(1+\frac{r}{n})^{nt}\),
where P is the initial principal, r is the rate of interest, n is the number of times interest was charged for each time period, t is the amount of time that has passed and A is the final amount.
Here, P = 8192, r = 10% = 10/100 = 0.01, n = 12 and A = 25,710
So, we can write
\(8192(1+\frac{0.01}{12} )^{12t} = 25710\)
Therefore the required equation is
\(8192(1+\frac{0.01}{12} )^{12t} = 25710\)
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Which is the graph of a logarithmic function?
Find the volume of the cylinder. Round your answer to the nearest tenth.
Step-by-step explanation:
the formula for finding the area of cylinder is πr²h
Leta's mother drove for 4 hours
to visit her friend. She drove
40 miles each hour. How many
miles did Leta's mother travel to
her friend's house?
Answer: 160 miles
Step-by-step explanation: 40 miles each hour is a quarter of the 4 hours, meaning we multiply 4x40. We get 160. You can also add 40 4 times. 40, 80, 120, 160.
Answer: 160 miles
Step-by-step explanation: If Leta's mother drove 40 miles an hour you can either add 40 4 times or multiply 40 by 4 and you will get your answer as 160 so the 160 is the number of miles she drove to get to her friend's house
Which graph displays points that correspond to the x and y values in the table?
hm this is weird, i thought i answered the question. or maybe they're two different questions? line graph because i said so. i know im so helpful
Determine whether the following procedure is a binomial experiment.
If it is not, explain why. Drawing 5 marbles from a bag with 10 red, 8 green and 12 yellow marbles without replacement and finding out how many of these five are green.
a. Yes, this is a binomial experiment.
b. No, the outcomes cannot be classified into two categories.
c. No, the trials are not independent
Answer:
C. The trails are not independent.
The probability of drawing one marble will not be independent of others thus option (c) is correct.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
As per the given,
Drawing 5 marbles from a bag with 10 red, 8 green, and 12 yellow marbles without replacement.
In without replacement, the remaining balls in each draw will go to be decreased thus they will be dependent events so binomial distribution will not be applied.
Hence "One marble's likelihood of being drawn won't be independent of the other marbles".
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How many triangles can be constructed with angles measuring 50°, 90°, and 40°?
A.one
B.none
C.more than one
The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 200,000 mosquitoes in the area initially, and predators (e.g. birds, bats) eat 20,000 mosquitoes/day. Determine the population of mosquitoes in the area at any given time.
So far, I have used the equation, P = P0 e^-kt The population of mosquitoes in a certain area inc where P0=200,000 and P(7)=400,000 (I figured time should be measured in days since you are given the number of mosquitoes eaten per day) to solve for k:
400,000 = 200,00 e^-k(7) >> K=-ln(2)/7=-.099
Using that, I figured I should put that into the differential equation (change in population = birthrate - deathrate)
dp/dt = kP - 20,00t ---> dp/dt = -099P - 20,000t
I thought I knew how to solve this and everything, but once I got an answer and plugged in different times, the model says the population decreases, which doesn't seem to make sense. So please check my reasoning up to this point and show the solution so I can check mine.
The equation you used is correct, but the differential equation does not include the growth rate. The growth rate is proportional to the current population, so the differential equation should look like this: dp/dt = kP - 20,000t
dp/dt = kP - 20,000t , Where k is the growth rate. To solve this equation, we can use the separation of variables: dp/P = kdt - 20,000tdt
Integrating both sides, we get:
ln|P| = kt - 20,000t^2/2 + C, Where C is the integration constant. To find C, we can use the initial population of 200,000:
ln|200,000| = -0.099t - 20,000t^2/2 + C
=>C = ln|200,000| + 0.099t + 20,000t^2/2 .Therefore, the population of mosquitoes at any given time t is:
P = 200,000e^(-0.099t - 20,000t^2/2 + ln|200,000| + 0.099t + 20,000t^2/2) = 200,000e^(ln|200,000|) = 200,000
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If a=-2 and b=-4 find the value of 3a+b+4
Answer:
-6
Step-by-step explanation:
hey laudu
\(3a + b + 4\)
\(3( - 2) + ( - 4) + 4\)
\( - 6 - 4 + 4\)
\( - 6\)
Step-by-step explanation:
❀ \( \underline{ \underline{ \text{Given}}} : \)
a = -2 & b = - 4❀ \( \underline{ \underline{ \text{To \: find}}} : \)
value of 3a + b + 4✏ \( \underline{ \underline{ \text{Solution}}} : \)
All you need to do is plug the value and simplify !
⟶ \( \tt{3 \times ( - 2) + ( - 4) + 4}\)
⟶ \( \tt{ - 6 + ( - 4) + 4}\)
⟶ \( \tt{ - 6 - 4 + 4}\)
⟶ \( \tt{ - 10 + 4}\)
⟶ \( \boxed{ \tt{ - 6}}\)
\( \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ - 6}}}}}}\)
Hope I helped ! ♪
Have a wonderful day / night ! ♡
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
is y=3x+5
-3x-y=9 perpendicular, parallel or neither
Answer:
neither
Step-by-step explanation:
Select the correct answer.
Which expression is equivalent to the given expression?
6ab / (a^0b^2)^4
A. 6a / b^5
B. 6a / b^7
C. 6 / a^3b^7
D. 6 / a^3b^5
-8 X-3x = -6 + 5 x
How to solve
Answer:
x = 7
Step-by-step explanation:
3x-5=x+9 (Adding 5 and -x to both signs of = Sign)
2x = 14
x = 7
Pre - Calculus evaluate exponential derivative at a point !
Answer:
\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)
Step-by-step explanation:
Use Quotient Rule to find f'(x)
\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)
Find f'(1) using f'(x)
\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)
Answer:
\(f'(1)=-\dfrac{9}{e^{3}}\)
Step-by-step explanation:
Given rational function:
\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)
To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.
\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)
\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)
\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)
Therefore:
\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)
\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)
\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)
To find f'(1), substitute x = 1 into f'(x):
\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)
\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)
\(f'(1)=-\dfrac{9}{e^{3}}\)
WILL GIVE BRAINLIEST
Find the value of x in each case:
Step-by-step explanation:
The sum of the interior angles of a triangle is 180:
\(\angle{EAB}+\angle{ABE}+\angle{AEB} = 180\)
\(\Rightarrow 2x + (180 - 4x) + (180 - 6x) = 180\)
\(\Rightarrow 180 - 8x = 0\)
Solving for x,
\(x = 22.5\)
The sum of the interior angles of a quadrilateral is 360:
\(\angle{DAB}+\angle{ADC}+\angle{DCB}+\angle{ABC}= 360\)
\(\Rightarrow 2x+79+32+(360 - 5x) = 360\)
\(\Rightarrow -3x + 111 = 0\)
Solving for x,
\(x = 37\)
15. COSS MODELING The break-even point is the point at which income equals expenses.
Ridgemont High School is paying $13,200 for the writing and research of their
yearbook plus a printing fee of $25 per book. If they sell the books for $40 each,
how many will they have to sell to break even? Explain.
Answer:
Step-by-step explanation:
The break-even point is the point at which income equals expenses.
Let that number of books sold be x
Printing costs = 13200 + 25x
Book sale = 40x
At break-even, the printing costs is the same as book sale.
13200 + 25x = 40x
15x = 13200
x = 13200/15 = 880
Let that be x
\(\\ \rm\Rrightarrow 13200+25x=40x\)
\(\\ \rm\Rrightarrow 40x-25x=13200\)
\(\\ \rm\Rrightarrow 15x=13200\)
\(\\ \rm\Rrightarrow x=13200/15\)
\(\\ \rm\Rrightarrow x=880\)
Lester Hollar is vice president for human resources for a large manufacturing company. In recent years he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months. Below are the results. At the .05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.
Employee Before After
1 6 5
2 6 2
3 7 1
4 7 3
5 4 3
6 3 6
7 5 3
8 6 7
Answer:
t >± 1.895
t= 0.1705
Step-by-step explanation:
The null and alternative hypotheses are
H0: μd=0 Ha: μd>0
Significance level is set at ∝= 0.05
The critical region for t df=7 t >± 1.895
The test statistic under H0 is
t = d/ sd/ √n
Which has t distribution with n-1 degrees of freedom
Employee After Before d = after - before d²
1 6 5 1 1
2 6 2 4 16
3 7 1 6 36
4 7 3 4 16
5 4 3 1 1
6 3 6 -3 9
7 5 3 2 4
8 6 7 -1 1
∑ 14 84
d`= ∑d/n= 14/8= 1.75
sd²= 1/8( 84- 14²/8) = 1/8 ( 84 - 24.5) = 59.5
sd= 7.7136
t= 3/ 7.7136/ √8
t= 0.1705
Since the calculated value of t= 0.1705 < ± 1.895 therefore reject the null hypothesis at 5 % significance level . On the basis of this we cannot conclude that the number of absences has declined.