Answer:
x is 10.66
Step-by-step explanation:
What are complementary angles?
They are angles that up to 90
So we have Sin A and Cos B
4x + 10+ 2x + 16= 90
collect like terms
6x+ 26= 90
6x= 90-26
6x= 64
x= 64/6
x= 10.66
Hence the value of x is 10.66
Answer:
not 10.66
Step-by-step explanation:
Make a substitution to express the integrand as a rational function and then evaluate the integral. int_(25)^(81) sqrt(x)/(x-1) dx
Let y = √x, so that y ² = x and 2y dy = dx. Then the integral becomes
[tex]\displaystyle \int_{25}^{81} \frac{\sqrt x}{x-1}\,\mathrm dx = \int_{\sqrt{25}}^{\sqrt{81}} \frac y{y^2-1}(2y\,\mathrm dy) = 2 \int_5^9 \frac{y^2}{y^2-1}\,\mathrm dy[/tex]
Now,
y ² / (y ² - 1) = 1 + 1 / (y ² - 1) = 1 + 1/2 (1/(y - 1) - 1/(y + 1))
so integrating gives us
[tex]\displaystyle 2\int_5^9\frac{y^2}{y^2-1}\,\mathrm dy= \int_5^9\left(2+\frac1{y-1}-\frac1{y+1}\right)\,\mathrm dy \\\\= (2y+\ln|y-1|-\ln|y+1|)\bigg|_5^9 \\\\= \boxed{8+\ln\left(\dfrac65\right)}[/tex]
the expression when b=3 and y= -3
5b-y
Answer:
18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
b = 3
y = -3
5b - y
Step 2: Evaluate
Substitute in variables: 5(3) - -3Multiply: 15 - - 3Subtract: 18Jessica purchases a kayak in Florida, where the state sales taxes are 6%. She paid $72 in sales tax. What was the retail price of the kayak?
Answer:
72 is 6% of 1200.
Step-by-step explanation:
Multiply 72 by 100.
72*100
Then divide the number by 6
(72*100)/6
You should get 1200.
A cylindrical jug that carries 2ℓ of water when it is filled to the brim has a base surface with a diameter of 8cm. What is the length of the jug in cm, rounded to two decimal places?
Answer:
39.79 cm
Step-by-step explanation:
a few things to make sure :
1 liter = 1 dm³ (a cube of 10cm length of edges) =
= 10×10×10 = 1000 cm³
the volume of a cylinder is
base area × height (or length, as it is called in this question).
and the base area is a circle
area = pi×r²
and r (radius) is half of the diameter.
so, we know r = diameter/2 = 4cm
and the volume is 2 liter = 2 dm³ = 2000 cm³
so, we have
2000 = pi×r² × length = pi×4² × length = pi×16 × length
length = 2000 / (pi × 16) cm = 125 / pi cm =
= 39.79 cm
Can the following two triangles be proven congruent through AAS?
A. Yes, since three pairs of angles are congruent, ∠C≅∠V
∠
C
≅
∠
V
, ∠B≅∠W
∠
B
≅
∠
W
, and ∠A≅∠U
∠
A
≅
∠
U
, the triangles are congruent through AAS.
B.No, since ∠C≅∠V
∠
C
≅
∠
V
, ∠B≅∠W
∠
B
≅
∠
W
, and a pair of included sides are congruent, AC⎯⎯⎯⎯⎯⎯⎯⎯≅UV⎯⎯⎯⎯⎯⎯⎯⎯⎯
A
C
¯
≅
U
V
¯
, the triangles aren’t congruent through AAS.
C.Yes, since two pairs of angles are congruent,∠C≅∠V
∠
C
≅
∠
V
and ∠B≅∠W
∠
B
≅
∠
W
, and a pair of non-included sides are congruent, AC⎯⎯⎯⎯⎯⎯⎯⎯≅UV⎯⎯⎯⎯⎯⎯⎯⎯⎯
AC¯≅UV¯, the triangles are congruent through AAS.
D.No, since only two pairs of angles are congruent, the triangles aren’t congruent through AAS.
Answer:
C. YES
Step-by-step explanation:
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
NEEED HELP FROM BRAINLIEST??????
If the point (1,4) is on the graph of an equation, which statement must be
true?
A. The values x= 1 and y= 4 make the equation true.
B. The values x= 4 and y= 1 make the equation true.
C. The values x= 1 and y= 4 are the only values that make the
equation true.
D. There are solutions to the equation for the values x= 1 and x= 4.
Answer:
A
Step-by-step explanation:
URGENT HELP
Find the points of intersection of the graphs involving the following pair of functions.
f(x)=2x^2 + 3x - 3 and g(x) = -x^2
Answer:
[tex]{ \tt{f(x) = 2 {x}^{2} + 3x - 3 }} \\ { \tt{g(x) = - {x}^{2} }} \\ f(x) + 2 \times g(x) : \\ 0 {x}^{2} + 3x - 3 = 0 \\ x = 1 [/tex]
point's (1, 0)
What is 75% as a fraction
Answer:
[tex]\frac{75}{100}[/tex]
Step-by-step explanation:
Find the missing term in the following pattern.
320, 160, 80 blank space then, 20, 10
40
Step-by-step explanation:
Each number is followed by a number that is half its value, so the sequence goes like
320, 160, 80, 40, 20, 10.
divide 18/7 by 8/26. Pls give the correct ans
Answer:
8.35714285714
Step-by-step explanation:
Hope it help you
Help me plz I can’t figure it out
Answer:
m = 60
Step-by-step explanation:
The context is very important, the 'm' represents the minutes late the parents are and from this we can eliminate some options :
- The last one because then a parent would drop their child off earlier
- The first one and the third one because it is too long
Need help on this problem
Answer:
Step-by-step explanation:
[tex]2(x-2)^2=8(7+y)\\2(x-2)^2=56+8y \Rightarrow y={1\over{8}}[2(x-2)^2-56]={1\over{4}}(x-2)^2-7\\finally\\y={1\over{4}}(x-2)^2-7\\let ~change~x~and~y\\x={1\over{4}}(y-2)^2-7\\x+7={1\over{4}}(y-2)^2\\4(x+7)=(y-2)^2\\y-2=\pm\sqrt{4(x+7)}\\\\y=2\pm\sqrt{4x+28}[/tex]
The cone and the cylinder below have equal surface area. O A. True O B. False
Answer:
the answer is false
Step-by-step explanation:
comment if you want explanation
Answer:
True
Step-by-step explanation:
When using the formulas to find the surface area, both have equal surface area
Mr. Pinter's class has twice as many students as Mrs. Rupert's class. Mrs. Althouse's class has 20 less than three times Mrs. Rupert's class. Together they have 106 students. How many are in each class?
Answer:
Mr. Pinter's class has 42 students, Mrs. Rupert's class has 21 students, and Mrs. Althouse's class has 43 students.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
Mr. Pinter's class has x students.
Mrs. Rupert's class has y students.
Mrs. Althouse's class has z students.
Mr. Pinter's class has twice as many students as Mrs. Rupert's class.
This means that:
[tex]x = 2y[/tex]
Mrs. Althouse's class has 20 less than three times Mrs. Rupert's class.
This means that:
[tex]z = 3y - 20[/tex]
Together they have 106 students.
This means that:
[tex]x + y + z = 106[/tex]
We have x and z has a function of y, so:
[tex]2y + y + 3y - 20 = 106[/tex]
[tex]6y = 126[/tex]
[tex]y = \frac{126}{6}[/tex]
[tex]y = 21[/tex]
And:
[tex]x = 2y = 2(21) = 42[/tex]
[tex]z = 3y - 20 = 3(21) - 20 = 63 - 20 = 43[/tex]
Mr. Pinter's class has 42 students, Mrs. Rupert's class has 21 students, and Mrs. Althouse's class has 43 students.
A telephone exchange operator assumes that 7% of the phone calls are wrong numbers. If the operator is accurate, what is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Answer:
0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A telephone exchange operator assumes that 7% of the phone calls are wrong numbers.
This means that [tex]p = 0.07[/tex]
Sample of 459 phone calls:
This means that [tex]n = 459[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.07[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\sqrt{\frac{0.07*0.93}{459}}} = 0.0119[/tex]
What is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%?
Proportion below 0.07 - 0.03 = 0.04 or above 0.07 + 0.03 = 0.1. Since the normal distribution is symmetric, these probabilities are the same, which means that we find one of them and multiply by 2.
Probability the proportion is below 0.04.
p-value of Z when X = 0.04. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.04 - 0.07}{0.0119}[/tex]
[tex]Z = -2.52[/tex]
[tex]Z = -2.52[/tex] has a p-value of 0.0059
2*0.0059 = 0.0118
0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Use the tangent to find the unknown side lengths.
Answer:
4.076
Step-by-step explanation:
tan27°= |AC|/8
8*tan27°= 4.076
Use the tangent to find the unknown side lengths.
This is the answer
Ac= 4.07
Ab=8.97
A three-dimensional object's measurement(s) include which of the following?
Check all that apply.
A. Width
B. Length
C. Height
D. None of these
Answer:
A.
B.
C.
Step-by-step explanation:
all three are used in 3 dimensional objects hence the name 3 dimensions.
Chris is riding her bike for 10 miles. She averages 12 mi/h. how many more minutes must she ride before she travels 60 miles?
Answer:
5 Minutes
take 10 and add 12 for each minute until you pass 60
Which of the following is a correctly written algebraic equation?
a + 0.2x
5b - 5x + 2
a- 3x = 0
The equation "a - 3x = 0" is correctly written because it follows the standard format of an algebraic equation.
Given that,
All the equations are,
1. a + 0.2x
2. 5b - 5x + 2
3. a - 3x = 0
Now, from equation ''a - 3x = 0'',
In this equation, the variable "a" subtracted from 3 times the variable "x" equals zero.
The equal sign (=) indicates that the expression on both sides of the equation is equivalent.
The equation is properly balanced and expresses equality between the two sides.
It accurately represents a relationship between the variables "a" and "x" where the value of "a" is dependent on the value of "x" in order to satisfy the equation.
So, The correctly written algebraic equation is:
a - 3x = 0
To learn more about the equation visit:
brainly.com/question/28871326
#SPJ4
Plz help I’ll mark you
Answer:
option (B) is the answer
Help please!!!!!!!!!!!
Answer:
AB IS THE ANSWER !!!!!!!!!!
Answer: AB
Step-by-step explanation:
Hi! I don't know if you need help anymore ,but here you go!
Because BC=ED, I asume that AE=AB
You buy a six pack of Gatorade for $9.00. What is the unit price or the price per bottle?
$1.50/bottle
$2/bottle
$1.75 per bottle
Answer:
The answer is $1.50/bottle.
Step-by-step explanation:
To get the unit price, you need to divide the total by the amount of bottles.
[tex]9.00/6=1.50[/tex]
Write the rule that describes the first transformation?
RED —> BLUE
Looking at Point A to A', the rectangle moves 5 places to the left which is the x value + 5 and it shifts 1 place down which would be the y value - 1
This gets written as:
(x+5, y-1)
The following data includes the year, make, model, mileage (in thousands of miles) and asking price (in US dollars) for each of 13 used Honda Odyssey minivans. The data was collected from the Web site.
year make model mileage price
2004 Honda Odyssey EXL 20 26900
2004 Honda Odyssey EX 21 23000
2002 Honda Odyssey 33 17500
2002 Honda Odyssey 41 18999
2001 Honda Odyssey EX 43 17200
2001 Honda Odyssey EX 67 18995
2000 Honda Odyssey LX 46 13900
Required:
Compute the correlation between age (in years) and price for these minivans.
Find complete data below :
Answer:
R = - 0.94
Step-by-step explanation:
Since data was collected in 2005 ; we subtract the data collection year from the make year to obtain the age :
Age (x) :
1,1, 3,3,4,4,5,5,5,5,6,7,10
Price (y) :
26900,23000,17500,18999,17200,18995,13900,15250,13200,11000,13900,8350,5800
Using technology, the correlation Coefficient between age of car and price is : - 0.94
With a correlation Coefficient of - 0.94, we can conclude that there exists a strong negative correlation between age and price of the Odyssey mini vans. This could be interpreted to mean that ; As the age of cars in increases, the price decreases
What is the following product?
(Xv7-3v8)(xv7-3v8)
Answer:
B
Step-by-step explanation:
I'm not really sure tho
Please help me with solving these. I’d really appreciate your help. Thank you very much.
Answer:
Problem 17)
[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]
Problem 18)
[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]
Step-by-step explanation:
Problem 17)
We have the curve represented by the equation:
[tex]\displaystyle 4x^2+2xy+y^2=7[/tex]
And we want to find the equation of the tangent line to the point (1, 1).
First, let's find the derivative dy/dx. Take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\left[4x^2+2xy+y^2\right]=\frac{d}{dx}[7][/tex]
Simplify. Recall that the derivative of a constant is zero.
[tex]\displaystyle \frac{d}{dx}[4x^2]+\frac{d}{dx}[2xy]+\frac{d}{dx}[y^2]=0[/tex]
Differentiate. We can differentiate the first term normally. The second term will require the product rule. Hence:
[tex]\displaystyle 8x+\left(2y+2x\frac{dy}{dx}\right)+2y\frac{dy}{dx}=0[/tex]
Rewrite:
[tex]\displaystyle \frac{dy}{dx}\left(2x+2y\right)=-8x-2y[/tex]
Therefore:
[tex]\displaystyle \frac{dy}{dx}=\frac{-8x-2y}{2x+2y}=-\frac{4x+y}{x+y}[/tex]
So, the slope of the tangent line at the point (1, 1) is:
[tex]\displaystyle \frac{dy}{dx}\Big|_{(1, 1)}=-\frac{4(1)+(1)}{(1)+(1)}=-\frac{5}{2}[/tex]
And since we know that it passes through the point (1, 1), by the point-slope form:
[tex]\displaystyle y-1=-\frac{5}{2}(x-1)[/tex]
If desired, we can simplify this into slope-intercept form. Therefore, our equation is:
[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]
Problem 18)
We have the equation:
[tex]\displaystyle y=\tan^{-1}\left(x^3\right)[/tex]
And we want to find the equation of the tangent line to the graph at the point (1, π/4).
Take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{dy}{dx}=\frac{d}{dx}\left[\tan^{-1}(x^3)][/tex]
We can use the chain rule:
[tex]\displaystyle \frac{d}{dx}[u(v(x))]=u'(v(x))\cdot v(x)[/tex]
Let u(x) = tan⁻¹(x) and let v(x) = x³. Thus:
(Recall that d/dx [arctan(x)] = 1 / (1 + x²).)
[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2[/tex]
Substitute and simplify. Hence:
[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2=\frac{3x^2}{1+x^6}[/tex]
Then the slope of the tangent line at the point (1, π/4) is:
[tex]\displaystyle \frac{dy}{dx}\Big|_{x=1}=\frac{3(1)^2}{1+(1)^6}=\frac{3}{2}[/tex]
Then by the point-slope form:
[tex]\displaystyle y-\frac{\pi}{4}=\frac{3}{2}(x-1)[/tex]
Or in slope-intercept form:
[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]
Last year, each Capulet wrote 4 essays, each Montague wrote 6 essays, and both families wrote 100 essays in total.
This year, each Capulet wrote 8 essays, each Montague wrote 12 essays, and both families wrote 200 essays in total.
How many Capulets and Montagues are there?
Choose 1 answer:
A: There is not enough information to determine the exact number of Capulets and Montagues.
B: The given information describes an impossible situation.
C: There are 16 Capulets and 6 Montagues.
D: There are 6 Capulets and 16 Montagues
Answer: There are 16 Capulets and 6 Montaques.
Step-by-step explanation:Other choices were either less than or greater than 200 multiplied by each other. If we do 16x8 which is 128 for the Capulets. Also, if we do 12x6 which is 72 for the Montaques. 128+72=200 essays in total
A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 3% margin of error at a 99% confidence level, what size of sample is needed
Answer:
1849
Step-by-step explanation:
Margin of error, E=0.03
Confidence level=0.99
z=2.58
No prior estimate of p is given, so consider p=0.5
Sample size required ,n=2.58^2*0.5*(1-0.5)/0.03^2
n=1849
what is the measure of an angle if it is 120 less than 5 times its own complement
Answer:
The measure of the angle is 55º.
Step-by-step explanation:
Complement of angle x:
If two angles are complementary, the sum of their measures is of 90º. Thus, the complement of an angle x is 90 - x.
In this question:
Angle is 120 less than 5 times its own complement, so:
[tex]x = 5(90 - x) - 120[/tex]
We have to solve for x
[tex]x = 450 - 5x - 120[/tex]
[tex]6x = 330[/tex]
[tex]x = \frac{330}{6}[/tex]
[tex]x = 55[/tex]
The measure of the angle is 55º.
The sum of three numbers is 3. The first number minus the second plus the third is -3. The first minus the third is 1 more than the second.
Find the numbers. What is the first number? What is the second number? What is the third number?
Answer: The first number is 2, the second number is 3 and the third number is -2
Step-by-step explanation:
Let the first number be 'x', the second number be 'y' and the third number be 'z'
The equations according to the question becomes:
⇒ x + y + z = 3 ....(1)
⇒ x - y + z = -3 ....(2)
⇒ x - z = 1 + y ....(3)
Rearranging equation 3:
⇒ x - y = 1 + z .....(4)
Putting in equation 2:
⇒ 1 + z + z = -3
⇒ 1 + 2z = -3
⇒ z = -2
Putting this value in equation 4 and equation 1, we get:
⇒ x - y = -1
⇒ x + y = 5
Cancelling 'y' by eliminiation method and equation becomes:
⇒ 2x = 4
⇒ x = 2
Putting value of 'x' and 'z' in equation 1:
⇒ 2 + y - 2 = 3
⇒ y = 3
Hence, the first number is 2, the second number is 3 and the third number is -2