Step-by-step explanation:
( secA + 1)( sec A - 1)
Using the expansion
( a + b)( a - b) = a² - b²
Expand the expression
We have
sec²A + secA - secA - 1
That's
sec² A - 1
From trigonometric identities
sec²A - 1 = tan ²ASo we have the final answer as
tan²AAs proven
Hope this helps you
Step-by-step explanation:
Here,
LHS
= (SecA+1)(secA -1)
[tex] = {sec}^{2} A - 1[/tex]
[tex]{as{a}^{2} - {b}^{2} =(a + b)(a - b)[/tex]
Now, we have formula that:
[tex] {sec}^{2} \alpha - {tan \alpha }^{2} = 1[/tex]
[tex] {tan}^{2} \alpha = {sec }^{2} \alpha - 1[/tex]
as we got ,
[tex] = {sec}^{2} A- 1[/tex]
This is equal to:
[tex] = {tan}^{2} A[/tex]
= RHS proved.
Hope it helps....
As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?
Answer:
154.2
Step-by-step explanation:
143 plus
156 plus
172 plus
133 plus
167 = 771
divide by 5 equals 154.2
Consider the polynomial 2x5 + 4x3 - 3x8
Part A The polynomial in standard form is:
Part B: The degree of the polynomial is:
Part C: The number of terms in the polynomial is:
Part D: The leading term of the polynomials:
Part E: The leading coefficient of the polynomial is:
Answer:
Step-by-step explanation:
Considering the polynomial 2x⁵ + 4x³ - 3x⁸. The polynomial is not yet in standard form. For a polynomial to be in standard form, the power of the variables must decrease as we progress to the right of the expression.
A) The polynomial in standard form is therefore - 3x⁸ + 2x⁵ + 4x³. We can see that the power are reducing as we move through each terms i.e from 8 to 5 then to 3.
B) The degree of a polynomial is the maximum degree among all the terms of the polynomial. The term that has the maximum degree is -3x⁸. Hence, the degree of the polynomial is 8
C) There are only 3 terms in the polynomial given. The terms are separated by mathematical signs. The terms if the polynomial are 2x⁵, 4x³ and - 3x⁸.
D) The leading term of the polynomial is the term that comes first after rewriting the polynomial in standard format. Given the standard from of the polynomial given as -3x⁸ + 2x⁵ + 4x³, the leading term will be - 3x⁸
E) Given the leading term to be - 3x⁸, the leading coefficient of the polynomial will be the coefficient of the leading term. The coefficient of -3x⁸ is -3
se pueden calcular las edades de Juanita y de su madre si se sabe que:
1) actualmente la suma de sus edades es 44 años
2) dentro de 11 años la edad de juanita será la mitad de la edad de su mamá
Responder:
Juanita = 11, madre = 33
Explicación paso a paso:
Dado lo siguiente:
Suma de sus edades = 44
En 11 años, Juanita tendrá la mitad de la edad de su madre
Sea la edad de la madre = my la edad de juanita = j
m + j = 44 - - - - (1)
(j + 11) = 1/2 (m + 11)
j + 11 = 1/2 m + 5,5; j - 1/2 m = - 5,5; 2j - m = - 11
2j - m = - 11 - - - - (2)
Desde (1): m = 44 - j
Sustituyendo m = 44- j en (2)
2j - (44 - j) = - 11
2j - 44 + j = - 11
3j = - 11 + 44
3j = 33
j = 11
De 1)
m + j = 44
m + 11 = 44
m = 44 - 11
m = 33
Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers (k)left parenthesis, k, right parenthesis she can drive with 12 liters of fuel. She assumes the relationship between kilometers and fuel is proportional.
How many kilometers can Pamela drive with 12 liters of fuel?
Answer:
132 kilo meters
Step-by-step explanation:
Pro por tions:
9 lite rs ⇒ 99 km
12 lite rs ⇒ P km
P = 99*12/9
P = 132 km
Answer:
132
Step-by-step explanation:
give person above brainliest :))
Your friend Stacy has given you the following algebraic expression: "Subtract 20
times a number n from twice the cube of the number. What is the expression that your
friend is saying?
Answer:
Expression = 2n³ - 20n
Step-by-step explanation:
Find:
Expression
Computation:
Assume given number is 'n'
Cube of number = n³
Twice of cube = 2n³
Subtract number = 20n
Expression = 2n³ - 20n
the terms in this sequence increase by the same amount each time. _19_ _ 34_ a) work out the missing terms.
Answer:
The sequence is 14, 19, 24, 29, 34, 39.
Step-by-step explanation:
Let's call the common difference (the difference between two consecutive terms) as d. We see that the second term is 19 and the 5th term is 34 and since 5 - 2 = 3, we add d 3 times to 19 to get 34 so therefore:
19 + 3d = 34
3d = 15
d = 5 so the first term is 19 - 5 = 14, the third would be 19 + 5 = 24, the fourth would be 24 + 5 = 29 and the sixth would be 34 + 5 = 39.
What is the slope of the line showed?
Answer:
2
Step-by-step explanation:
The formula for the slope of a line is rise over run. We know that the slope of the line will be positive because the line is going up from left to right.
Rise is the change on the y-axis, going up and down. Run is the change on the x-axis, going from left to right.
Let's start from the origin (0,0). To reach the next point on the line, we have to go up two points (rise) and over one point (run).
Slope = rise/run
Slope = 2/1
Slope = 2
Hope that helps.
Answer:
slope=2
Step-by-step explanation:
take two points from graph (0,0) and (1,2)
m=y2-y1/x2-x1
m=2-0/1-0
m=2
Subtract 750 -389 plzzz help
A certain dataset of systolic blood pressure measurements has a mean of 80 and a standard deviation of 3. Assuming the distribution is bell-shaped and we randomly select a measurement:
a) What percentage of measurements are between 71 and 89?
b) What is the probability a person's blood systolic pressure measures more than 89?
c) What is the probability a person's blood systolic pressure being at most 75?
d) We should expect 15% of patients have a blood pressure below what measurement?
e) Would it be unusual for 3 patients to have a mean blood pressure measurement of more than 84? Explain.
Answer:
Explained below.
Step-by-step explanation:
Let X = systolic blood pressure measurements.
It is provided that, [tex]X\sim N(\mu=80,\sigma^{2}=3^{2})[/tex].
(a)
Compute the percentage of measurements that are between 71 and 89 as follows:
[tex]P(71<X<89)=P(\frac{71-80}{3}<\frac{X-\mu}{\sigma}<\frac{89-80}{3})[/tex]
[tex]=P(-3<Z<3)\\=P(Z<3)-P(Z<-3)\\=0.99865-0.00135\\=0.9973[/tex]
The percentage is, 0.9973 × 100 = 99.73%.
Thus, the percentage of measurements that are between 71 and 89 is 99.73%.
(b)
Compute the probability that a person's blood systolic pressure measures more than 89 as follows:
[tex]P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})[/tex]
[tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]
Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.
(c)
Compute the probability that a person's blood systolic pressure being at most 75 as follows:
Apply continuity correction:
[tex]P(X\leq 75)=P(X<75-0.5)[/tex]
[tex]=P(X<74.5)\\\\=P(\frac{X-\mu}{\sigma}<\frac{74.5-80}{3})\\\\=P(Z<-1.83)\\\\=0.03362\\\\\approx 0.034[/tex]
Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.
(d)
Let x be the blood pressure required.
Then,
P (X < x) = 0.15
⇒ P (Z < z) = 0.15
⇒ z = -1.04
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9[/tex]
Thus, the 15% of patients are expected to have a blood pressure below 76.9.
(e)
A z-score more than 2 or less than -2 are considered as unusual.
Compute the z score for [tex]\bar x[/tex] as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{84-80}{3/\sqrt{3}}\\\\=2.31[/tex]
The z-score for the mean blood pressure measurement of 3 patients is more than 2.
Thus, it would be unusual.
An evergreen nursery usually sells a certain shrub after 9 years of growth and shaping. The growth rate during those 9 years is approximated by
dh/dt = 1.8t + 3,
where t is the time (in years) and h is the height (in centimeters). The seedlings are 10 centimeters tall when planted (t = 0).
(a) Find the height after t years.
h(t) =
(b) How tall are the shrubs when they are sold?
cm
Answer:
(a) After t years, the height is
18t² + 3t + 10
(b) The shrubs are847 cm tall when they are sold.
Step-by-step explanation:
Given growth rate
dh/dt = 1.8t + 3
dh = (18t + 3)dt
Integrating this, we have
h = 18t² + 3t + C
When t = 0, h = 10cm
Then
10 = C
So
(a) h = 18t² + 3t + 10
(b) Because they are sold after every 9 years, then at t = 9
h = 18(9)² + 3(9) + 10
= 810 + 27 + 10
= 847 cm
Mary subscribed to a cell phone plan with a $50 monthly fee and a charge of $0.25 for each minute she talks. Find an equation for the total cost for her plan when she uses minutes.
Answer:
c = 0.25m + 50
Step-by-step explanation:
Let c = cost; let m = number of minutes.
c = 0.25m + 50
Factorise the following using the Difference of Two Squares or Perfect Squares rule: a) (2x-2)^2 - (x+4)^2 b) (3x+4) (3x-4)
Answer:
Step-by-step explanation:
Hello, please consider the following.
a)
[tex](2x-2)^2 - (x+4)^2 \\\\=(2x-2-(x+4))(2x-2+x+4)\\\\=(2x-2-x-4)(3x+2)\\\\=\boxed{(x-6)(3x+2)}[/tex]
b)
[tex](3x+4) (3x-4)\\\\=(3x)^2-4^2\\\\=\boxed{9x^2-16}[/tex]
Thank you.
When all possible differences between pairs of population means are evaluated not with an F test, but with a series of regular t tests, the probability of at least one:
Answer:
When all possible differences between pairs of population means are evaluated not with an F test, but with a series of regular t tests, the probability of at least one:
A. type I error is larger than the specified level of significance.
B. type II error is larger than the specified level of significance.
C. type I error is smaller than the specified level of significance.
D. type II error is smaller than the specified level of significance.
Answer : Type I error is larger than the specified level of significance.( A )
Step-by-step explanation:
An F test is a test that is used to test whether the variances between pairs of populations are equal while a T test is a test used to check if a pair of population are equal not considering the fact that the variances of the population are different .
When a T test is used to evaluate all possible differences between pairs of population instead of F test there is a probability of atleast one type 1 error larger than the specified level of significance.
Consider the function f(x) = (x − 3)2(x + 2)2(x − 1). The zero has a multiplicity of 1. The zero −2 has a multiplicity of .
Answer:
The zero 1 has a multiplicity of 1.
The zero -2 has a multiplicity of 2.
Hope this clears up any confusion :)
Step-by-step explanation:
Answer:
The zero 1 has a multiplicity of 1.
The zero −2 has a multiplicity of 2 .
Step-by-step explanation:
Jayden, who burns 345 calories in 45 min
while hiking is preparing for a 6 hour hike.
He uses a special supplement beverage
pack that provides water, needed
electrolytes, and 310 calories. The goal is to
replace roughly 1/3 of the calories burned
while carrying as light a load as possible.
How many packs should he take?
This question is solved using proportions.
First, we find how many calories he will burn in the hike.Then, we find how many calories he will need to replace, and the number of packs needed.Doing this, we get that he should take 3 packs.
How many calories he burns in the hike?
In 45 minutes, he burns 345 calories. How many calories in 6*60 = 360 minutes?
45 minutes - 345 calories
360 minutes - x calories
Applying cross multiplication:
[tex]45x = 345*360[/tex]
[tex]x = \frac{345*360}{45}[/tex]
[tex]x = 2760[/tex]
He burns 2760 calories in the hike.
How many calories he wants to replace?
Roughly 1/3, so he have to find one third of 2760, that is:
[tex]\frac{2760}{3} = 920[/tex]
How many packs?
One pack recovers 310 calories, how many packs for 920 calories?
1 pack - 310 calories
x packs - 920 calories
Applying cross multiplication:
[tex]310x = 920[/tex]
[tex]x = \frac{920}{310}[/tex]
[tex]x = 2.97[/tex]
Rounding up, he should take 3 packs.
A similar question is found at https://brainly.com/question/14426926
9. Find the mean of the following data :
Х
8
10
12
20
16
F
2
3
7
2
5
Answer:
[tex] \boxed{13.15}[/tex]Step-by-step explanation:
( See the attached picture )
Now,
Mean = [tex] \mathsf{\frac{Σfx}{n} }[/tex]
[tex] \mathsf{ = \frac{250}{19} }[/tex]
[tex] \mathsf{ = 13.15}[/tex]
------------------------------------------------------------------------
In the case of repeated data , follow the steps given below to calculate the mean :
Draw a table with 3 columnsWrite down the items ( x ) in ascending or descending order in the first column and the corresponding frequencies in the second column.Find the product of each item and it's frequency ( fx ) and write in the third column.Find the total of f column and fx column.Divide the sum of fx by the sum of f ( total number of items ) , the quotient is the required mean.Hope I helped!
Best regards!
what are the comparison symbols for 5/6 and 2/5, 4/10 and 7/8, and 3/12 and 1/4
Answer like this: Example
=
<
>
Answer:
5/6 > 2/44/10 < 7/83/12 = 1/4Step-by-step explanation:
The comparison will be the same if you subtract the right side and compare to zero:
a/b ?? c/d . . . . . . . using ?? for the unknown comparison symbol
a/b - c/d ?? 0 . . . . subtract the fraction on the right
(ad -bc)/bd ?? 0 . . . combine the two fractions
ad - bc ?? 0 . . . . . . multiply by bd to make the job easier
__
5/6 and 2/5
5(5) -6(2) = 25 -12 > 0 ⇒ 5/6 > 2/5
4/10 and 7/8
4(8) -10(7) = 48 - 70 < 0 ⇒ 4/10 < 7/8
3/12 and 1/4
3(4) -12(1) = 0 ⇒ 3/12 = 1/4
_____
Of course, you can use your calculator (or your memory) to change each of these to a decimal equivalent. The comparison should be easy at that point.
0.833 > 0.400
0.400 < 0.875
0.250 = 0.250
The range of values for x?
Answer:
x = 32
but
I would say anything from 30 to 33
but truly i have no clue about the range
Step-by-step explanation:
3x-9=87 (because 180 -93 =87)
3x = 96
x = 32
Answer:
it is 32
Step-by-step explanation:
can you please help ?
Answer:
69
Step-by-step explanation:
The order of operations is PEMDAS; parentheses, exponents, multiplication and division, and finally addition and subtraction.
We know that x is the first row, and if there are 30 spots in the first row, then x=30. Using this information, all we have to do now is plug in 30 for x and solve.
[tex]\frac{5(x)}{2} -6[/tex]
[tex]\frac{5(30)}{2}-6[/tex]
[tex]\frac{150}{2}-6[/tex]
[tex]75-6[/tex]
[tex]69[/tex]
How would the margin of error change if the sample size increased from 200 to 400 students? Assume that the proportion of students who say yes does not change significantly.
Answer:
(MOE) the Margin of Error will decrease by the square root of 2
Step-by-step explanation:
The Margin of Error (MOE) is an inverse function of sample size n ( more precisely of the square root of sample size ). That relation means changes in sample size ( keeping constant other variables of the distribution) will imply opposite changes in the Margin of Error. If we double the sample size increasing it from 200 up to 400, the Margin of Error will decrease by the square root of 2
You catch an expected number of 1.51.5 fish per hour. You can catch a fish at any instant of time. Which distribution best characterizes the number of fish you catch in one hour of fishing
Answer:
The distribution is Poisson distribution
Step-by-step explanation:
From the question we are told that
An expected number of fish was caught per hour is 1.5
The distribution that best characterize the number of fish you catch in one hour of fishing is the Poisson distribution
This because generally the Poisson distribution is a distribution that shows the number of times a given event will occur within a defined period of time
Can someone help??????????
Answer:
(C) 1 and 3
Step-by-step explanation:
Corresponding angles are angles that are at the same corner at the different intersections.
We can see that 1 is on the bottom right corner of the bottom line, now we need to see what angle is at the bottom right corner of the top line?
That's 3.
So 1 and 3 are congruent because they are corresponding.
Hope this helped!
6x - 10 = 4(x + 3) x = ? x = 9 x = 10 x = 11 x = 12
Answer:
x=11
Step-by-step explanation:
Answer:
x = 11
Step-by-step explanation:
6x - 10 = 4(x+3)
6x - 10 = 4*x + 4*3
6x - 10 = 4x + 12
6x - 4x = 12 + 10
2x = 22
x = 22/2
x = 11
check:
6*11 - 10 = 4(11+3)
66 - 10 = 4*14 = 56
Does coordinate x or coordinate y represent a greater number?
Answer:
Y
Step-by-step explanation:
You see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.
Y represents the greater number.
We see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.
What is an example of a coordinate?A set of values that display an actual role. On graphs it is also a pair of numbers: the first variety indicates the gap along, and the second variety indicates the distance up or down. As an example, the factor (12,5) is 12 units long, and five units up.
Learn more about coordinate here: https://brainly.com/question/11337174
#SPJ2
Complete each ordered pair so that it is a solution of the given linear equation.
x - 4y = 4; (_,3), (4,_)
Answer: (16,3) and (4,0)
Step-by-step explanation:
Using the equation x-4y=4 is asking what is the value of x if the value of y is 3. So plot it into the equation and solve for x.
x-4(3)=4 multiply the left side
x - 12 = 4 add 12 to both sides
x= 16
You will now have the coordinates (16,3)
In the second pair it gives the x coordinate which is 4 but we need to solve for y.
4 - 4y=4 subtract 4 from both sides
-4 -4
-4y = 0 Divide both sides by 4
y = 0
The ordered pair will be (4,0)
PLEASE HELPPPP
A standard I.Q. test produces normally distributed results with a mean of 100 and a standard deviation of 15 for the city of New York. Out of approximately 8,400,000 citizens, how many of these people would have I.Q.s below 67?
Answer:
approx 193200
Step-by-step explanation:
As known for normal distribution is correct the rule 95.4% of the results are situation within mean+-2*s ( where s is a standard deviation)
So the border is 100+-2*15=70 and that is approx=67.
95.4% of 84000000 citizens are= 8 400 000*0.954=8013600 persons
So the residual number of the citizens =8400000-8013600=386400 citizens
Because of the simmetry of normal distribution to find the number of the citizens that have IQ below 67 we have to divide 386400 by 2.
N=386000/2=193200
The graph shown below expresses a radical function that can be written in the form f(x)=a(x+k)^1/n + c. What does the graph tell you about the value of n in this function?
Answer: n is a positive odd number.
Step-by-step explanation:
Ok, we know that the function is something like:
f(x)=a(x+k)^1/n + c
In the graph we can see two thigns:
All the values of the graph are positive values (even for the negative values of x), but in the left side we can see that the function decreases and is different than the right side.
So this is not an even function, then n must be an odd number (n odd allows us to have negative values for y = f(x) that happen when x + k is negative).
Also, we can see that the function increases, if n was a negative number, like: n = -N
we would have:
[tex]f(x) = \frac{a}{(x+k)^{1/N}} + c[/tex]
So in this case x is in the denominator, so as x increases, we would see that the value of y decreases, but that does not happen, so we can conclude that the value of n must be positive.
Then n is a positive odd number.
Answer:
D) Positive Even Integer
Step-by-step explanation:
just did it
for the first one the answer are
add 5 to both sides
subtract 5 from both sides
add 1/2x to both sides
subtract 1/2 from both sides
the second one is
multiply both sides by 1/5
dived both sides by 1/5
multiply both sides by 6/7
dived both sides by 6/7
Answer:
1. add 1/2x to both sides
a. you want to combine the like terms. in this case, it is the x variable.
you are left with 7/6x = 5
2. multiply by 6/7
a. the reciprocal of 7/6 will cancel out the values
The numbers 1,2,3,4,5,6,7,8,9. How would you put them in each of a square block to create the sum on each line to make the number 15. The sum of each diagonals should also be 15.
Answer:
Here's one way:
4 9 2
3 5 7
8 1 6
Step-by-step explanation:
LOOK AT CAPTURE AND ASNWER 100 POINTS
Answer:
132 degrees
Step-by-step explanation:
Looking at angle A and angle B, they are alternate interior angles. That means they are congruent to one another. Knowing that, we can set up an equation A=B
We can now fill A and B with their given equations
5x-18=3x+42
Now we solve
2x=60
x=30
Now that we know x is 30, we can replace it in the equation for A
5x-18
5(30)-18
150-18
132 degrees
Answer:
132
Step-by-step explanation:
ANGLE A = ANGLE B
(INTERIOR ALTERNATE ANGLES)
5x - 18 = 3x + 42
2x = 60
x = 30
angle a = 150 - 18
= 132
