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....
The average age of a part-time seasonal employee at a Vail Resorts ski mountain has historically been 37 years. A random sample of 50 part-time seasonal employees in 2010 had a mean of 38.5 years with a standard deviation of 16 years. Required:a. At the 5 percent level of significance, does this sample show that the average age was different in 2010? b. Which is the right hypotheses to test the statement?c. What are the test statistic and critical value?
Answer:
No the sample does not show that the average age was different in 2010
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The sample mean is [tex]\= x = 38.5[/tex]
The population mean is [tex]\mu = 37[/tex]
The standard deviation is [tex]\sigma = 16[/tex]
The level of significance is [tex]\alpha = 5 \% = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 37[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 37[/tex]
The critical value of the level of significance obtained from the normal distribution table is ([tex]Z_{\alpha } = 1.645[/tex] )
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 38.5 - 37}{ \frac{16}{\sqrt{50} } }[/tex]
[tex]t = 0.663[/tex]
Now looking at the value t and [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis.
This mean that there is no sufficient evidence to state that the sample shows that the average age was different in 2010
Un taxímetro inicia con 50 unidades y el banderazo o arranque es de $4500, las unidades comienzan a cambiar p0r cada kilometros recorrido. La función lineal que representa esta situación es y = 50x +4500 donde y representa el precio que cuesta la carrera y x la distancia recorrida en kilómetros. a) ¿ Cuanto cuesta una carrera si la distancia recorrida fue de 23 kilómetros?
Answer: $5650
Step-by-step explanation:
El precio de la carrera es:
y = ($50/km)*x + $4500.
Donde x representa la cantidad recorrida en Km.
Ahora se nos pregunta:
¿ Cuanto cuesta una carrera si la distancia recorrida fue de 23 kilómetros?
Para esto, debemos reemplazar la variable en la equacion por 23km:
x = 23km
y = ($50/km)*23km + $4500 = $5650
I tried something similar to the notation of (x+2)^7, etc, did not get close at all, how would this be solved?
[tex] 24 = 3 \cdot 2^3 [/tex]
[tex]96=3\cdot 2^5 [/tex]
[tex] 384=3\cdot2^7[/tex]
hence it is a geometric progression, with a multiplied constant [tex]3[/tex]
Sum of G.P. of [tex]n[/tex] terms [tex] S_n = a\dfrac{r^n-1}{r-1}\quad \text{where } r \text{ is the common ratio and } a \text{ is the first term} [/tex]
and [tex] r=-2^2=-4[/tex]
Note that the constant should be separated, so
[tex] a= -8 [\tex]
after plugging the values, you'll get the answer
[tex] -26216 \times 3 [/tex]
which option C
Answer:
C
Step-by-step explanation:
-24+96-384+...
a=-24
r=96/(-24)=-4
[tex]s_{7}=a\frac{1-r^7}{1-r} \\=-24\frac{1-(-4)^7}{1-(-4)}\\=-24\frac{1+4^7}{1+4} \\=-24\frac{1+16384}{5} \\=-24\frac{16385}{5} \\=-24 \times 3277\\=-78648[/tex]
Need Help
Please Show Work
Answer:
1= 65 degrees
2=115 degrees
3=115 degrees
Step-by-step explanation: supplementary angles where 115 + x = 180 so go backwards by 180 - 115=65 to find corresponding angles. Angle 3 is also corresponding with the given angle of 115. Angle 2 is opposite the 115 so they have to be equal
Armando is baking 36 batches of brownies for the bake sale. Each batch of brownies takes cups of flour. What is a reasonable estimate of the amount of flour that he will need to bake all thirty-six batches of brownies?
Answer:
Well, let's assume that "cups" = 3 cups of flour.
Step-by-step explanation:
First, multiply 3x36.
If for some reason this is incorrect, try 2 cups instead of 3. Both are reasonable measurements when it comes to baking.
A detective knows what time of day it is based on the angle at which the sun is hitting a man. Suppose a detective is looking at a photograph of a 6-foot tall man with a shadow that is 3.5 feet. Find the angle at which the sun is hitting the ground.
Answer:
The angle [tex]\theta[/tex] at which the sun is hitting the ground is:
[tex]\theta\approx 59.74^o[/tex]
Step-by-step explanation:
You can use right angle trigonometry to solve this, since the man (6 ft tall) and the shadow on the ground (3.5 ft long) form a right angle triangle as shown on the attached image.
The use the tangent function to find the angle that the sun's rays make with the ground:
[tex]tan(\theta)=\frac{opposite}{adjacent} \\tan(\theta)=\frac{6}{3.5} \\\theta=arctan(\frac{6}{3.5})\\\theta\approx 59.74^o[/tex]
1) Find the volume and surface area of the composite figure below
2) Find the surface area of the composite figure below
1.
[tex]volume = 64(21 + 4\pi) = 2148.5714 \: cubic \: feets[/tex]
[tex]surface \: area = 752 + 64\pi = 953.143 \: square \: feets[/tex]
2.
[tex]surface \: area = 220 + 9\pi = 248.257 \: square \: feets[/tex]
What is 9.3 to the 8th power
Answer: 55958180.97
Step-by-step explanation:
9.3 x 9.3 x 9.3 x 9.3 x 9.3 x 9.3 x 9.3 x 9.3
86.49 x 86.49 x 86.49 x 86.49
= 55958180.97
In hypothesis testing, does choosing between the critical value method or the P-value method affect your conclusion? Explain.
Answer:
The correct answer is No.
Choosing between the critical value method or the P-value method does not affect one's conclusion because both methods look at the probability of the test statistic's and its level of significance .
Given the methodology utilized by both methods, they usually arrive at the same conclusion.
Cheers!
Translate this sentence into a equation. 42 decreased by Jose’s savings is 16. Use the variable j to represent Jose’s savings.
Answer:
[tex]42-j=16[/tex]
Step-by-step explanation:
"Decreased by" means subtraction.
The information says 42 decreased "by Jose's savings", which is represented by j.
"Is" means equal to.
Put it all together:
[tex]42-j=16[/tex]
:Done
Answer:
j - 42 = 16
Step-by-step explanation:
J = Jose Savings
42 = the amount decreased
16 = the left amount
J-42 = 16
j = 16+42
J = 58
Jose's savings was $58.
I’m struggling to understand this problem somebody please explain it to me thanks!!
ax-5d=3cx-2+7
Answer:
x = (5 +5d)/(a -3c)
Step-by-step explanation:
Maybe you're to solve for x.
__
This is a typical "3-step" linear equation.
First, you collect terms with the variable x on one side of the equation. You do that by subtracting from both sides the x-term you don't want where it is.
We choose to remove the 3cx term from the right side, so we subtract it from both sides.
ax -3cx -5d = 3cx -3cx +5 . . . . . . we have combined the constants, too
x(a -3c) -5d = 5 . . . . . . simplify and factor out x
Second, you remove any terms not containing x from the side of the equation with the x-terms. You do that by adding their opposite to both sides of the equation.
We need to remove the -5d term, so we add 5d to both sides.
x(a -3c) -5d +5d = 5 +5d
x(a -3c) = 5 +5d . . . . . . . . . . simplify
Third, we divide by the coefficient of x. We do that to both sides of the equation. We had to put parentheses around the terms on the right, because we're dividing the whole right side of the equation by (a-3c).
x(a -3c)/(a -3c) = (5 +5d)/(a -3c)
x = (5 +5d)/(a -3c)
PLEASE ANSWER ASAP!!!
Answer options given in picture
Michael can skateboard 100 feet in 5.4 seconds. Which choice below shows how fast Micheal is going miles per 1 hour? Remember that since you are using multiplication to make conversions, you need to set up the units diagonal from each other in order to cancel.
any unrelated answer will be reported
Answer:
A
Step-by-step explanation:
Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5 cups of sugar, and the brownie recipe requires 1.25 cups of sugar. Write an addition equation to represent the total amount of sugar Dante needs.
Answer: 1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar for both recipes.
Step-by-step explanation:
Dante is baking two recipes.
A cookie recipe, that needs 1.5 cups of sugar.
A brownie recipe, that needs 1.25 cups of sugar.
So the total sugar that he needs is:
The sugar for the cookies + the sugar for the brownies:
The equation is:
1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar.
A normal population has a mean of 65 and a standard deviation of 13. You select a random sample of 25. Compute the probability that the sample mean is: (Round your z values to 2 decimal places and final answers to 4 decimal places): Greater than 69.
Answer:
0.0618
Step-by-step explanation:
z = (x - μ)/σ, where
x is the raw score = 69
μ is the sample mean = population mean = 65
σ is the sample standard deviation
This is calculated as:
= Population standard deviation/√n
Where n = number of samples = 25
σ = 13/√25
σ = 13/5 = 2.6
Sample standard deviation = 2.6
z = (69 - 65) / 2.6
z = 4/2.6
z = 1.53846
Approximately to 2 decimal places = 1.54
Using the z score table to determine the probability,
P(x = 69) = P(z = 1.54)
= 0.93822.
The probability that the sample mean is greater than 69 is
P(x>Z) = 1 - 0.93822
P(x>Z) = 0.06178
Approximately to 4 decimal places = 0.0618
Find the value of x show your work
Answer:
x≈13.08
Step-by-step explanation:
We use the pythagora's theorem
[tex]a^{2} +b^2=c^2\\a=5\\b=x\\c=14\\5^2+x^2=14^2\\x^2=196-25\\x^2=171\\x=3\sqrt{19} =13.08[/tex]
Prove that if n is an integer, these four statements are equivalent: (i) n is even, (ii) n 1 is odd, (iii) 3n 1 is odd, (iv) 3n is even.
Answer:
Step-by-step explanation:
Hello,
If n is even, it means that we can find k integer such that n = 2 * k.
Then n+1=2*k+1 is odd.
3n+1=6k+1=2*(3k)+1 where 3k is an integer so 3n+1 is odd.
3n = 2*(3k) is even.
Besides, if n+1 is odd we can find an integer p so that n+1=2p+1 so n = 2p is even.
3n+1 is odd means that we can find an integer q such that 3n+1=2q+1 so 3n=2q as 3 is not dividable by 2, it means that n is a multiple of 2, then n is even.
3n is even means that we can write 3n = 2z where z is an integer and again it means that n is a multiple of 2 and then n is even.
Thank you.
can you help me with this homework please?
Answer:
hey I was wondering if you still needed help?
Help with a problem again please
Answer:
9x³ + 27x²
Step-by-step explanation:
What the question is asking is to multiply f(x) and g(x) together:
Step 1: Write out expression
(fg)(x) = 3x²(3x + 9)
Step 2: Distribute
(fg)(x) = 9x³ + 27x²
Answer:
[tex]\huge\boxed{Option \ 3 : (fg)(x) = 9x^3+27x^2}[/tex]
Step-by-step explanation:
[tex]f(x) = 3x+9\\g(x) = 3x^2[/tex]
Multiplying both
[tex](fg)(x) = (3x+9)(3x^2)\\(fg)(x) = 9x^3+27x^2[/tex]
In Omarion's bag of M&Ms, 1/3 were red, 1/4 were yellow, 1/6 were blue, and 1/4 were orange. He picks out a candy without looking. What color candy is he least likely to choose?
Answer:
RED
Step-by-step explanation:
First of all, we will make all candies common, so we will expand the denominators.1/3
1/4
1/6
1/4
all equal at 12So there is a total of 12 candiesthen the new version of the candies is4/12
3/12
2/12
3/12
the most red sugar#achievements
Ax + By = C for x. plz sove
Answer:
[tex]\boxed{\boxed{ x=\frac{C-By}{A}; A\neq 0}}[/tex]
Step-by-step explanation:
[tex]Ax+By=C\\\\Ax+By-By=C-By\\\\Ax=C-By\\\\\frac{Ax=C-By}{A}\\\\\boxed{ x=\frac{C-By}{A}; A\neq 0}[/tex]
Hope this helps.
In the following equation, when x=3, what is the value of y? -4x + 3y = 12 A. 9 B. 3 C. 0 D. 8 PLZ HURRY IM TIMED WILL MARK BRAINLIEST
Answer:
[tex]\huge\boxed{y = 8}[/tex]
Step-by-step explanation:
-4x + 3y = 12
Given that x = 3
-4 (3) + 3y = 12
-12 + 3y = 12
Adding 12 to both sides
3y = 12+12
3y = 24
Dividing both sides by 3
y = 8
Answer:
y =8
Step-by-step explanation:
-4x + 3y = 12
Let x = 3
-4(3) +3y = 12
-12+3y = 12
Add 12 to each side
-12+12+3y =12+12
3y =24
Divide each side by 3
3y/3 = 24/3
y =8
what is the prime factorization of 7?
As Prime factorization is a process of writing all numbers as a product of primes then The prime factorization of number 7 is 7.
What is Number system?A number system is defined as a system of writing to express numbers.
Prime factorization is a process of writing all numbers as a product of primes
The number 7 is a prime number, which means it is only divisible by 1 and itself.
Therefore, the prime factorization of 7 is simply 7 itself.
Hence, the prime factorization of number 7 is 7.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ2
Explain how to perform a two-sample z-test for the difference between two population means using independent samples with known.
Answer:
The steps 1-7 have been explained
Step-by-step explanation:
The steps are;
1) We will verify that the population standard deviations are known and that the population is normally distributed which means the sample size must be a minimum of 30.
2) We will state the null and alternative hypothesis
3) We will determine the critical values from the relevant tables
4) From the critical values gotten, we will determine it's corresponding region where it can be rejected.
5)We will calculate the value of the test statistic from the formula;
z = [(x1' - x2') - (μ1 - μ2)]/√[((σ1)²/n1) + ((σ2)²/n2)]
6) If the value of the test statistic gotten from step 5 above falls in the region of rejection noted in step 4,then we will reject the null hypothesis
7) After rejection of the null hypothesis, we will now give a decision/conclusion on the claim.
At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
Answer:
a) What is the cost of a chicken shawarma wrap?
$10.99
b) What is the cost of one order of spiced potatoes?
$4.99
c) If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
Step-by-step explanation:
Let x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes,
Cost of a chicken sharwarma wrap = x
Cost of an order of spiced potatoes = y
Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.
3x + 2y = $42.95 .............Equation 1
Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.
5x + 4y = $74.91 ................Equation 2
Hence, the Equations needed to solve the question is:
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
We use Elimination method to solve for this.
Multiply Equation 1 by coefficient of x in Equation 2
Equation 2 by coefficient of x in Equation 1
3x + 2y = $42.95 .............Equation 1 × 5
5x + 4y = $74.91 ................Equation 2 × 3
15x + 10y = 214.75..............Equation 3
15x + 12y = 224.73..............Equation 4
Subtract Equation 3 from Equation 4
2y = 9.98
y = 9.98/2
y = 4.99
Therefore, y = Cost of an order of spiced potatoes = $4.99
Subtitute 4.99 for y in Equation 1
3x + 2y = $42.95 .............Equation 1
3x +2(4.99) = 42.95
3x + 9.98 = 42.95
3x = 42.95 - 9.98
3x = 32.97
x = 32.97/3
x = 10.99
x = Cost of a chicken sharwarma wrap = $10.99
Therefore,
The cost of a chicken sharwarma wrap = $10.99
The cost of an order of spiced potatoes = $4.99
Can anyone please help : show that cos^{2} (θ)= 1 + cos(2θ) / 2 , using the compound angle formula
Answer:
Below
Step-by-step explanation:
Let's prove that cos^2(O) = 1+ cos(2O)/2
We khow that cos(2O) = 2 cos^2-1
● cos(2O) = 2 cos^2-1
Add one to both sides:
● cos(2O) +1 = 2 cos^2-1+1
● cos(2O) +1 = 2 cos ^2
Divide both sides by 2
● [cos(2O)+1]/2 = cos^2
Which expression gives the area of the triangle shown below?
A.
(r)(x)
B.
px
C.
(p)(x)
D.
rx
base = r
height = x
area of triangle = (1/2)*(base*height)
area of triangle = (1/2)*(r*x)
area of triangle = (1/2)rx
Answer: Choice D2. Place the following values in scientific notation:
2020000 m
C. 0.003020 km
9901000 m/s
d. 0.001100 mm
Answer: a. [tex]2.02\times10^6\ m[/tex]
b. [tex]9.901\times10^6\ m/s[/tex]
c. [tex]3.02\times10 ^{-3}\ km[/tex]
d. [tex]1.1\times10^{-3}\ mm[/tex]
Step-by-step explanation:
Scientific notation is a technique to express a very big or a very small number in the product of a decimal form of number ( between 1 and 10) and powers of 10.
a. [tex]2,020,000 m\ = 2.02\times1,000,000=2.02\times10^6\ m[/tex]
b. [tex]9,901,000\ m/s =9.901\times1000000=9.901\times10^6\ m/s[/tex]
c. [tex]0.003020\ km=\dfrac{3020}{1000000}[/tex]
[tex]=3.02\times10 ^{-3}\ km[/tex]
d. [tex]0.001100\ mm=\dfrac{1100}{1000000}=\dfrac{11}{10000}[/tex]
[tex]1.1\times10^{-3}\ mm[/tex]
HELP ME!
A standard I.Q. test produces normally distributed results with a mean of 104 and a standard deviation of 16 for 52,000 students in grade 12 in the state. Approximately how many of these students would have I.Q.s above 140?
Answer: approx 1196 students.
Step-by-step explanation:
As known for normal distribution 95.4% of all results are situating at +-2*s distance from the mean. (s is the standard deviation)
2s=16*2=32 . The mean +2s= 104+32=136 = approx 140.
95.4% from 52000 = 49608 students. The residual amont ( which is out of the border mean+-2s)= 52000-49608=2392
Because of the normal distribution simmetry the number of the students which has IQ 140 and more is twice less than 2392.
N=2392:2=1196
HELP PLEASE 50 POINTS
A mechanic charges $125 plus $25 per hour of labor. The equation c=25n+125
describes the total she would charge for a service visit, where n represents the number of
hours of labor and c is the total cost. Graph the equation and using the graph, find how
much he charges when she works 3 hours.
Answer:
See Attachment for graph
Charges = $200 when number of she works for 3 hours
Step-by-step explanation:
Given
Charges = $25 per hour + $125 (c = 25n + 125)
Required
Graph the equation.
From the graph, determine c when n = 3
To plot the graph; first, we have to determine the points to use;
When n = 1
[tex]c = 25 * 1 + 125[/tex]
[tex]c = 25 + 125[/tex]
[tex]c = 150[/tex]
When n = 2
[tex]c = 25 * 2 + 125[/tex]
[tex]c = 50 + 125[/tex]
[tex]c = 175[/tex]
When n = 3
[tex]c = 25 * 3 + 125[/tex]
[tex]c = 75 + 125[/tex]
[tex]c = 200[/tex]
When n = 4
[tex]c = 25 * 4 + 125[/tex]
[tex]c = 100 + 125[/tex]
[tex]c = 225[/tex]
Plotting n on the x axis and c on the y axis; we have
c || n
1 || 150
2 || 175
3 || 200
4 || 225
(See attachment)
From the attachment;
When she works for 3 hour; This implies that n = 3
And c = $200 when n = 3
See Proof
[tex]c = 25n + 125[/tex]
Substitute 3 for n
[tex]c = 25 * 3 + 125[/tex]
[tex]c = 75 + 125[/tex]
[tex]c = 200[/tex]
whats is 5% in words?
Here are a few ways 5% could be written in words:
-five percent
-five thousandths (0.05)
Hope this helps! :)
Answer:
0.05
Step-by-step explanation:
Assuming you mean as a decimal...
5/100 = 0.05
ALTERNATIVELY
5% = Five Percent
0.05 = Five Thousandths, Zero Point Zero Five
