Identity to verify:
[tex]\dfrac{\cot x}{1+\csc x}=\dfrac{\csc x-1}{\cot x}[/tex]
Recall that
[tex]\cos^2x+\sin^2x=1[/tex]
Divide both sides by [tex]\sin^2x[/tex] and we get
[tex]\cot^2x+1=\csc^2x[/tex]
or
[tex]\cot^2x=\csc^2x-1=(\csc x-1)(\csc x+1)[/tex]
So if we multiply the numerator and denominator of
[tex]\dfrac{\cot x}{1+\csc x}[/tex]
by [tex]\csc x-1[/tex], we get
[tex]\dfrac{\cot x(\csc x-1)}{(1+\csc x)(\csc x-1)}=\dfrac{\cot x(\csc x-1)}{\csc^2x-1}=\dfrac{\cot x(\csc x-1)}{\cot^2x}[/tex]
Then as long as [tex]\cot x\neq0[/tex], we can cancel terms to end up with
[tex]\dfrac{\csc x-1}{\cot x}[/tex]
and establish the identity.
Consider 8x² - 48x = -104.
Write the equation so that
a = 1: x² + ___ x = ___
When a = 1, the equation becomes x² - 6x = -13.
To rewrite the equation 8x² - 48x = -104 with the coefficient of x² as 1,
you can divide the entire equation by 8,
which is the coefficient of x²:
(8x² - 48x) / 8 = (-104) / 8
Now, simplify:
x² - 6x = -13
So, when a = 1, the equation becomes x² - 6x = -13.
for such more question on coefficient
https://brainly.com/question/30845099
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12.) Find the value of x and y. Show ALL work.
Answer: The value of x = 90°
and the value of y = 43°
Step-by-step explanation:
Since we have given that
In ΔABC,
∠B=∠C=47°
As we know that "Sum of all three angles of a triangle is 180° ".
So, it becomes,
[tex]\angle A+\angle B+\angle C=180\textdegree\\\\\angle A+47\textdegree+47\textdegree=180\textdegree\\\\\angle A+94\textdegree=180\textdegree\\\\\angle A=180\textdegree-94\textdegree\\\\\angle A=86\textdegree\\\\So,\\\\y=\frac{86}{2}=43\textdegree[/tex]
Similarly,
Now, in ΔABD,
[tex]\angle A+\angle B+\angle ADB=180\textdegree\\\\43\textdegree+47\textdegree+\angle ADB=180\textdegree\\\\90\textdegree+\angle ADB=180\textdegree\\\\\angle ADB=180\textdegree-90\textdegree\\\\\angle ADB=90\textdegree[/tex]
Hence, the value of x = 90°
and the value of y = 43°
DHL Shipping claims that it ships 95% of its orders within three working days. You select a simple random sample of 100 orders and discover that only 91 of them shipped on time.
a) If DHL really does ship 95% on time, what is the probability that the company shipped 91 or fewer out of 100 orders were shipped on time?
b) A marketer from UPS jumps on the research stating, "They claim 95% on time, but by their own research they only ship 91% on time!" Provide a rebuttal to the UPS marketer in non-statistical terms.
Answer:
a) 5.4%
Step-by-step explanation:
a) We will use the binomial distribution, with n = 100 and p(success) = 0.95
We need to calculate
P(X=x) = [tex]\binom{n}{x}p^{x}q^{n-x}[/tex]
P(X ≤91) = [tex]\sum_{k=1}^{91}\binom{100}{k}0.95^{k}0.5^{n-k}[/tex]
As we know that binomial distribution can be approximated to normal distribution if np≥5 and nq≥5 as in this case.
Therefore, P(x,n,p) →N[tex](\mu, \sigma )[/tex]
[tex]\mu[/tex] = np = 95
[tex]\sigma[/tex] = √npq = 2.`79
P(X≤91) ≅ P(X≤91.5) = P( Z≤[tex]\frac{91.5-95}{2.179}[/tex]
= P( Z≤ -1.6)
= 0.054
Probability = 5.4%
b) If the probability was less than 5% then we must say that the DHL Shipping company don not ships 95% of its orders on time but as we can see that the probability is more that 5% that is 5.4%. So, we cannot say that the company does not ships the orders on time. But we cannot say with confirmation, we need more samples so as to judge accordingly.
The present population of a town is 52,728. If the population grew at a rate of 4% per annum, what was the population three years ago?
Hannah has 89 of a pound of birdseed. She put 23 of a pound of birdseed into her bird feeders. How much birdseed does Hannah have remaining?
Final answer:
Hannah initially has 8/9 of a pound of birdseed, and after using 2/3 of a pound, she has 2/9 of a pound remaining, which is calculated by finding a common denominator and subtracting the second fraction from the first.
Explanation:
Hannah initially has 8/9 of a pound of birdseed. After filling her bird feeders with 2/3 of a pound of birdseed, we need to subtract the amount she used from what she started with to find out how much birdseed she has left. The calculation we'll use is:
(initial amount) - (amount used) = (amount remaining)
In fractional form, this becomes:
8/9 - 2/3
To subtract these fractions, we need a common denominator. The smallest common denominator for 9 and 3 is 9. We can convert 2/3 to 6/9 by multiplying the numerator and the denominator by 3. After this step, the subtraction is straightforward:
8/9 - 6/9 = 2/9
Hence, Hannah has 2/9 of a pound of birdseed remaining.
Hey guys! I have a paper due and I need help desperately. I don't need an explanation just the answers!! Thanks! You don't have to do all of them. I Will Do BRAINLIEST!!
In which quadrant does the point that is graphed lie?
A) I
B) II
C) III
D) IV
A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 2 bags of chips for $9.00. Another customer buys 5 hot dogs and 3 bags of chips for $11.75. Find the cost of a hot dog.
Answer: hot dog = $1.75
Step-by-step explanation:
Let h represent hot dogs and c represent bags of chips.
Customer 1: 4h + 2c = 9.00 → 3(4h + 2c = 9.00) → 12h + 6c = 27.00
Customer 2: 5h + 3c = 11.75 → -2(5h + 3c = 11.75) → -10h - 6c = -23.50
2h = 3.50
÷2 ÷2
h = 1.75
Final answer:
The cost of one hot dog is determined to be $1.75.
Explanation:
To find the cost of a hot dog, we will use the information given in two different customer purchases to set up a system of linear equations. Let's define H as the cost of one hot dog and C as the cost of a bag of chips. The first customer buys 4 hot dogs and 2 bags of chips for $9.00, which gives us the first equation:
4H + 2C = 9.00 ...(1)
The second customer buys 5 hot dogs and 3 bags of chips for $11.75, which provides us with the second equation:
5H + 3C = 11.75 ...(2)
With two equations, we can solve for H by either substitution or elimination. Let's multiply equation (1) by 3 and equation (2) by 2 to eliminate C:
12H + 6C = 27.00 ...(3)10H + 6C = 23.50 ...(4)Subtracting equation (4) from equation (3) gives us:
2H = 3.50
And dividing both sides by 2:
H = 1.75
Therefore, the cost of one hot dog is $1.75.
what is h(x)=|3x|-1 ? x=7. Insert 7 for x. Thanks!!
Answer: 20
Step-by-step explanation:
h(x) = |3x| - 1
h(7) = |3(7)| - 1
= |21| - 1
= 21 - 1
= 20
Jose bought a bag of 6 oranges for $2.82.He also bought 5 pineapples.He gave the cashier $20 and received $1.43 change.What did each pineapple cost?
Answer:
$3.15
Step-by-step explanation:
What is the average rate of change of the function over the interval x = 0 to x = 5? f(x)=4^2x+1
Enter your answer, as a simplified fraction,
Answer: 838860
=========================================
Plug in x = 0 to find y = f(x)
f(x) = 4^(2x+1)
f(0) = 4^(2*0+1)
f(0) = 4
The point (0,4) is on the function curve
Plug in x = 5 and compute
f(x) = 4^(2x+1)
f(5) = 4^(2*5+1)
f(5) = 4194304
The point (5, 4194304) is on the function curve
Once you have these two points, you use the slope formula to compute the average rate of change
m = (y2-y1)/(x2-x1)
m = (4194304 - 4)/(5-0)
m = 838860
The slope of the line through the two points found earlier is m = 838860, so this is the average rate of change on f(x) for the interval from x = 0 to x = 5.
SOMEONE PLEASE HELP ALL THE QUESTIONS R ATTACHED AS WELL AS THE ANSWERS!!!!!!!!!!!!!!
The error is in Step-4.
A negative exponent does NOT mean that the number turns negative. A negative exponent means the number is in the denominator.
(4)⁻⁴ means (1/4⁴) . That's (1/256) . All positive numbers.
How do I solve for a? 15a²+45=0
[tex]15a^2+45=0\qquad\text{subtract 45 from both sides}\\\\15a^2=-45\qquad\text{divide both sides by 15}\\\\a^2=-3<0\\\\\text{NO REAL SOLUTION}\\\\\text{in the complex set}\\\\a^2=-3\to a=\pm\sqrt{-3}\\\\a=\pm\sqrt{(-1)(3)}\\\\a=\pm\sqrt{-1}\cdot\sqrt3\\\\\boxed{a=-i\sqrt3\ \vee\ a=i\sqrt3}\\\\------------------\\\\i=\sqrt{-1}[/tex]
This box plot shows the heights ( in feet) of a sample of pine trees
Answer:
D
Step-by-step explanation:
The new one would have a long gap between the Q3 and the maximum of the box and whisker plot, therefore it should create a positive skew.
Answer:
D
Step-by-step explanation:
It will be positively skewed (skewed right), because that means that the longer segment would be on the right side of the median.
140 is a major outlier and a lot larger than the more central numbers. However, it's only 1 number, so the median (location of the "box") would remain similar or the same. The end on the right, however, would move far to the right, extending the "line" on that side.
Help please answer this .... is this bettter?
Answer:
x = 53 degrees
Step-by-step explanation:
Alternate exterior angles are equal if two parallel lines are cut by a transversal.
If m and n are parallel, then
3x-28 = 2x+25
Subtract 2x from each side.
3x-28-2x = 2x+25-2x
x-28 =25
Add 28 to each side.
x-28+28 = 25+28
x = 53
An alloy composed of nickel, zinc, and copper in a 4:1:2 ratio. How many kilograms of each metal are needed to make 35 kg of this alloy?
Answer:
Step-by-step explanation:
The ration of weight of nickel, zinc, and copper in an alloy is 4:1:2
The weight of alloy can be written as
4x + x + 2x = 35 Kg
7 x = 35 Kg
X = 35 Kg/7
X = 5kg
The weight of nickel the alloy = 4 x 5 = 20 Kg
The weight of zinc in the alloy= 1 x 5 = 5kg
The weight of copper in the alloy = 2 x 5 = 10 kg
Answer:
Let X be the amount of each metal needed to make 35 Kg of this alloy.
We know that an alloy is composed of nickel, zinc and copper in a proportion
4:1:2. Therefore, we have:
[tex]4X+1X+2X = 35[/tex]
[tex]7X = 35[/tex]
[tex]X=\frac{35}{7}[/tex]
[tex]X=5[/tex] Kg
Therefore, there are [tex]5 \times 4 =20[/tex] kg of nickel, [tex]1 \times 5 =5[/tex] kg of zinc, and [tex]2 \times 5 = 10[/tex] kg of copper needed to make 35 kg of this alloy
first number plus twice a second number is 8. Twice the first number plus the second totals 31. Find the number
Answer:
1st number = 18
2nd number = -5
Step-by-step explanation:
Let x be first number and y be the 2nd number.
We have been given that first number plus twice a second number is 8. We can represent this information as:
[tex]x+2y=8...(1)[/tex]
We are also given that twice the first number plus the second totals 31. We can represent this information as:
[tex]2x+y=31...(2)[/tex]
Now let us solve our system of equations using substitution method.
From equation (1) we will get,
[tex]x=8-2y[/tex]
Substituting [tex]x=8-2y[/tex] in equation (2) we will get,
[tex]2(8-2y)+y=31[/tex]
[tex]16-4y+y=31[/tex]
[tex]-4y+y=31-16[/tex]
[tex]-3y=15[/tex]
[tex]y=\frac{15}{-3}[/tex]
[tex]y=-5[/tex]
Therefore, the second number is -5.
Now let us substitute y=-5 in equation (1).
[tex]x+(2*-5)=8[/tex]
[tex]x-10=8[/tex]
[tex]x=8+10[/tex]
[tex]x=18[/tex]
Therefore, the first number is 18.
The numbers are x = 18 and y = -5.
The question involves a system of linear equations and requires solving for two unknown numbers. Using variables to represent these numbers, the system can be written as:
First equation: x + 2y = 8,
Second equation: 2x + y = 31.
To solve this system, follow these steps:
Multiply the first equation by 2, obtaining the equation 2x + 4y = 16.
Subtract the second equation from this result to eliminate x, leading to 3y = -15.
Divide by 3 to find y = -5.
Substitute y = -5 into any original equation to solve for x.
Using the first equation: x + 2(-5) = 8, therefore x = 18.
The solution to the system is x = 18 and y = -5.
is 3/7 and 8/28 proportional or not proportional??
Answer:
Yes they are proportional!
The factors of 28 that we can use in these fractions are 4 and 7. To find if these are proportional, just simplify 8/28. To do so divide the numerator (top) and the denominator (bottom) both by 4...
8/28 / 4 = 4/7
Now that you have both with the same denominator, you can evaluate if 3/7 and 4/7 are proportional. In this case they are.
Hope this helps! :)
Marcus estimates that 230 people will attend the choir contrary there was an actual total of 300 people who attended the choir concert What is the answer to this?
Answer:
23% error since 70 more people attended then Marcus counted
Step-by-step explanation:
To calculate the percent error:
We find the difference between the predicted and the actual.We divide the absolute value of the difference by the actual recorded value.Convert to a percent by multiplying by 100 and adding a % sign.Marcus counted 230 and 300 actually came.
1. 230-300=-70 but the absolute value is 70
2. 70/300=0.23
3. 0.23(100)=23%
Marcus' estimated had a 23% error.
please help me
im stuck
Answer:
See the attachmentCStep-by-step explanation:
1. If you work these out in detail, they are tedious, but not difficult. Fortunately, you can take advantage of certain clues to simplify the work.
There is only one expression with a fraction bar.b(2x) means the exponent of 2 will be 2x. There is only one of those.There is only one expression that is a product (not a sum).There is only one expression with 2(2^x) in it.After the above, there is only one expression left.___
2. You know the -x as an argument of the function will flip the curve left-to-right, so only C and D are potential choices. One way to resolve the ambiguity is to see what the function value is for x=0. You find they are the same:
... f(0) = root(3)(0 -1) = g(0) = root(3)(-0-1) = root(3)(-1)
Only graph C has the two curves crossing at x=0.
___
f(x) = root(3)(x -1) is a shift to the right of the parent function root(3)(x).
Replacing x by -x reflects that function across the y-axis, so what was a shift to the right now becomes a shift to the left, as seen in graph C.
An angle measures 50° more than the measure of a supplementary angle. What is the measure of each angle?
Answer:
65° and 115°
Step-by-step explanation:
let one angle be x then the other is x + 50
The sum of 2 supplementary angles = 180°, hence
x + x + 50 = 180
2x + 50 = 180 ( subtract 50 from both sides )
2x = 130 ( divide both sides by 2 )
x = 65
Thus the 2 angles are x = 65° and x + 50 = 65 + 50 = 115°
A pipe that's 36 inches long needs to be cut into 2 1/4-inch long pieces. How many pieces can be cut from this length of pipe? Hint: Change 2 1/4 to an improper fraction before calculating.
A. 9
B. 11 1/4
C. 4 4/9
D. 16
Answer:
16 inches
Step-by-step explanation:
2 1/4 = 9/4 inches
Number of pieces = 36 / 9/4
= 36 + 4/9
= 16 inches
Answer:
D. 16
Step-by-step explanation:
I divided 36 from 2.25.
Show and justify the steps for solving ax=bx+c where a≠b. then use the literal equation's solution to obtain the solution of 2x=x+7.
Answer: [tex]\bold{x=\dfrac{c}{a-b},\qquad x=7}[/tex]
Step-by-step explanation:
Move all of the x's to one side and everything else on the other.
ax = bx + c
ax - bx = c subtracted bx from both sides
x(a - b) = c factored out the like term of "x" on left side
[tex]x=\dfrac{c}{a-b}[/tex] divided both sides by (a- b)
2x = x + 7 → a = 2, b = 1, c = 7
[tex]x=\dfrac{7}{2-1}[/tex]
x = 7
Check:
2x = x + 7
-x -x
x = 7
Mrs. Siebenaller bought a bus for 25,000 with a 7% interest rate mrs s gets a loan payoff of 60 months how much interest would she pay
Answer:
[tex]\$4701.80[/tex]
Step-by-step explanation:
Mrs. Siebenaller bought a bus for 25,000 with a 7% interest rate and she gets a loan payoff of 60 months,
We know that,
[tex]\text{PV of annuity}=P\left[\dfrac{1-(1+r)^{-n}}{r}\right][/tex]
Where,
PV = Present value of annuity = 25000,
r = rate of interest of each period = [tex]\dfrac{7}{12}[/tex]% monthly
n = number of periods = 60 months,
Putting the values,
[tex]\Rightarrow 25000=P\left[\dfrac{1-(1+\frac{0.07}{12})^{-60}}{\frac{0.07}{12}}\right][/tex]
[tex]\Rightarrow P=\dfrac{25000}{\left[\dfrac{1-(1+\frac{0.07}{12})^{-60}}{\frac{0.07}{12}}\right]}[/tex]
[tex]\Rightarrow P=\$495.03[/tex]
Hence total amount paid is,
[tex]=495.03\times 60=\$29,701.80[/tex]
Therefore interest amount is,
[tex]=29,701.80-25,000=\$4701.80[/tex]
25 POINTS + BRAINLIEST IF YOU EXPLAIN ANSWER
Answer:
4th degree
Step-by-step explanation:
We can use a technique called finite differences.
In column 1 put the differences between the y values (y2-y1)
Keep adding columns with the differences until they become constant.
Column 2 is column1 differences (-2- -30) etc
Column3 is column 2 differences
Column 4 is column3 differences
The differences in column4 are the same, so we can stop
This will be a 4th degree polynomial
x y column 1 column 2 column 3 column 4
-2 30
-1 0 -30
0 -2 -2 28
1 0 2 4 -24
2 30 30 28 24 48
3 160 130 100 72 48
4 510 350 220 120 48
Answer:
4th degree ...........
Dominik uses 20 grams of filling for each dumpling he makes. He has 1500 grams of dumpling filling. The grams F of filling remaining is a function of d, the number of dumplings Dominik makes. Write the function's formula.
Answer:F=−20d+1500
Step-by-step explanation:he amount of filling used to make each dumpling is constant, so we're dealing with a linear relationship.
We could write the desired formula in slope-intercept form: F=\greenD md+\maroonD bF=md+b. In this form, \greenD mm gives us the slope of the graph of the function and \maroonD bb gives us the yy-intercept. Our goal is to find the values of \greenD mm and \maroonD bb and substitute them into this formula.
Hint #22 / 3
We know that each dumpling Dominik makes decreases the filling remaining by 2020 grams, so the slope \greenD mm is \greenD{-20}−20, and our function looks like F=\greenD{-20}d+\maroonD bF=−20d+b.
We also know that Dominik has 15001500 grams of filling initially, so the yy-intercept \maroonD{b}b is \maroonD{1500}1500.
Hint #33 / 3
Since \greenD{m}=\greenD{-20}m=−20 and \maroonD{b}=\maroonD{1500}b=1500, the desired formula is:
The function's formula for the grams F of filling remaining as a function of d, the number of dumplings Dominik makes, is given by:F(d) = 1500 - 20d
To derive this formula, we start by considering the total amount of filling Dominik has, which is 1500 grams. Each dumpling uses 20 grams of filling. Therefore, if Dominik makes d dumplings, he will have used 20d grams of filling. To find the remaining filling, we subtract the amount used from the total amount initially available:
[tex]\[ F(d) = \text{Total filling} - (\text{Filling per dumpling} \times \text{Number of dumplings}) \] \[ F(d) = 1500 - (20 \times d) \] \[ F(d) = 1500 - 20d \][/tex]
This function gives us the amount of filling, in grams, that remains after Dominik has made d dumplings.
What is the effect on the graph of the function f(x) =5x when f(x) is replaced with f(x) + 9?
Answer:
When we add 9 to the function we are shifting the function up 9 units.
Step-by-step explanation:
If it were added inside the function, it woulds shift it left or right.
But since it is outside the function, we will shift it up or down
When we add 9 to the function we are shifting the function up 9 units.
Answer:
add 9 to the function we are shifting the function up 9 units
Step-by-step explanation:
Mario is setting up a new tent during a camping trip. The tent came with 7 feet of rope. The instructions were to use 34.5 inches of the rope to tie a tarp on top of the tent. Then, the remaining rope should be cut into 8 1/4 inch sections to tie the tent to stakes in the ground. Mario will use al the rope as instructed. Write and solve an equation to determine the number of 8 1/4 inch sections of rope Mario can cut from the rope.
Answer:
[tex] The\ number\ of\ 8 \frac{1}{4}\ inches\ of\ section\ of\ rope\ be\ 6. [/tex]
Step-by-step explanation:
As given
Mario is setting up a new tent during a camping trip.
The tent came with 7 feet of rope.
As 1 foot = 12 inches
Now convert 7 feet into inches.
7 feet = 7 × 12 inches
= 84 inches
As given
The instructions were to use 34.5 inches of the rope to tie a tarp on top of the tent.
Than
Rope left after tie a tarp on top of the tent = 84 - 34.5
= 49.5 inches
As given
[tex]The\ remaining\ rope\ should\ be\ cut\ into\ 8 \frac{1}{4}\ inch\ sections\ to\ tie\ the\ tent\ to\ stakes\ in\ the\ ground.[/tex]
i.e
[tex]The\ remaining\ rope\ should\ be\ cut\ into\ \frac{33}{4}\ inch\ sections\ to\ tie\ the\ tent\ to\ stakes\ in\ the\ ground.[/tex]
[tex]Let\ us\ assume\ the\ number\ of\ \frac{33}{4}\ inches\ section\ of\ rope\ be\ x.[/tex]
Than the equation becomes
[tex]\frac{33\times x}{4} = 49.5[/tex]
[tex]x = \frac{49.5\times 4}{33}[/tex]
[tex]x = \frac{198}{33}[/tex]
x = 6
Answer:
6
Step-by-step explanation:
Converting 7 ft to inches:
[tex]7*12=84[/tex] inches
34.5 inches is used, and remaining is used for [tex]8\frac{1}{4}[/tex] in. sections. Let [tex]x[/tex] be the number of [tex]8\frac{1}{4}[/tex] in. sections. ([tex]8\frac{1}{4}[/tex] can be written as 8.25 inches)We set up the equation as:
[tex]34.5+8.25x=84[/tex]
Now solving for [tex]x[/tex] would give us the number of 8.25 inch sections:
[tex]8.25x=84-34.5\\8.25x=49.5\\x=\frac{49.5}{8.25}=6[/tex]
Hence, Mario can cut 6 (8.25 inch) sections from the rope
A rally car race course covers 515.97 miles. The winning car completed the course in 6.5 hours. What was the average speed of the winning car?
Answer:
79.38 miles per hour
Step-by-step explanation:
average speed = miles covered / hours
= 515.97 / 6.5
= 79.38
Answer: 79.38 miles per hour
Step-by-step explanation:
Given : Distance covered by rally car race course = 515.97 miles
Time taken to complete the course by winning car = 6.5 hours
The average speed of the winning car = ( Distance covered by rally car race course) ÷ (Time taken to complete the course by winning car)
= (515.97)÷ (6.5) miles per hour
= 79.38 miles per hour
Hence, the average speed of the winning car = 79.38 miles per hour.
You have 16 oz of orange juice. It has 200 mg of vitamin c in it. That is 250% of the daily allowance for adults. WhAt is 100% of the daily allowance?
Answer:
80 mg
Step-by-step explanation:
By proportion the daily allowance is 200 * 100/250
= 200 * 10/25
= 80 mg