Answer:
✔ a strong positive
✔ strengthen
✔ increase
ED2021
Answer:
- a strong positive
- strengthen
- increase
Find cos(2x) from the given information. tan(x)= 9/8, x in quadrant I
Answer:
cos2x=-17/145
Step-by-step explanation:
Recall cos2x=cos^2x-sin^2x
Or cos2x=cos^2x-(1-cos^2x)*
Or cos2x=2cos^2x-1**
*By a Pythagorean Identity
**Combined like terms
I'm going to use third identity from above because I only have to find cosx or cos^2x to get requested answer for cos2x.
Recall Pythagorean identity 1+tan^2x=sec^2x.
Plug in our tangent valuem...
1+(9/8)^2=sec^2x
1+81/64=sec^2x
145/64=sec^2x
Cosine and secant are reciprocals of each other.
64/145=cos^2x
Now we are ready to plug in and get final answer:
cos2x=2cos^2x-1
cos2x=2(64/145)-1
cos2x=128/145-1
cos2x=-17/145
A drinking container is shaped like a cone and must hold at least 10 ounces of fluid. The radius of the top of the container is 2.25 inches. The steps for determining the height of the cone-shaped container are shown below.
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Answer:
C. h ≥ 1.9 in
Step-by-step explanation:
As the final step, divide both sides of the inequality by 5.3:
(5.3h)/5.3 ≥ 10/5.3
h ≥ 1.9
The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,450. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 570 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time? (Round z value to 2 decimal places. Round your answer to the nearest whole number.)
Answer:
The manufacturer should advertise 11720 pages.
Step-by-step explanation:
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.
Mean of 12450, standard deviation of 570:
This means that [tex]\mu = 12450, \sigma = 570[/tex]
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time?
They should advertise the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 12450}{570}[/tex]
[tex]X - 12450 = -1.28*570[/tex]
[tex]X = 11720[/tex]
The manufacturer should advertise 11720 pages.
Use a table of values to graph the function ƒ(x) = x−−√. Choose the correct graph from the options below.
Answer:
B
Step-by-step explanation:
The square root function's graph is graph (b). This makes logical sense, because, when taking the square root (the principal root in particular), a general rule is that both the input and the output must be positive. Moreover, if one were to create a table of values to find points on the graph of the function, each of the points can be found on graph (b).
[tex]f(x)=\sqrt{x}[/tex]
x y
1 1
4 2
9 3
16 4
Therefore graph (B) is the correct answer.
A jar contains 11red marbles, 12 blue marbles and 6 white marbles. Four marbles from the jar are selected. With each marble being replaced after each selection. What is the probability that the first red marble chosen is on the 5th selection?
Answer:
Red on the 5th draw = 0.0907
Step-by-step explanation:
The first to fourth selections are all the same.
Blue + white = 12 + 6 = 18
The total number of marbles is 11 + 12 + 6 = 29
P(~ red) for the first four times = (18/29)^4 = 0,1484
Now on the 5th time, the first red is 11/18
So the Probability is 0.1484 * 11/18 = 0.0907
13 A traffic roundabout has a circular garden
in the centre and two lanes for traffic
encircling the garden. The diameter of the
garden is 16 metres and each lane is 3 metres
wide. Each lane is to be resurfaced. Calculate
the area to be resurfaced. Answer in square
metres to the nearest whole number.
Answer:
Step-by-step explanation:
The area to be resurfaced is the area of the
whole circle including garden and lanes minus
the area of the garden.
Area of a circle is (pi)r2
radius of garden is (1/2)diameter = 8 m
Garden area: (pi)82 = 64(pi) m2
Diameter of garden plus traffic lanes is
16 + 2(6) because we add 6 m to both sides
of the diameter of the garden.
Full diameter = 16+12 = 28 m
Full radius = 28/2 = 14 m
Full area: (pi)142 = 196(pi) m2
Area to be resurfaced:
196(pi) - 64(pi) = 132(pi) m2 ≅ 415 m2
What is the area of xyz pleae help?
Step-by-step explanation:
here's the answer to your question
Answer:
A = 14 in²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 7 and h = 4 , then
A = [tex]\frac{1}{2}[/tex] × 7 × 4 = [tex]\frac{1}{2}[/tex] × 28 = 14 in²
solve each question please thank you
Answer:
SURE
Step-by-step explanation:
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 35113511 grams and a variance of 253,009253,009. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 46174617 grams. Round your answer to four decimal places.
Answer:
The answer is "0.1397".
Step-by-step explanation:
[tex]\mu=3511\\\\[/tex]
variance [tex]\ S^2= 253,009\\\\[/tex]
standard deviation [tex]\sigma =\sqrt{253,009}=503\\\\[/tex]
Finding the probability in which the weight will be less than [tex]4617 \ grams\\\\[/tex]
[tex]P(X<4617)=p[z<\frac{4617-3511}{503}]\\\\[/tex]
[tex]=p[z<\frac{1106}{503}]\\\\=p[z< 2.198]\\\\= .013975\approx 0.1397[/tex]
he radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 77.8 % of their carbon-14. How old were the bones at the time they were discovered?
Answer:
The bones were 12,485 years old at the time they were discovered.
Step-by-step explanation:
Amount of the element:
The amount of the element after t years is given by the following equation, considering the decay rate proportional to the amount present:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which A(0) is the initial amount and k is the decay rate, as a decimal.
The radioactive element carbon-14 has a half-life of 5750 years.
This means that [tex]A(5750) = 0.5A(0)[/tex], and we use this to find k. So
[tex]A(t) = A(0)e^{-kt}[/tex]
[tex]0.5A(0) = A(0)e^{-5750k}[/tex]
[tex]e^{-5750k} = 0.5[/tex]
[tex]\ln{e^{-5750k}} = \ln{0.5}[/tex]
[tex]-5750k = \ln{0.5}[/tex]
[tex]k = -\frac{\ln{0.5}}{5750}[/tex]
[tex]k = 0.00012054733[/tex]
So
[tex]A(t) = A(0)e^{-0.00012054733t}[/tex]
A scientist determined that the bones from a mastodon had lost 77.8 % of their carbon-14. How old were the bones at the time they were discovered?
Had 100 - 77.8 = 22.2% remaining, so this is t for which:
[tex]A(t) = 0.222A(0)[/tex]
Then
[tex]0.222A(0) = A(0)e^{-0.00012054733t}[/tex]
[tex]e^{-0.00012054733t} = 0.222[/tex]
[tex]\ln{e^{-0.00012054733t}} = \ln{0.222}[/tex]
[tex]-0.00012054733t = \ln{0.222}[/tex]
[tex]t = -\frac{\ln{0.222}}{0.00012054733}[/tex]
[tex]t = 12485[/tex]
The bones were 12,485 years old at the time they were discovered.
PLEASE HELP QUICKLY
Determine whether the given sequence could be arithmetic. If so, identify the first difference and the next term.
-6, -11, -16, -21, -26.....
Answer:
The first difference is -5. The next term is -31.
Step-by-step explanation:
If you find the difference between -6 and -11, then you get -5.
And, all the other ones also have differences of -5, so basically, the next term is -31.
Thanks! Please mark me Brainliest!
Answer:
It could be arithmeticIf so, then the first difference is -5 and the next term is -31===================================================
Explanation:
Pick any term and subtract off the previous term
term2 - term1 = -11 - (-6) = -11 + 6 = -5term3 - term2 = -16 - (-11) = -16 + 11 = -5term4 - term3 = -21 - (-16) = -21 + 16 = -5term5 - term4 = -26 - (-21) = -26 + 21 = -5No matter what we picked, we end up with the same result which is -5. This is the common difference aka first difference.
If this pattern keeps up forever, then the sequence is arithmetic.
And if the pattern keeps up, then the next term would be
term6 = term5 + (common difference)
term6 = -26 + (-5)
term6 = -31
Note: Adding -5 is the same as subtracting 5.
the measures of three angles of a triangle are given by (8x-10), (2x), and (3x-5). What is the measure of the larges tangle
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Answer:
110°
Step-by-step explanation:
The sum of angles of a triangle is 180°.
(8x -10) +(2x) +(3x -5) = 180
13x -15 = 180
13x = 195
x = 15
The largest angle is ...
8x -10 = 8(15) -10 = 110 . . . . degrees
The credit department of Lion's Department Store in Anaheim, California, reported that 30% of their sales are cash, 30% are paid with a credit card, and 40% with a debit card. Twenty percent of the cash purchases, 90% of the credit card purchases, and 60% of the debit card purchases are for more than $50. Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability that she paid cash?
Answer:
Hence the probability that she paid cash is 0.105
Step-by-step explanation:
P(cash) = 0.3
P(credit card ) = 0.3
P(debit card ) = 0.4
P ( more than $50 | cash ) = 0.2
P (more than $50 | credit card ) =0.9
P (more than $ 50 |debit card ) = 0.6
P ( more than $50) = P ( more than $50 | cash )* P (cash) + P (more than $50 credit card ) * P(credit card ) + P (more than $ 50 |debit card )* P(debit card )
= 0.2 * 0.3 + 0.9 * 0.3 + 0.6* 0.4
= 0.57
P ( more than $50) = P ( more than $50 | cash )* P (cash) / P ( more than $50)
= 0.2* 0.3 / 0.57
= 0.105
What is the least common denominator that will allow you to combine the constant terms? 10 21 35 or 42
Answer:
[tex]LCM = 21[/tex]
Step-by-step explanation:
Given
[tex]-\frac{3}{5}y + \frac{1}{7}= \frac{1}{3}y -\frac{2}{3}[/tex]
Required
LCM of the constant terms
Collect like terms
[tex]\frac{1}{3}y+\frac{3}{5}y = \frac{1}{7}+\frac{2}{3}[/tex]
The constant terms are on the right-hand side
To combine them, we simply take the LCM of the denominator, i.e. 7 and 3
The prime factorization of 3 and 7 are:
[tex]3 = 3[/tex]
[tex]7 = 7[/tex]
So:
[tex]LCM = 3 * 7[/tex]
[tex]LCM = 21[/tex]
The mortgage on your new house is $180,000. Your monthly mortgage payment is $839 for 30 years. How much interest will be paid if the house is kept for the full 30 years?
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Answer:
$122,040
Step-by-step explanation:
The interest is the difference between the mortgage value and the total amount paid.
($839/mo)×(12 mo/yr)×(30 yr) -180,000 = $302,400 -180,000 = $122,040
$122,040 will be paid in interest.
Find the expression that is equivalent to 7(x2 – 5x + 1).
Answer:
7x^2 -35x +7
Step-by-step explanation:
7(x^2 – 5x + 1)
Distribute
7x^2 -7*5x +7*1
7x^2 -35x +7
Noah charges $20 for each lawn that he mows.
Answer:
m = 20 * n
Step-by-step explanation:
The money that he earns is equal the amount earned per lawn times the amount of lawns that he mows
m = 20 * n
Answer:
60 = 3 x 20
Step-by-step explanation:
60 = m
3 = c
20 = n
The width of a rectangle measures (7k-2m)(7k−2m) centimeters, and its length measures (5k-m)(5k−m) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
[tex]P = 24k-6m[/tex]
Step-by-step explanation:
The correct expressions are:
[tex]W = 7k - 2m[/tex]
[tex]L = 5k - m[/tex]
Required
The perimeter (P)
This is calculated as:
[tex]P = 2 *(L + W)[/tex]
So, we have:
[tex]P = 2 *(5k - m + 7k -2m)[/tex]
Collect like terms
[tex]P = 2 *(5k + 7k- m -2m)[/tex]
[tex]P = 2 *(12k-3m)[/tex]
Open bracket
[tex]P = 24k-6m[/tex]
A sofa regularly sells for $760. The sale price is $676.40. Find the percent decrease of the sale price from the regular price.
Answer: (760 - 676. 40) × 100 ÷ 760 = 11%
Step-by-step explanation:
Answer:
11% decrease
Step-by-step explanation:
Concepts:
Percent change is the change between an old value and its new value represented as a %. If a percent change is a decrease, it means that the new value is less than the old value. If a percent change is a increase, it means that the old value is less than the new value. The formula for percent change is: (NV - OV)/OV · 100 = C, where NV = New Value, OV = Old Value, and C = Percent Change.The sale price is the price at which something sells or sold after the price has been reduced by sales, discounts, etc.Solving:
Let's find the percent change by using the formula.
1. Formula for Percent Change
(NV - OV)/OV · 100 = C2. Plug in the values of NV and OV
(676.40 - 760)/760 · 100 = C3. Simplify
-83.6/760 · 100 = C-0.11 · 100 = C-11 = CTherefore, our percent decrease is 11% decrease.
moses is inviting 10 friends to a party each friend wants 4 cookies and each box has 10 cookies how many boxes should moses get?
Answer:
4
Step-by-step explanation:
Since each friend wants 4 cookies, and there are 10 friends, there are 10 x 4 = 40 cookies total Moses should buy. Since each cookie box has 10 cookies in it, he should buy 40/10 = 4 total cookie boxes.
Dave's favorite recipe (spaghetti pie) calls for 20 ounces of ground sausage. Since it's awesome, everybody wants some, so he decided to make five pies and pass them out to the select few in his inner circle. The sausage comes in one-pound tubes. How many tubes did Dave need, and how many grams of delicious sausage were left over for his omelet the next morning
Answer:
hi
Step-by-step explanation:
Find the intersection of the line and the circle given below
y=-x-3
x^2+y^2=17
Answer:
There are two points of intersection
(-4,1) and (1,-4)
Step-by-step explanation:
Answer:
the guy above me is correct
Step-by-step explanation:
JK=8x+6 KL=6x+20 find JL
Answer:
14x + 26
Step-by-step explanation:
JL = JK + KL
= 8x + 6 + 6x + 20
= 8x + 6x + 6 + 20
JL = 14x + 26
Julio has a net pay of $ 537.00 each paycheck. He pays $ 142.00 in pre-tax deductions and taxes each paycheck. What is Julio's gross income before the tax deductions?
Answer:
Julio's gross income before the tax deductions is $ 405.
Step-by-step explanation:
Given that Julio has a net pay of $ 537.00 each paycheck, and he pays $ 142.00 in pre-tax deductions and taxes each paycheck, to determine what is Julio's gross income before the tax deductions the following calculation must be performed:
547 - 142 = X
405 = X
Therefore, Julio's gross income before the tax deductions is $ 405.
Find the number that comes after 144five
Answer:
The number that comes after 144five is:
= 200five.
Step-by-step explanation:
Adding 1 to 144 base 5 will result in:
144
+ 1
= 200
b) To obtain the next number that comes after 144five, add 1five to 144five. Since the numbers are in base 5, 1five added to 4five will result in 0 with 1 carried backward. When 1 is added to the next 4, the result will be 0 with 1 carried backward. 1 added to 1 = 2, all in base 5. Figures in base 5 cannot exceed 4. The usual numbers for a base 5 operation are 0, 1, 2, 3, and 4.
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within with % confidence if (a) she uses a previous estimate of ? (b) she does not use any prior estimates?
Answer:
732 samples ;
752 samples
Step-by-step explanation:
Given :
α = 90% ; M.E = 0.03 ; p = 0.58 ; 1 - p = 1 - 0.58 = 0.42
Using the relation :
n = (Z² * p * (1 - p)) / M.E²
Zcritical at 90% = 1.645
n = (1.645² * 0.58 * 0.42) / 0.03²
n = 0.65918769 / 0.0009
n = 732.43076
n = 732 samples
B.)
If no prior estimate is given, then p = 0.5 ; 1 - p = 1 - 0.5 = 0.5
n = (Z² * p * (1 - p)) / M.E²
Zcritical at 90% = 1.645
n = (1.645² * 0.5 * 0.5) / 0.03²
n = 0.67650625 / 0.0009
n = 751.67361
n = 752 samples
The sum of two integers is 90 and their difference is 30. Find the larger number
Answer:
60 is the larger number
Step-by-step explanation:
Let the two numbers be a and y
x+y = 90
x-y = 30
Add the two equations together
x+y = 90
x-y = 30
-----------------
2x = 120
Divide by 2
2x/2 =120/2
x = 60
x+y =90
60+y = 90
y = 90-60
y = 30
The numbers are 60 and 30
Coefficient of y in the equation: 3(2x -1/3y) = 0 is equal to a) 3 b) 1 c)-3 d)-1
Answer:
d is the right answer because the coefficient of y is 3*(-1/3) which results -1 so d is the right answer
The coefficient of y in the given equation is 1. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 3(2x -1/3y)=0.
Now, 6x-1/y=0
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Here, coefficient of y is 1.
Therefore, option B is the correct answer.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
A sequence is defined recursively by the formula f(n+1)=-2f(n). The first term of the sequence is -1.5. What is the next term in the sequence ?
Answer:
next term is 3
Step-by-step explanation:
[tex]f(n+1)=-2f(n)\\\\f(1)=-1.5=-\frac{3}{2}f(2)=-2f(1)=-2*(-\frac{3}{2})=3[/tex]
Answer:
3
Step-by-step explanation:
Took the test and got this right.
please help me its timed -H.M
Answer:
f(3) = g(3)
General Formulas and Concepts:
Algebra I
Functions
Function NotationGraphingStep-by-step explanation:
We can see from the graph that the lines intersect at (3, 6). If this is the case, then that means that when x = 3 for both functions, it outputs f(x) = 6.
Rewriting this in terms of function notation:
f(3) = 6, g(3) = 6
∴ f(3) = g(3)
