Answer:
Step-by-step explanation:
Given that:
The height of the dock (h) = 6
Let represent d to be the distance between the boat and the dock
Let the length of the rope between the boat and the drum be denoted by (l)
Then, the rate of change for the length of the rope be:
dl/dt = -5 ft/s
Using Pythagoras rule to determine the relationship between these values, we have:
[tex]l^2 = h^2 +d^2[/tex]
[tex]l^2 = 6^2 + d^2[/tex]
[tex]l^2 = 36 + d^2[/tex]
We relate to: [tex]2l * \dfrac{dl}{dt} = 2d* \dfrac{dd}{dt}[/tex]
From the question;
l = 34,
So to find [tex]\dfrac{dd}{dt}[/tex], we get;
[tex]d = \sqrt{l^2 - 36}[/tex]
[tex]d = \sqrt{34^2 - 36}[/tex]
[tex]d = \sqrt{1156- 36}[/tex]
[tex]d = \sqrt{1120}[/tex]
d = 33.46
So, we have:
[tex]\dfrac{dd}{dt}= \dfrac{l}{d} \times \dfrac{dl}{dt}[/tex]
[tex]\dfrac{dd}{dt}= \dfrac{34}{33.46} \times - 5[/tex]
[tex]\dfrac{dd}{dt}= 1.016 \times - 5[/tex]
[tex]\dfrac{dd}{dt}=-5.08 \ ft/sec[/tex]
What value of x makes the following equation true?
15+3x=3(2−2x)
Answer:
[tex]\boxed {x = -1}[/tex]
Step-by-step explanation:
Solve for the value of [tex]x[/tex]:
[tex]15 + 3x = 3(2 - 2x)[/tex]
-Use Distributive Property:
[tex]15 + 3x = 3(2 - 2x)[/tex]
[tex]15 + 3x = 6 - 6x[/tex]
-Take [tex]6x[/tex] and add it to [tex]3x[/tex]:
[tex]15 + 3x + 6x = 6 + 6x - 6x[/tex]
[tex]15 + 9x = 6[/tex]
-Subtract both sides by [tex]15[/tex]:
[tex]15 - 15 + 9x = 6 - 15[/tex]
[tex]9x = -9[/tex]
-Divide both sides by [tex]9[/tex]:
[tex]\frac{9x}{9} = \frac{-9}{9}[/tex]
[tex]\boxed {x = -1}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]-1[/tex].
Which statements best describes the difference between interest and debt
Answer:
I think the answer is C, interest is a fee charged for borrowing money, dept is the total amount of money owed.
Which statement about the diagram is true
Answer:
AB have the length of 9
Step-by-step explanation:
5 is to short 14 is too long in between would be 9
7 cards are drawn from a standard deck of 52 playing cards. How many different 7-card hands are possible if the drawing is done without replacement?
Answer:
The number of different 7 card hands possibility is 133784560
Step-by-step explanation:
The computation of the number of different 7 card hands possibility is shown below:
Here we use the combination as the orders of choosing it is not significant
So,
The number of the different hands possible would be
= [tex]^{52}C_7[/tex]
= 52! ÷ (7! × (52 - 7)!)
= 133784560
Hence, the number of different 7 card hands possibility is 133784560
brainliest be good peeps Calculate the missing term in each
proportion.
2/11= /55
36/42= /
9/ = 21/28
6/9= /15
Answer:
10/55
6/7
9/12
10/15
4xº
(2x – 6°
33°
A. x= 31, y = 91
B. x= 31, y = 116
C. x = 56, y=91
D. x= 56, y = 116
For the number line shown which statement is not true
upload the picture...
What is the solution to this inequality?
4x + 2 5 -14 or 3x-5 > 16
OA.
X3-4 or x>7
OB.
-45x<7
O C.
xs-5 or x>8
OD.
x=-4
Answer:
A is the answer x ≤-4 or x>7
Step-by-step explanation:
Answer:
The answer is A, because they both have answers for each one.
A certain bacteria multiply exponentially at a rate of 8% per day. If 2 bacteria exist initially, how many
will be present after 25 days?
Answer:
After 25 days will be present about 13.70 ≅ 13 bacteria
Step-by-step explanation:
The form of the exponential function is y = a [tex](1+r)^{x}[/tex] , where
a is the initial valuer is the rate in decimal∵ A certain bacteria multiply exponentially at a rate of 8% per day
→ Assume that y is the number of bacteria, x is the number of days
∴ r = 8% = [tex]\frac{8}{100}[/tex] = 0.08
∵ 2 bacteria exist initially
∴ a = 2
→ Substitute them in the form of the equation above
∵ y = 2 [tex](1+0.08)^{x}[/tex]
∴ y = 2 [tex](1.08)^{x}[/tex]
∵ x = 25
→ Substitute x in the equation by 25
∴ y = 2 [tex](1.08)^{25}[/tex]
∴ y = 13.69695
∴ After 25 days will be present about 13.70 bacteria
Note: The number of bacteria must be the whole number so the answer should be 13 bacteria will be present after 25 days.
Pete wants to buy a new bike that costs $120 before any discount. Which offer should he choose to pay the least amount for the bike? NEED HELP PLEASE
For many important processes that occur in the body, direct measurement of characteristics of the process is not possible. In many cases, however, we can measure a biomarker, a biochemical substance that is relatively easy to measure and is associated with the process of interest. Bone turnover is the net effect of two processes: the breaking down of old bone, called resorption, and the building of new bone, called formation. A biomarker for bone formation measured was osteocalcin (OC), measured in the blood. The units are nanograms per milliliter (ng/ml). For the 31 subjects in the study the mean was 33.4 ng/ml. Assume that the standard deviation is known to be 19.6 ng/ml.
Required:
Give the margin of error and find a 95% confidence interval for the mean TRAP amount in young women represented by this sample.
Answer:
The margin of error is [tex]E = 6.9 [/tex]
The 95% confidence interval is [tex] 26.5 < \mu < 40.3 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 31
The mean is [tex]\mu = 33.4 \ ng/ml[/tex]
The standard deviation is [tex]\sigma = 19.6 \ ng/ml[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{19.6 }{\sqrt{31 } }[/tex]
=> [tex]E = 6.9 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 33.4 - 6.9 < \mu < 33.4 + 6.9 [/tex]
=> [tex] 26.5 < \mu < 40.3 [/tex]
A triangle has angles of 30° 60° and 90° It is dilated by a scale factor of three give the angle measures of the dilation of the triangle
The scale factor will create a similar triangle and thus there will be no change in angles so angles will still be 30° 60° and 90°.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
The scale factor is done due to the unpractical measurement of any figure.
Scale factor gives either a small or big similar image of a triangle, for example, if we have a triangle with vertices 2,4,6 and it is scaled by 1/2 then the resultant dimension will 1,2,3 but angles still remain the same.
Hence "The scale factor will create a similar triangle and thus there will be no change in angles so angles will still be 30° 60° and 90°".
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ANOTHER QUESTION PLEASE HELP
Answer:
c) 4
Step-by-step explanation:
Area of a square is its length times its length, or length²
Square root of 16 is 4
(04.04 LC)
On a coordinate grid, point T is at (2,-4) and point S is at (2,6). The distance (in units) between points T and S is
numbers, such as 2.)
Answer:
The distance between T and S is 10 units.
Step-by-step explanation:
Given the points
T(2, -4)S(2, 6)[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
The distance between T and S is:
[tex]=\sqrt{\left(2-2\right)^2+\left(6-\left(-4\right)\right)^2}[/tex]
[tex]=\sqrt{\left(2-2\right)^2+\left(6+4\right)^2}[/tex]
[tex]=\sqrt{0+10^2}[/tex]
[tex]=\sqrt{10^2}[/tex]
[tex]=10[/tex] ∵ [tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
Therefore, the distance between T and S is 10 units.
HELP ME PLEASEEEE!!
High School is selling Valentine's Day gifts as a fundraising event. One long stemmed rose costs $3.00 while one long stemmed carnation costs $1.50. If 50 orders were placed and they totaled $195, how many roses and carnations were ordered?
Answer:
11 roses and 12 carnations
Step-by-step explanation:
(11*3)+(1.50*3)=195
You walking against the wind. Your normal speed without the wind is 5mph. How long will it takes you to cover a distance of 5miles if the wind slow you down to 4/5 of your normal speed?
Answer:
1.25 hours
Step-by-step explanation:
So if you walk at 5 mph without wind, it takes you 1 hour to cover a 5 mile distance since you travel at a speed of 5 every hour. (5 mph). with the wind, your speed is 4 miles per hour because the wind slows you down to 4/5ths of your normal speed. 4/5ths of 5 is 4. It takes 1.25 hours to walk with the wind because 5(miles)/4(mph) is 1.25 hours. Hope this helps bud!
Equivalent fraction of 12/126
Answer:
2/21
Step-by-step explanation:
When do you draw a hole in a piecewise function?
Answer:
you just draw a circle indicating that it is a hole. Your welcome
Student can eat 1/8 of a pizza. If there are 24 students in David's class how many pizzas does David need
Answer: 7 boxes of pizza
Step-by-step explanation:
8x3=24
Answer:
David needs 3 pizzas.
Step-by-step explanation:
This is grammatically incorrect, but based on the information provided, I would infer that each student eats *only* 1/8 of a pizza. You would need 3 pizzas, as 3 x 8 =24.
Emily simplified this expression.
Expression: (5−2)2+23×4
Step 1: (3)2+23×4
Step 2: 9+23×4
Step 3: 9+9×4
Step 4: 9+36
Step 5: 45
Emily made a mistake. Which step shows her first mistake?
Step 1
Step 2
Step 3
Step 4
How many factors are in a B + CD + EF + GH
The given expression is
=ab+cd+ef+gh
The meaning of expression is equal to terms which contains variables and constants and operation between them is Addition, Subtraction, Multiplication and Division.
→The expression consists of four terms which are, ab, cd, ef, and gh.
→Each term contains
Two factors.
plz mark as brainliest
Total emissions of carbon dioxide from the burning of fossil fuels have been increasing at about 5% per year (data from 2010 to 2011). If emissions continue to increase at this rate, about how much higher will total emissions be in 2035 than in 2010? Using the approximate formula, emissions will increase by a factor of between 2010 and 2035. Using the exact formula, emissions will increase by a factor of between 2010 and 2035. (Round to two decimal places as needed.)
Answer:
125%
Step-by-step explanation:
5% multipled by 25 years (from 2010 - 2035) = 125%
And i aint never seen to pretty best friendsssss
If emissions continue to increase at this rate, then about 125% higher total emissions will be in 2035 than in 2010.
What is the fundamental principlmultipliediplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that Total emissions of carbon dioxide from the burning of fossil fuels have been increasing at about 5% per year.
Using the approximate formula, we can see that the emissions will increase by a factor of between 2010 and 2035.
Using the exact formula, it can be seen that the emissions will increase by a factor of between 2010 and 2035.
Therefore, 5% multipled by 25 years (from 2010 - 2035)
0.05 x 25 = 125%
If emissions continue to increase at this rate, then about 125% higher total emissions will be in 2035 than in 2010.
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The following steps show how the right side of 1 – cos(2x) = tan(x)sin(2x) can be rewritten to show it is an identity.
tan(x)sin(2x)
= tan(x)∙[2sin(x)cos(x)]
= StartFraction sine (x) Over cosine (x) EndFraction times 2 sine (x) cosine (x)
= 2sin2(x)
= 1 – cos(2x)
What are the correct justifications, listed in proper order?
Double Angle Identity, Quotient Identity for Tangent, Simplify, Double Angle Identity
Double Angle Identity, Simplify, Double Angle Identity, Quotient Identity for Tangent
Double Angle Identity, Simplify, Quotient Identity for Tangent, Double Angle Identity
Double Angle Identity, Quotient Identity for Tangent, Double Angle Identity, Simplify
Double Angle Identity, Quotient Identity for Tangent, Simplify, Double Angle Identity
The following steps show how the right side of 1 – cos(2x) = tan(x)sin(2x) can be rewritten to show it is an identity is option A
Double Angle Identity, Quotient Identity for Tangent, Simplify, Double Angle Identity.
What is double angle identity?The sin2x formula is the double angle identity used for sine function in trigonometry. Trigonometry is a branch of mathematics where we study the relationship between the angles and sides of a right-angled triangle. The formula for sin2x: sin2x = 2 sin x cos x (in terms of sin and cos)
Given
1 – cos(2x) = tan(x)sin(2x)
Taking R.H.S
tanx.sin2x
= tanx(2 sinx cosx)
2 sinx cosx is a double angle identity
= [tex]\frac{sinx}{cosx} .(2 sinxcosx)[/tex]
[tex]\frac{sinx}{cosx}[/tex] is a quotient identity for tangent
= [tex]2sin^{2} x[/tex]
We have simplify by cancelling out cosx.
= 1 - cos(2x)
It is a double angle identity.
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Given the point and slope write the equation of the line (6, -6); slope = 5/6
Answer:
y=5/6x-11
Step-by-step explanation:
Slope intercept form: y=mx+b
With slope: y=5/6x+b
Replace x with 6 and y with -6
[To figure out which one is x or y remember (x,y) so if you compare (6,-6) then you will find that 6 is x and -6 is y]
-6=5/6(6)+b
Simplify:
-6=5+b
Subtract 5 on both sides:
-11=b or b=-11
Answer:y=5/6x-11 (Replace the b in y=5/6x+b with -11 since -11 is equal to b)
Hope this helps!
Help me plzzz i need help.
Answer:
Perimeter: 7.8Area: 3.1Step-by-step explanation:
Perimeter = all sides added up together2.8 + 2.8 + 1.1 + 1.1 = 7.8Area = L × W2.8 × 1.1 = 3.08Round 3.08 to the nearest tenth: 3.08 → 3.1I hope this helps!
Enter the sum of the numbers as the product of their GCF and another sum.
35 + 56
The sum of the numbers as a product of their GCF is . please help im on a test!
Answer:
8
Step-by-step explanation:
Explanation: The GCF of 56 and 64 is 8 , as 8 goes into 56 exactly 7 times and into 64 exactly 8 times. 8(8)+7(8)=8(7+8).
which expression is equivalent to 2n+n-0.65n
3n-0.65
3n - 0.35
2.65n
2.35n
Evaluate the expression 2x^2-y^1+3x^0 for x=3 and y=7
Answer:
14
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Suppose a team is to be formed consisting of a head chef, sous chef, and dishwasher, in that order. What is the probability of forming such a team with 6 people?
Answer:
0.0083
Step-by-step explanation:
From the given information;
The total number of individual in the team = 3
The number of ways the team, which comprises of head chef, sous chef, and dishwasher can be arranged = [tex]^{6}P_3[/tex]
= (6×5×4×3!)/3!
= 6×5×4
= 120 ways
The probability of forming such a team with 6 people = 1/120
= 0.0083
The diameter of a circle is 6 millimeters. What is the circle's area?
d=6 mm
Use 3.14 pi
Answer:
28.26 mm
Step-by-step explanation:
The equation used to solve for the area of a circle is;
A=pi x r^2.
The radius is half the diameter, 6mm/2= 3mm.
A= 3.14 x 3^2
3^2= 9
3.14 x 9 = 28.26 mm
or you could just type 3.14 x (3^2) = 28.26mm