It takes 14.4 minutes for the radiator fluid temperature to reach 60 degrees Fahrenheit
A function is said to be linear if it is a straight line graph and it can be represented by the equation:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the temperature in Fahrenheit of the radiator after t minutes.
Stanley’s car is Negative 18 degrees Fahrenheit. Hence b = -18. The temperature of the fluid goes up 5.4 degrees Fahrenheit per minute. hence m = 5.4. The equation becomes:
y = 5.4x - 18
For the radiator fluid temperature to reach 60 degrees Fahrenheit:
60 = 5.4x - 18
5.4x = 78
x = 14.4 minutes
It takes 14.4 minutes for the radiator fluid temperature to reach 60 degrees Fahrenheit
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1) A very lucrative savings account earns 2.8% annual interest, compounded monthly. It is currently worth $10,427.39. How much was it worth a year and a half ago?
926+729299277=5289+83783
Plx = 3 + 5x+2
Degree
Leading coefficient
Turning Points
End
Behavior of the
Graph
Answer:
cost of renting from company A
C = 15 + 2.30x
cost of renting from company B
C = 22 + 1.90x
equate both the equations
15 + 2.30x = 22 + 1.90x
2.30x - 1.90x = 22-15
0.4x = 7
x = 7/0.4 = 17.5
At 17.5 miles, cost will be equal.
Answer: 17.5 miles
If the Owen family has a child in two years, how much can they expect to spend, per year, to raise the child from its birth to when it is five years old?
Answer: A. 65,250+139,560= 204,810. 204,810/18=11,378
I hope it is right
Answer:
The answer would be 13,050
Step-by-step explanation:
In order to get the answer, you have to do 65,250 divided by 5 years and you should get 13,050 on your calculator.
problem referred below
pls help
Answer:
B
7 less than 3 times a number (X) is (3x-7), and then the sum of these two numbers means we have (3x-7)+X, and then we know this equals 109, leaving us with:
(3x-7)+x = 109
is {(-2,1),(-1,2),(0,3),(1,4) } a function?
Think of it this way, a function must pass the vertical line test. There may not be 2 outputs for one input for example (0, 1) (0, 2) However, you can have something like this (1, 0) (2, 0)
This is indeed a function as it meets those criterion. There are no two outputs for one input.
A student is failed due to 10 marks after obtaining 90 marks in full marks of 250. what percentage marks does he require to pass?
Answer:40
Step-by-step explanation:
[tex] \displaystyle \int \limits_{0}^{ \frac{ \pi}{2} } \tt\tan (x) \ln ( \sin (x))[/tex]
Let [tex]x = \arcsin(y)[/tex], so that
[tex]\sin(x) = y[/tex]
[tex]\tan(x)=\dfrac y{\sqrt{1-y^2}}[/tex]
[tex]dx = \dfrac{dy}{\sqrt{1-y^2}}[/tex]
Then the integral transforms to
[tex]\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_{y=\sin(0)}^{y=\sin\left(\frac\pi2\right)} \frac{y}{\sqrt{1-y^2}} \ln(y) \frac{dy}{\sqrt{1-y^2}}[/tex]
[tex]\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy[/tex]
Integrate by parts, taking
[tex]u = \ln(y) \implies du = \dfrac{dy}y[/tex]
[tex]dv = \dfrac{y}{1-y^2} \, dy \implies v = -\dfrac12 \ln|1-y^2|[/tex]
For 0 < y < 1, we have |1 - y²| = 1 - y², so
[tex]\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = uv \bigg|_{y\to0^+}^{y\to1^-} + \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy[/tex]
It's easy to show that uv approaches 0 as y approaches either 0 or 1, so we just have
[tex]\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy[/tex]
Recall the Taylor series for ln(1 + y),
[tex]\displaystyle \ln(1+y) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n y^n[/tex]
Replacing y with -y² gives the Taylor series
[tex]\displaystyle \ln(1-y^2) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n (-y^2)^n = - \sum_{n=1}^\infty \frac1n y^{2n}[/tex]
and replacing ln(1 - y²) in the integral with its series representation gives
[tex]\displaystyle -\frac12 \int_0^1 \frac1y \sum_{n=1}^\infty \frac{y^{2n}}n \, dy = -\frac12 \int_0^1 \sum_{n=1}^\infty \frac{y^{2n-1}}n \, dy[/tex]
Interchanging the integral and sum (see Fubini's theorem) gives
[tex]\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy[/tex]
Compute the integral:
[tex]\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy = -\frac12 \sum_{n=1}^\infty \frac{y^{2n}}{2n^2} \bigg|_0^1 = -\frac14 \sum_{n=1}^\infty \frac1{n^2}[/tex]
and we recognize the famous sum (see Basel's problem),
[tex]\displaystyle \sum_{n=1}^\infty \frac1{n^2} = \frac{\pi^2}6[/tex]
So, the value of our integral is
[tex]\displaystyle \int_0^{\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \boxed{-\frac{\pi^2}{24}}[/tex]
[tex]\displaystyle \int \limits_{0}^{ \frac{ \pi}{2} } \tt\tan (x) \ln ( \sin (x))\\ \\\displaystyle \sf{ \implies \: I = \int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin \left( \dfrac{\pi}{2} - x \right) \right) \: dx } \\ \\\displaystyle \sf{ \implies \: I = \int^{ \frac{\pi}{2} }_{0} \: \ln \left( cos(x) \right) \: dx } \\ \\\displaystyle \sf{ \implies \:2I =\int^{ \frac{\pi}{2} }_{0} \:\ln \left( sin(x) \right) \: dx + \int^{ \frac{\pi}{2} }_{0} \: \ln \left( cos(x) \right) \: dx } \\ \\\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin(x) \right) +\ln\left( cos(x) \right) \: dx }[/tex]
[tex]\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin(x) \: cos(x) \right) \: dx } \\ \\\displaystyle\sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( \dfrac{sin(2x)}{2}\right) \: dx } \\ \\\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \:\ln \left( sin(2x) \right)\:dx-\ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx}[/tex]
Put 2x = t, so,[tex]\displaystyle\sf{ \implies \: 2I = \dfrac{1}{2} \int^{ \pi}_{0} \: \ln \left( sin(t) \right) \:dt - \ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx} \\ \\\displaystyle\tt{ \implies \: 2I = \dfrac{1}{2} \cdot2 \int^{ \frac{\pi}{2}}_{0} \: \ln \left( sin(t) \right) \: dt - \ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx}[/tex]
[tex]\displaystyle \tt{ \implies \: 2I =\int^{ \frac{\pi}{2}}_{0} \: \ln \left( sin(t) \right) \: dt - \ln(2)\int^{ \frac{\pi}{2} }_{0} \: dx} \\ \\ \displaystyle \tt{ \implies \: 2I = I - \ln(2) \left[x \right] ^{ \frac{\pi}{2} }_{0} } \\ \\ \displaystyle \tt{ \implies \: I = -\ln(2)\left[ \dfrac{\pi}{2} - 0 \right] }[/tex]
[tex]\displaystyle \sf{ \implies \: I = - \dfrac{\pi}{2} \ln(2) }[/tex]
_____________________☞︎︎︎Apologies,if incorrect.
please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1 is 12
2 is 106
3 is 42
Step-by-step explanation:
1: PEMDAS. 5x2=10 4 to the power of 2 is 16 so 18-16=2 2+10=12
2: 9 to the power of 2 is 81. 4x7=28 28-3=25 81+25=106
3: 5 to the power of 2 is 25 7x3=21 25-4=21 21+21=42
Productivity gains are an important factor in the expenditure model because
A. companies can “squeeze” workers more than normal
B. it shifts the AD curve to the left
C. the investments made are cheaper and allows companies to
D. it shifts the AS curve to the right
Answer:
A
Step-by-step explanation:
companies can squeeze workers more than normal
Where , the distance between the points ( a, c) and ( b, c) is ( ) units
Answer:
I would love to help but there is no upload. Would you mind creating a new question with a picture or data of the graph
Step-by-step explanation:
please help with t his question
Answer: 15 inches
Step-by-step explanation:
15 × 1 ÷ 12 = 1.25 ft
1.25 ft = 1.25 × 12 = 15 in
Leonard conducts a study to see if the number of hawks in a park affects the number
of squirrels. What is the response variable in this study?
A.The number of hawks in the park
B.The number of squirrels in the park
In the experiment, the response variable is the dependent variable, or the measured variable.
The response variable in the study is; B. The number of squirrels in the parkReasons:
The study Leonard conducts is a study to determine if the number of
hawks located in the park affects the number of squirrels in the park.
The response variable is the variable of the experimental result, which is
the dependent or output variable obtained by manipulating the input
variable.
In the experiment conducted by Leonard, the variable that is being
manipulated, which is the input variable is the number of hawks in the park
The variable that is being measured, which is the output variable or the
response variable, is; B. the number squirrels in the park.
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Whats the area and the perimeter of this shape. show calculations
Answer:
The answer is 15 cm
Step-by-step explanation:
as one square is 1 cm and there are 15 squares used for this shape then it is 15 cm
1 pts
Compute the total amount accumulated if you invested $850 for 4 years at 2.4% compounded
semiannually. Round your answer to the nearest cent and include '$' in your response.
9514 1404 393
Answer:
$935.11
Step-by-step explanation:
The amount is given by the formula ...
A = P(1 +r/n)^(nt) . . . P invested at rate r for t years compounded n per year
A = $850(1 +0.024/2)^(2·4) = $935.11
The amount accumulated will be $935.11 after 4 years.
simplify the expression (b+3)+(2b-2)
Answer:
if you meant (b+3)+(2^b-2), the answer is b+1+2^b
Step-by-step explanation:
but if you meant (b+3)+(2b-2), the aanswer is 3b+1
Answer:
3b+1
Step-by-step explanation:
(b+3)+(2b-2)
b+3+2b-2
3-2
b+1+2b
b+2b
3b+1
Toby and Emily went to the grocery store to buy food for breakfast for the week. They needed 8 bananas, 2 loaves of bread, 1 bottle of OJ, 1 gallon of milk and a dozen eggs. Each banana was .25, each loaf of bread was 2.55, a bottle of OJ was $2.45 and dozen eggs were $3.15. How much money in total did Toby & Emily spend?
Answer:
$12.70
Step-by-step explanation:
8 x .25 = 2
2 x 2.55 = 5.10
1 x 2.45 = 2.45
1 x 3.15 = 3.15
__________
2 + 5.10 + 2.45 + 3.15 = 12.70 = $12.70
Answer:
they spent $15.85 in all.
Step-by-step explanation:
2.00 banana 5.10 bread 2.45 oj and 3.15 egg, add it all.
From a club with 12 members, how many ways could you choose a committee of 5?
Step-by-step explanation:
that is 12 over 5
12! / (5! × (12-5)!) = 12×11×10×9×8/5×4×3×2 =
= 11×9×8 = 792
Write each decimal as a percent. 1. 0.74
4. 0.617 =
Write each percent as a decimal. 6. 68%
9. 175% =
2. 0.15 =
5. 0.834 =
7. 34% =
10. 200% =
3. 0.09 =
8. 58.5% =
Answer:
1. 0.74 = 74%
4. 0.617 = 61.7
6. 68% = 0.68
9. 175% = 1.75
2. 0.15 = 15%
5. 0.834 = 83.4%
7. 34% = 0.34
10. 200% = 2.00
3. 0.09 = 9%
8. 58.5% = 0.585
Step-by-step explanation:
A desk is 39 inches wide. What is the width in yards
Answer:
1.0833 yd
Step-by-step explanation:
Inches Yards
37" 1.0278 yd
38" 1.0556 yd
39" 1.0833 yd
40" 1.1111 yd
Have a great day! :D
Flying Home A bird flies from the bottom of a canyon that is 844 9/10 feet below sea level to a nest that is 55 4/5 feet above sea level. What is the difference in elevation between the bottom of the canyon and the bird's nest? The difference between the elevation of the canyon and the bird's nest is enter your response here feet. (Simplify your answer. Type an integer, proper fraction, or mixed number.)
Answer:
900 7/10
Step-by-step explanation:
you add the numbers to gether
Kim Barney pays a $290.00 annual premium for an insurance plan with a $500 deductible. The company pays 80% of the remaining expense. If Kim had $2,500.00 in medical expenses, calculate the following.
The amount that Kim Barney spends is $342 for medical expenses.
What is buying cost?Buying cost is the cost at which someone buys or is willing to buy shares, bonds.( including the tax)
here, we have,
Given that,
Kim Barney pays a $290.00 yearly premium for a $500.00 deductible insurance plan. 80 percent of the remaining cost is covered by the business. If Kim has medical costs of $2,500.00
To find : The amount that Kim barney spends for the medical expenses.
If the business covers 80% of the remaining balance ($1710), they will be responsible for paying $1368 of it.
10% of 1710 is 171
171x8=1368
The insurance provider covers the $1368.
Kim Barney spends $342.
Consequently, Kim Barney spends the following amount on medical costs $342.
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How many gallons of a 90% antifreeze solution must be mixed with 100 gallons of 10% antifreeze to get a mixture that is 80% antifreeze? Use the six-step method.
2. In the formula I = P x r x t, what does r stand for? a. Rate: the percent that interest is paid annually as a decimal b. Ratio: the size of the interest interval compared to time c. Return: how much money you end up earning d. Reserves: how much money you have in the investment
Answer:
I will answer this soon I don't remember
Answer:
A. Rate: the percent that interest is paid annually as a decimal
Step-by-step explanation:
Edge 2022 got the answer right :)
Subtraction as Adding the Opposite
please help i am stuck
Explanation:
All of these are done the same way.
1. Set your compass to a distance slightly longer than the distance from the point to the line you want the perpendicular to.
2. Using the point as a center, draw an arc that intersects the line in 2 places. Consider those points to be "P" and "Q".
3. You can leave the compass as is, or set it to any other distance longer than half the distance between P and Q. Using this radius, and using P and Q as centers, draw intersecting arcs on the other side of the line from the original point. Consider the intersection of those arcs to be point "R".
4. A line through the original point and point R will be perpendicular to the line, as you want.
_____
In problem 1, the point and line are obvious.
In problem 2, the point is the vertex opposite the line of interest. (There will be 3 similar constructions.)
Select all ratios equivalent to 4:16.
3:12
6:48
5:4
Answer
Step-by-step explanation:
neither
brainlest
4(x - 4) + 2x -10 and what the answer
Answer:
Expression: 6x - 26. Equation: 3
Step-by-step explanation:
EXPRESSION
4x - 16 + 2x - 10
6x - 26
EQUATION 1
4x - 16 = 2x - 10 (Seems reasonable. Sorry if this isn't it)
4x = 2x + 6
2x = 6
x = 3
EQUATION 2
4x - 16 + 2x = - 10
6x - 16= -10
6x = 6
x = 1
the ratio of collectible pennants kyle owns to pennants that yasmine owns is 3:2 yasmine has 36 pennants . How will the ratio of kyles pennants to yasmines pennants change if they both sell half of their pennants Explain
Answer:
If they both sell half then Kyle would have 1.5:1 and Yasmine would have 18 pennants.
Step-by-step explanation:
It will change because if they both sell half, they would have to multiply by .05 or divide by 2 because that is half of something.
3/2 or 3*0.5 = 1.5
2/2 or 2*0.5 = 1
36/2 or 36*0.5 = 18
So Kyle would have 1.5:1 pennants left and Yasmine would have 18 pennants left.
A dozen gulab jamuns cost 3.49 how much will 5 dozen cost
Answer:
17.44
Step-by-step explanation:
if one dozen cost $3.49 than 3.49 × 5 = 17.44
At the beginning of spring, Caroline planted a small sunflower in her
backyard. When it was first planted, the sunflower was 15 inches tall.
The sunflower then began to grow at a rate of 2.5 inches per week.
How tall would the sunflower be after 10 weeks? How tall would the
sunflower be after w weeks?
Height after 10 weeks:
Answer:
After 10 weeks: 40 inches
Step-by-step explanation:
Equation
15 + 2.5w = h
15 = beginning height
2.5 = rate per week
w = weeks passed
h = total height
Two or more expressions with an Equal sign is called as Equation.15+2.5W tall l would the sunflower be after w weeks and 40 inches tall after 10 weeks.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that, At the beginning of spring, Caroline planted a small sunflower in her backyard
The initial height of the sunflower was 15 inches tall.
The sunflower then began to grow at a rate of 2.5 inches per week.
We need to find the height of the tree after 10 weeks.
15+2.5(10)
15+25
40 inches tall after 10 weeks.
the sunflower height after w weeks
15+2.5W
Hence 15+2.5W tall l would the sunflower be after w weeks and 40 inches tall after 10 weeks.
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