Hooke's Law says that the force exerted by the spring in a spring scale varies directly with the distance that the spring is stretched. If a 20 pound mass suspended on a spring scale stretches the spring 20 inches, how far will a 29 pound mass stretch the spring? Round your answer to one decimal place if necessary.
The Hooke's law is given by:
F = k*x
Where:
F = force
k = constant factor
x = distance
If F = 20 and x = 20
20 = k*20
Solving for k:
20/20 = k
k = 1
So: how far will a 29 pound mass stretch the spring?
29 = 1* x
Solving for x:
29/1 = x
x = 29 in
A firm incurs $70,000 in interest expenses each year. If the tax rate of the firm is 30%, what is the effective after-tax interest rate expense for the firm?
Answer:
After tax interest expenses = Interest expenses x (100 - Tax Rate)
= 70000 x (100 - 30)%
= 70000 x 70%
= $49,000.00
Step-by-step explanation:
740In the table on the right there are grades that were earned by students on a midtermbusiness math exam What percent of the students earned a grade below 80?83977084986685687783958879648890859396The percent of students with grade below 80 is(Round to the nearest whole number as needed)
Notice that the number of students that got a grade below 80 is:
[tex]7,[/tex]and the total number of students is:
[tex]20.[/tex]Therefore, we have to determine what percentage 7 represents from 20. To determine the percentage that x represents from y, we can use the following expression:
[tex]\frac{x}{y}*100.[/tex]Finally, we get that 7 represents the
[tex]\frac{7}{20}*100=35\%,[/tex]of 20.
Answer:
[tex]35\%.[/tex]Sonia opened a savings account and then added the same amount to the savings account every week. After 5 weeks, her savings account had a total of $45. After 10 weeks, her savings account had a total of $70. Which equation represents the amount of money (y), in dollars, in Sonia's savings account after x weeks?
First let's find the amount Sonia puts in her account each week.
To do so, let's find the amount increased between weeks 5 and 10:
[tex]70-45=25[/tex]The account increased $25 in 5 weeks, so for each week, we have:
[tex]\frac{25}{5}=5[/tex]So Sonia puts $5 in her account each week. Now, we need to find the initial value in the account. If after 5 weeks the account has $45, we can subtract $45 by 5 times the amount per week:
[tex]45-5\cdot5=45-25=20[/tex]So the initial amount is $20.
Now that we have the initial amount and the amount she puts per week, we have the following equation for the amount of money y after x weeks:
[tex]y=5x+20_{}[/tex]So the correct option is the third one.
Part 1: Factorial! 3. What are the pros and cons to using the factorial function on your calculator in terms of understanding and/or thecalculation itself?
Explanation
We are required to determine the pros and cons of using the factorial function on the calculator.
Hence, the answers are:
- Pros
• It makes calculation easier.
,• It makes calculations to be done in an efficient manner.
,• It helps students to solve complicated questions seamlessly.
- Cons
• It cannot help with large numbers as the calculator has limited space for answer preview.
,• It does not help to understand better how the calculation is done.
Glven: 3x - 2 = 2(x + 1)Prove: x=4REASONSTATEMENT1. 3x - 2 = 2(x + 1)30.2. 3x - 2 = 2x + 231.3. X-2= 232.4. x= 433.Word Bank:A. Distributive PropE. Transitive PropC. Substituion PropD. Subtraction PropB. GivenF. Addition Prop
you have the following equation:
3x - 2 = 2(x+1)
You have to specify the property used in each step to get the solution of the previous equation. You obtain the following:
1. 3x - 2 = 2(x + 1) given
2. 3x - 2 = 2x + 2 distribution prop
3. 3x - 2x - 2 = 2x - 2x + 2 subtraction 2x both sides - subtraction prop
x - 2 = 2
4. x - 2 + 2 = 2 + 2 summation 2 both sides - addition prop
x = 4
Use the graph of 'f' in the figure below to answer the following questions. 1. State the domain and range of 'f'.2. Find the average rate of change of 'f' over the interval [0,6].
The domain of the given function corresponds to:
[tex]\lbrack-4,-2)\cup(-2,6)[/tex]And the range of the function is:
[tex](-2,6)[/tex]The average rate of change of f over the interval [0,6] is:
[tex]\frac{5.5-(-2)}{0-6}=\frac{7.5}{-6}=-\frac{5}{4}=-1.25[/tex]what is the solution to the system 3x-y+5=02x+3y-4=0A. X= -1, Y= -2B. X= -1, Y= 2C. X= 2, Y= -1D. X= 2, Y= 1
To find the solution to the system of equation
we will use the elimination method
3x - y = - 5 ----------------------------(1)
2x + 3y = 4 -------------------------------(2)
We will eliminate y and solve for x
multiply equation (1) through by 3
9x - 3y = - 15 ------------------------------------(3)
add equation (2) and equation (3)
11x = -11
divide both-side of the equation by 11
x = -1
substitute x = -1 in equation (1) and solve for y
3x - y = - 5
3(-1) - y = -5
-3 - y = -5
add 3 to both-side of the equation
- y = -5 +3
-y = -2
multiply through byb -1
y = 2
Hence, the correct option is B
Find an equation for the line that passes through the points (-2,-6) and (6,-4).
Answer:
[tex](y+6)=\frac{2}{8} (x+2)[/tex]
Step-by-step explanation:
First, find the slope
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
-4+6=2
6+2=8
m=2/8
With the slop, you have everything you need to stick one of your points in point-slope form. I chose (-2,-6)
[tex](y-y1)=m(x-x1)\\(y+6)=\frac{2}{8} (x+2)[/tex]
Really, that's all you need as it is not an equation of a line. Not the most useful form, but works as an answer.
In which of the following triangles does m
Okay let's analyze each triangle
In triangles A, B, and D the angle
students at a local school were asked about how many hours do you spend on homework each week? the table shows the results of the survey classify the statement below as a true or false more students study for 3 to 4 hours than for 5 to 6 hours the statement is (true or false) because.... students study for 3 to 4 hours and..... students study for 5 to 6 hours.
The total of students that study for 3 to 4 h is 147
The total of students that study for 5 to 6 h is 107
Then, the statement: "more students study for 3 to 4 hours than for 5 to 6 hours" is true because 147 students study for 3 to 4 hours and 107 students study for 5 to 6 hours.
Help me pls on math homework!!!!!
He sold 28 watermelons on Friday.
How to find the number of watermelons sold on Friday?The number of watermelons sold during the entire week is of 60, hence we find the daily amounts and add them, and this has to reach 60. The daily amounts are given as follows:
Monday: x.Tuesday: 2x. (twice as many as Monday).Wednesday: 0.5x. (half as many as Monday).Thursday: 18.Friday: 6x + 4. (four more than twice the amount sold on Monday).Hence the following equation is built, and we can solve for the unknown variable x as follows:
x + 2x + 0.5x + 18 + 6x + 4 = 60.
9.5x = 38
x = 38/9.5
x = 4
Then the amount sold on Friday is calculated as follows:
Friday = 6x + 4 = 6(4) + 4 = 24 + 4 = 28 watermelons.
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He sold 28 watermelons on Friday
What is the number of watermelons he sold on Friday?The total number of watermelons sold for the whole summer week is 60
He sold x watermelons on Monday
On Tuesday, he sold twice the numbers sold on Monday: 2x
On Wednesday, he sold half the numbers sold on Monday: x/2
On Thursday, he sold 18
On Friday, he sold:
= 2(x+2x) + 4 = 2(3x) + 4 = 6x + 4
And we know that the total number of watermelons is 60. Therefore:
x + 2x + x/2 + 18 + 6x+4 = 60
9.5x + 22 = 60
9.5x = 60 - 22
9.5x = 38
x = 4
since the amount sold on Friday is 6x+4:
= 6 x 4 + 4
= 24 + 4 = 28
Therefore, he sold 28 watermelons on Friday
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Two cars are driving on the same road, in the same
direction. They start driving from the same place and are
traveling at a constant speed. The second car started
driving 1.5 hours after the first car started driving. If the
second car drives 60 miles per hour and the first drives 40
miles per hour, how many miles will each car have
traveled when the second car catches up to the first?
Answer:
180 miles
Step-by-step explanation:
distance = rate x time
t = time
1st car:
distance = 40t
2nd car:
distance = 60(t - 1,5)
When the car catch up to each other the distances will be the same, so set the equation equal to each other. Calculate the time and then put the time back into either equation and solve for the distance.
40t = 60(t-1.5) Distribute the 60
40t = 60t -(60)1.5
40t = 60t - 90 Subtract 60t from both sides of the equation
-20t = -90 Divide both sides by -20
t = 4.5
Now that we know the time, substitue that back into either equaiton and solve for the time
distance = 40 (4.5)
180 miles
Kuta Sotware - Infinite Algebra 2 Solving Inequalities Solve each inequality and graphite 10 > Kuin Software - Infinite Algebra 2 Graphing Linear Inequalities Sketch the graph of each linear inequality. Name Samante 1) yz-2x-2 Y-2-2 2). ys - !
Could you please send a picture of the inequality you are asked to solve?
I'll be closing the session now if you cannot do it. Please ask your question again, and send the image in the question itself to avoid this problem of your uploaded images and messages not getting to me.
Thank you, and please re-submit your question request.
. Identify the difference. -2-(-6)
In this case,
This difference is made this way:
-2 - (-6) =
-2 +6 = 4
So there we have this identity. The minus before the parentheses turns the minus into plus sign.
Given that angle A lies in Quadrant IV and cos(A)= 7/10, evaluate sin(A).
The value of the trigonometric function is; sin(A) =√51/10.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We have been given that angle A lies in Quadrant IV and cos(A)= 7/10 then;
cos(A)= 7/10
Hence, base = 7
hypotenuse = 10
Therefore, perpendicular
h² = b² + p²
10² = 7² + p²
100 = 49 + p²
p = √51
Then sin(A = perpedicular/ hypotenuse
sin(A) = √51/10
Hence, the value of the trigonometric function is; sin(A) =√51/10.
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Write each of the following products (the result to a multiplication problem) using exponents to express the results in a simpler form.(3a)(5a) __________(5p)(2p) ___________(3 inches)(5 inches)___________(5 feet)(2 feet)_________
Let's do the mutiplications:
(3a)(5a) = 15a²
(5p)(2p) = 10p²
(3 inches)(5 inches) = 15 inches²
(5 feet)(2 feet) = 10 feet²mutiplic
The recursive rule for a sequence and one of the specific terms is given. Find the position of the giving term. f(1)= 8 1/2; f(n)= f(n-1) - 1/2; 5 1/2
f(7) gives 5 1/2.
the position is the 7th term
Explanation:
f(1)= 8 1/2
f(n)= f(n-1) - 1/2
we are looking for the function that gives 5 1/2
We have been given f(1), this means n = 1
f(1) = f(1-1) - 1/2
8 1/2 = f(0) - 1/2
f(0) = 8 1/2 + 1/2
f(0) = 8 + 1 = 9
when n = 2
f(2) = f(2-1) - 1/2
f(2) = f(1) - 1/2
f(2) = 8 1/2 - 1/2
f(2) = 8
when n = 3
f(3) = f(3-1) - 1/2
f(3) = f(2) - 1/2
f(3) = 8 - 1/2
f(3) = 7 1/2
when x = 4
f(4) = f(4-1) - 1/2
f(4) = f(3) - 1/2
f(4) = 7 1/2 - 1/2
f(4) = 7
when n = 5
f(5) = f(5-1) - 1/2
f(5) = f(4) - 1/2
f(5) = 7 - 1/2
f(5) = 6 1/2
f(6) = f(6-1) - 1/2
f(6) = f(5) - 1/2
f(6) = 6 1/2 - 1/2 = 6
when n = 7
f(7) = f(7-1) - 1/2
f(7) = f(6) - 1/2
f(7) = 6 -1/2 = 5 1/2
f(7) gives 5 1/2.
Hence, the position is the 7th term
what number is divisible by 5 ? 86,764,670,or27
The number divisible by 5 is 670.
Numbers divisible by 5 have their last digits as 0 or 5
Answer : 670
Alec wants to purchase a new phone that costs $219.00. His current average net pay is $212.34 each week. What percent of his weekdy net pay does Alec need to save each week, for the next seven weeks, to reach
his goal? Round to the nearest hundredth (1 point)
9.69%
14.73%
O 21.76%
31.28%
Answer:
14.73%
Step-by-step explanation:
firstly let's divide the phone price into 7 equal parts. by this equation 219.00/7=31.28
So Alec needs to save $31.28 but we want the percentage.
by equation x%*212.34=31.28
x=(31.28*100)/212.34=3128/212.34=14.73
so Alec needs to save 14.73% of 212.34 each week.
Which phrase represents the algebraic expression for n-4.A) The quotient of a number and 4. B) 4 less than a number. C) 4 minus a number. D) 4 more than a number.
B) 4 less than a number.
A rectangular room is 1.8 times as long as it is wide, and its perimeter is 29 meters. Find the dimension of the room. The length is : meters and the width is meters.
Let's say x is going to be the number meters of the width of the room:
x: width
Since its lenght is 1.8 as it is width, then it will be 1.8 · x long:
1.8x: lenght
Step 2: relating the expressions for each side to its perimeterWe know that the perimeter of a rectangle is given by
Perimeter = 2· (width + lenght)
We know that the perimeter is 29 meters, then
Perimeter = 29
↓
29 = 2· (width + lenght)
We do know an expression for its width and lenght, we replace them:
29 = 2· (width + lenght)
↓
29 = 2· (x + 1.8x)
Step 3: finding xSince x + 1.8x = 2.8x:
29 = 2· (x + 1.8x)
↓
29 = 2· (2.8x)
↓ 2· 2.8 = 5.6
29 = 5.6x
↓ dividing both sides by 5.6
29/5.6 = 5.6x/5.6
5.2 = x
Final step: finding its dimensionsSince
x: width
then
Width = 5.2 meters
Since
1.8x: lenght
then
Lenght = 1.8 · 5.2 meters = 9.36 meters
Answer: the dimensions of the room are Width = 5.2 meters and Lenght = 9.36 meters
Brian is looking to add tile to one wall in his kitchen, each tile is a rectangle that measures
14 inches by 2 inches. The wall that Brian wants to tile is a rectangle that measures
44.25inches by 51 inches. How many bie's will Brian need to cover the wall?
Using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.
What is a rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can also be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.So, tiles needed to cover the wall:
The formula for the area of a rectangle: l × bCalculate the area of a tile as follows:
l × b14 × 228 in²Now, calculate the area of the wall as follows:
l × b44.25 × 512,256.75 in²Then, tiles needed to cover the wall:
2,256.75/2880.59Which means: 80½
Therefore, using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.
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A pool is filled to 3/4 of its capacity 1/9 of water in the pool, evaporates. If the pool can hold 24,000 gallons when it is full, how many gallons of water will have to be added in order to fill the pool?A. 6,000B. 8,000C.12,000D.16,000
First, the pool was filled to 3/4 of its capacity, which is equal to:
[tex]24000\cdot\frac{3}{4}gal=18000gal.[/tex]Then, 1/9 of the water evaporated remaining 8/9 of the 18000 gal:
[tex]18000\text{gal}\frac{8}{9}=16000gal.[/tex]Therefore, to fill the pool we need to add:
[tex]24000-16000[/tex]gallons of water.
Answer: B. 8000.
Suppose that the velocity v (t) (in meters per second) of a sky diver falling near the Earth’s surface is given by the following exponential function, where time t is the time after diving measured in seconds.
The equation of the velocity is given by the exponential:
[tex]v(t)=53-53e^{-0.24t}[/tex]Let us say that the sky driver's velocity will be 47 m/s at t₁. Then, using the expression above:
[tex]\begin{gathered} v(t_1)=47 \\ 53-53e^{-0.24t_1}=47 \end{gathered}[/tex]Solving for t₁:
[tex]\begin{gathered} \frac{53-47}{53}=e^{-0.24t_1} \\ \ln (\frac{6}{53})=-0.24t_1 \\ t_1=9.1s \end{gathered}[/tex]The probability that a tourist- will spot a Cheetah in Kruger National park is 0.4, the probability that he will spot a Tiger, is 0.7, and the probability that he will spot a Cheetah, or a Tiger or both is 0.5. What is the probability that the tourist will spot: (a) both animals? (b) neither of the animals? (c) Determine with appropriate reason whether the event of spotting a Cheetah and a Tiger are independent or not?
Since the probability of Cheetah is 0.4
Since the probability of Tiger is 0.7
Since the probability of Cheetah or Tiger or both is 0.5
Let us draw a figure to show this information
Then we need to find both animals (x)
Since
[tex]0.5+x=0.7+0.4-x[/tex]Add x to both sides and subtract 0.5 from both sides
[tex]\begin{gathered} 0.5+x+x=0.7+0.4-x+x \\ 0.5+2x=1.1 \\ 0.5-0.5+2x=1.1-0.5 \\ 2x=0.6 \end{gathered}[/tex]Divide both sides by 2 to find x
[tex]\begin{gathered} \frac{2x}{2}=\frac{0.6}{2} \\ x=0.3 \end{gathered}[/tex]a) The probability of both animals is 0.3
Since the total of probability is 1, then to find the neither subtract (0.4 + 0.7 - 0.3) from 1
[tex]\begin{gathered} N=1-(0.4+0.7-0.3) \\ N=1-0.8 \\ N=0.2 \end{gathered}[/tex]b) the probability of neither is 0.2
Events A and B are independent if the equation P(A∩B) = P(A) · P(B)
Since
[tex]P(Ch\cap T)=0.3[/tex]Since P(Ch) . P(T) = 0.4 x 0.7 = 0.28
Then
[tex]P(Ch\cap T)\ne P(Ch).P(T)[/tex]c) The events are not independent
Solve the following logarithmic equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.(Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.)
Hello
We are given a log funtion to solve and see if it have a solution.
[tex]\log _2(x+2)=\log _2(15)[/tex]Step 1
we apply log rules
[tex]\begin{gathered} \log _2(x+2)=\log _215 \\ x+2=15 \end{gathered}[/tex]Step 2
Solve for x
[tex]\begin{gathered} x+2=15 \\ x=15-2 \\ x=13 \end{gathered}[/tex]From the calculation above, the solution of the set is 13; i.e x = 13
Evaluate.C15 3 It says I need to evaluate 15^C 3
Explanation
We are required to determine the value of the following:
[tex]_{15}C_3[/tex]This is achieved thus:
We know that the combination formula is given as:
Therefore, we have:
[tex]\begin{gathered} _{15}C_3=\frac{15!}{3!(15-3)!} \\ _{15}C_3=\frac{15!}{3!12!} \\ _{15}C_3=\frac{15\cdot14\cdot13\cdot12!}{3!12!} \\ _{15}C_3=\frac{15\cdot14\cdot13}{3!}=\frac{15\cdot14\cdot13}{3\cdot2\cdot1} \\ _{15}C_3=5\cdot7\cdot13 \\ _{15}C_3=455 \end{gathered}[/tex]Hence, the answer is:
[tex]455[/tex]By using the substitution u = 4 + 3x^2, or otherwise, find
Solution
We have the following integral:
[tex]\int \frac{2x}{(4+3x^{2})^{2}}dx[/tex]We can use the substitution u= 4 +3x² and we have du= 6x dx, then we have this:
[tex]\int \frac{2x}{(u^{})^2}\cdot\frac{du}{6x}=\frac{1}{3}\int u^{-2}du=\frac{1}{3}\cdot\frac{u^{-1}}{-1}+C=-\frac{1}{3u}+C=-\frac{1}{3(4+3x^{2})}+C[/tex]Solve this system of linear equations. Separatethe x- and y-values with a comma.18x - 10y = 749x - 9y = 45
Given,
[tex]\begin{gathered} \text{The system of pair of linear equation is,} \\ 18x-10y=74\ldots\ldots\ldots\ldots\ldots.\ldots.(i) \\ 9x-9y=45\ldots\ldots\ldots..\ldots\ldots\ldots.(ii) \end{gathered}[/tex]Multiplying equation (ii) by 2 as it make the coefficent of x in both equation equal.
[tex]\begin{gathered} 18x-10y=74\ldots\ldots\ldots\ldots\ldots.\ldots.(i) \\ 18x-18y=90\ldots\ldots\ldots..\ldots\ldots\ldots.(iii) \\ \end{gathered}[/tex]Substracting equation (i) from equation (iii) then we get,
[tex]\begin{gathered} 18x-18y-(18x-10y)=90-74 \\ 18x-18y-18x+10y=16 \\ -8y=16 \\ y=-2 \end{gathered}[/tex]The value of y is -2.
Substituting the value of y in equation (i) then,
[tex]\begin{gathered} 18x-10y=74 \\ 18x+20=74 \\ 18x=54 \\ x=3 \end{gathered}[/tex]Hence, the solution of the linear pair (x, y) is (3, -2).