The mass of the backpack is 1.02 kilograms.
What is the mass of the backpack?On earth, the weight of an object of mass M is given by:
W = M*g
Where g is the gravitational acceleration:
g = 9.8m/s^2
In this case, the weight is 10N, then we can write:
10N = M*9.8m/s^2
Solving this for M we get:
10N/(9.8m/s^2) = M = 1.02 kg
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some people advise that in every cold weather, you should keep the gas tank in your car more than half full. Lou's car had 5.7 gallons in the 14 gallon tank on the coldest day of the year. Lou filled the tank with gas that cost $3.60 per gallon. How much did Lou spend on gas?
The amount that Lou spent in gas is $20.52.
What is the cost?Lou's car had 5.7 gallons in the 14 gallon tank on the coldest day of the year and he filled the tank with gas that cost $3.60 per gallon.
The cost for the amount spent in gas will be:
= Gallons filled × Cost per gallon
= 5.7 × $3.60
= $20.52
The amount is $20.52.
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(3y+11) ° = _____ °
10y ° = ______ °
(4x-22) ° = _____ °
(7x+4) ° = _____ °
Answer:
(3y + 11)° = 50°
10y° = 130°
(4x - 22)° = 50°
(7x + 4)° = 130°
Explanation:
First, find the value of the variable. Let's find y.
(3y + 11) + 10y = 180 (sum of adjacent angles on a straight line)
Simplify and solve the equation.
13y + 11 = 180
13y = 169
y = 13
Substitute y into the angle measures to find values.
3(13) + 11 = 50
10(13) = 130
Hence, (3y + 11)° = 50° and 10y° = 130°.
Next, find x.
(7x + 4) + (4x - 22) = 180 (sum of adjacent angles on a straight line)
Simplify and solve the equation.
11x - 18 = 180
11x = 198
x = 18
Substitute x into the angle measures to find values.
4(18) - 22 = 50
7(18) + 4 = 130
Hence, (4x - 22)° = 50° and (7x + 4)° = 130°.
Alternatively, you do not have to find x to find (4x - 22)° and (7x + 4)°.
4x - 22 = 3y + 11 = 50° (vertically opposite angles)
7x + 4 = 10y = 130° (vertically opposite angles)
For every 20 minutes spent riding his bike, Tim stops 3 times to drink water. if he rides for 80 minutes how many times, he will stop to for a drink.
Answer:
Tim will stop for a drink 12 times
Step-by-step explanation:
Tim drinks water 3 times every twenty minutes. 80 divided by 20 equals 4. Take the 4 times and multiply it by 3 to get the amount of times he stopped to drink water.
I hope this helps
14% of what number is 21
Answer:
150 is the number
Step-by-step explanation:
The equation we should set up is from the sentence "14% of what number is 21"
To rearrange it into a proper equation, replace "of what number" with " * x "
and "is" with "="
The sentence becomes:
14% * x = 21
since 14% = 0.14, replace 14% with 0.14 in the equation
0.14 * x = 21
divide both sides by 0.14
x = 21 / 0.14
x = 150
The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $15 per month plus $0.03 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2 .
b. Explain the meaning of the answer to part a.
The fixed $30 unlimited calls charge for Plan 1 and the initial charge as well as a charge per call of $0.03 calls in Plan 2 gives;
a. The inequality that indicates the number of calls for which Plan 1 is more economical than Plan 2 is presented as follows;
30 > 15 + 0.03•x
Which gives;
x > 500
b. The meaning of the inequality, in part a. is that Plan 1 is more economical than Plan 2 when more than 500 calls are made
What is an inequality?An inequality makes a comparison between two values that are not equal.
The given parameters are;
The billing plan for Plan 1 is presented as follows;
Charges, C = $30
The charges of the billing plan for Plan 2 is presented as follows;
C = $15 + $0.03×xWhere;
x = The number of calls made per month
a. The inequality that can be used to find the number of monthly calls for which Plan 1 is more economical than Plan 2 is found as follows;
At the start of registration for each plan, we have;
Cost of Plan 1 = $30
Cost of Plan 2 = $15 + $0.03 × 0 = $15
Therefore, Plan 2 is initially more economical than Plan 1
At the point (or number of calls) at which the expenses for both plans are the same, we have;
30 = 15 + 0.03 × x
Which gives;
x = (30 - 15)/0.03 = 500From the above equation, we have that after 500 calls, the expenses of both plans will be the same
The inequality that gives the number of calls for which Plan 1 is more economical than Plan 2 is therefore;
30 > 15 + 0.03•x
Which gives;
x > 500b. The meaning of the inequality, x > 500 is that Plan 1 is becomes more economical than Plan 2 when a person makes more than 500 calls in a month
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An art store sells packages of two different-sized square picture frames. The side length of the larger frame, S(x), is modeled by the function S(a) = 3v2- - 1, where x is the area of the smaller frame in square inches. Which graph shows S(x)?
The graph A is the one that accurately represents the side length of the bigger frame S(x).
Modeling the function S(x) by
S(x) has experienced the following changes:
a 1 shift to the right, as shown by the square root's value of -1;
S(x) travels to the right by 1 = 0 + 1 = 1 whereas f(x) stays at 0.
The graph is stretched by a factor of 3 (a number that multiplied the square root).
Consequently, the graph A shows the two changes on S. (x). As a result, it is the best choice.
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P is a polynomial defined by P(x) = 4x³ - 11x² - 6x + 9. Two factors are (x - 3) and
(x + 1). Rewrite the expression for P as the product of linear factors. Here is a blank
diagram to use to organize your thinking, if needed.
[tex]f(x)=x^{3}-3x^{2} -4x+12[/tex]
Answer:
the answer is f'(x)=3x^2-6x-4
Step-by-step explanation:
Please help very confused
The correct explanations are;
2. Given
3. By definition of complementary angles.
5. ∠1 + ∠3 = 90°
6. By definition of complementary angles.
What are complementary angles?
Sum of two or more are angles are 90 degree then, angles are called Complementary angles.
Given that;
∠1 and ∠2 are complementary angles.
And, ∠2 ≅ ∠3
Now,
Statements Reasons
1. ∠1 is a complementary of ∠2. 1. Given
2. ∠2 ≅ ∠3 2. Given
3. m ∠1 + m ∠2 = 90° 3. By definition of
complementary angles.
4. m ∠2 = m ∠3 4. Definition of congruency.
5. m ∠1 + m ∠3 = 90° 5. Substitution property.
6. ∠1 is a complementary of ∠3. 6. By definition of
complementary angles.
Thus, The correct explanations are;
2. Given
3. By definition of complementary angles.
5. ∠1 + ∠3 = 90°
6. By definition of complementary angles.
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Help pls
A system of equations is shown below.
y=x²-11x - 36
y = - 12x + 36
What is the largest value of y in the solution set of the system?
Utilizing differentiation, the biggest value of y=0 in the system's solution set.
What is differentiation?One of the two fundamental concepts of calculus is differentiation. Differentiation is a method for finding a function's derivative. Differentiation is a mathematical technique used to calculate the instantaneous rate of change of a function based on one of its variables. Velocity, or how quickly a distance varies in respect to time, is the most common example. Differentiation's opposite is finding an antiderivative.
Differentiating the 1st equation, we get
x=5.5
Putting back in the equation.
y = -5.75
and differentiating the 2nd equation, we get
x=3
Putting back in the equation
y= 0
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In a box there a total of four prizes: Two of them are worth $3, a single prize worth $23, and a single prize worth $190. A player will reach into the box and draw one of the prizes at random. What is the fair price for this game?
Answer:
The fair price of the game is $54.75
The player is expected to win $54.75
Explanation:
Here, we want to get the fair prize of the game
From the question, there are 4 prizes
When reaching into the box, we can only pick 1
Assuming that each of the prizes have the same probability oof being picked, the probability of picking any of the prize is 1/4
Now, to get the fair price of the game (it is obviously positive as we do not know if the player has anything to lose)
We have to multiply the probability by each of the price tag, then sum
Mathematically,we have this as:
[tex]\begin{gathered} (2\times\frac{1}{4}\times\text{ \$3) + (}\frac{1}{4}\times\text{ \$23) + (}\frac{1}{4}\times\text{ \$190)} \\ \\ =\text{ \$1.5 + \$5.75 + \$47. 5 = \$54.75} \end{gathered}[/tex]Which equations can be used to find the lengths of thelegs of the triangle? Select three options.0.5(x)(x + 2) = 24x(x + 2) = 24x2 + 2x - 24 = 0x2 + 2x - 48 = 0x2 + (x + 2)2 = 100
Triangle area is equal to
1/2 base x height x 0.5 base = x feet.Height = (x + 2) feet
= 24 square feet
24 = 0.5(x)(x+2) \s0.5(x)(x + 2) = 24
The formulas that can be used to determine the triangle's leg lengths must be equivalent to 0.5(x)(x + 2).
To elaborate on this: 0.5(x)(x + 2) = 24
0.5(x2+2x) = 24 b) x(x + 2) = 24 c) x2 + 2x - 24 = 0 0.5(x2+2x) = 24 x(x + 2) is not equal to 0.5(x2+2x)0.5(x)(x + 2) = 24 12(x)(x + 2) = 24 x2 + 2x = 2(24) x2 + 2x - 48 = 0 x2 + (x + 2) is not comparable to x2+2x- 24 = 0 or x2+2x- 48 = 0.² = 100 \sx² + x² + 4x + 4 = 1002x² + 4x = 962(x2 + 2x + 48)= 0 is equivalent to 0.5(x2 + 2x) = 24.
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Find a polynomial function of degree 5 with -2 as a zero of multiplicity 3,0 as a zero of multiplicity 1, and 2 as a zero of multiplicity 1.
The zeros and their multiplicities are:
-2 with multiplicity 3
0 with multiplicity 1
2 with multiplicity 1
The polynomial function is therefore given as:
[tex]\begin{gathered} f(x)=(x+2)^3(x-0)^1(x-2)^1 \\ f(x)=x(x-2)(x+2)^3 \\ f(x)=(x^2-2x)(x^3+6x^2+12x+8) \\ f(x)=x^5+6x^4+12x^3+8x^2-2x^4-12x^3-24x^2-16x \\ f(x)=x^5+4x^4-16x^2-16x \end{gathered}[/tex]Therefore, the polynomial function of degree 5 is:
[tex]f(x)=x^5+4x^4-16x^2-16x[/tex]what is the discriminant of the equation-x^2-9x-9=0
Given data:
The given expression is -x^2-9x-9=0.
The descriminant of the given equation is,
[tex]\begin{gathered} D=(-9)^2-4(-1)(-9) \\ =81-36 \\ =45 \end{gathered}[/tex]Thus, the descriminant of the given equation is 45.
If I am given a line with the points (1,2) and (-1,-1) how would I find out what the slope-intercept form is?
Solution:
The slope-intercept form of a line with slope m and y-intercept b is given by the following formula:
[tex]y\text{ = mx+b}[/tex]On the other hand, the slope m is given by the following equation:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2,Y2) are points on the line. In this case, we can take the points:
(X1,Y1) = (1,2)
(X2,Y2) = (-1,-1)
replacing this data into the slope equation, we get:
[tex]m\text{ = }\frac{-1-2}{-1-1}\text{ = }\frac{-3}{-2}\text{ = }\frac{3}{2}[/tex]thus, the slope of the line would be:
[tex]m\text{ = }\frac{3}{2}[/tex]now, replacing this into the slope-intercept form of the line we get:
EQUATION 1
[tex]y\text{ = }\frac{3}{2}x\text{ + b}[/tex]We only need to find the y-intercept b. For that, take any point on the line, for example (x,y) = (1,2), and replace it into the previous equation:
[tex]2\text{ = }\frac{3}{2}(1)\text{ + b}[/tex]this is equivalent to:
[tex]2\text{ = }\frac{3}{2}+\text{ b}[/tex]solving for b, we get:
[tex]b\text{ = 2- }\frac{3}{2}\text{ = }\frac{1}{2}[/tex]that is:
[tex]b\text{ = }\frac{1}{2}[/tex]finally, replacing this into the EQUATION 1, we get:
[tex]y\text{ = }\frac{3}{2}x\text{ + }\frac{1}{2}[/tex]then, the slope-intercept form of a line with the points (1,2) and (-1,-1) would be:
[tex]y\text{ = }\frac{3}{2}x\text{ + }\frac{1}{2}[/tex]
cual es mayor, -4 o -3
Answer:
-3
Step-by-step explanation:
question is asking, which is larger. -3 is larger than -4
the table below shows the rebeltonshir betweenth number of miles travledet, and the number of salle
The question is really asking for the unit rate but on a supposedly linear graph that is not to scale, so it is difficult to evaluate real rates.
Richie Rich deposited $5,250 into an account. He made no additional deposits or withdrawals. Richie Rich earned 3.5% annual simple interest on the money in the account. What was the balance in dollars and cents in Richie Rich's account at the end of 5 years?
To calculate the balance on the account after 5 years you have to calculate the simple interest using the formula:
[tex]A=P(1-rt)[/tex]A= total accured amount
P= principal amount
r= interest rate expressed in decimals
t=time
For
P=$5250
r=0.035
t=5years
The balance on the account will be:
[tex]\begin{gathered} A=5250(1+0.035\cdot5) \\ A=6168.75 \end{gathered}[/tex]At the end of the 5 years there will be $6168.75
HELP ME WITH THESE THREE QUESTIONS PLEASE (GIVING BRAINLIEST TO THE BEST ANSWER.) 90 points
The perimeter of the figure is 18 units. Complete the statements to find the side lengths.
1. Find the distance from A to B. Explain how you found this distance.
2. Add the distances of the vertical and horizontal segments. These are the distances from A to B, B to C, and C to D. Show how you found the total.
3. Use the perimeter to find the length of segment AD. This is the distance from A to D. Explain how you found your answer.
From the given image, we have that:
1. The distance from A to B is of 6 units.
2. The lengths are given as follows:
Vertical semgents: AB = 6, CD = 3.Horizontal segment: BC = 4.3. The length of segment AD is of 5 units.
What are the side lengths?When two points have one equal coordinate, as is the case in this problem for AB, CD and BC, the distance is given by the subtraction of the different coordinate.
Hence, considering the coordinates of the vertices on the given image, the distances are given as follows:
AB = 2 - (-4) = 2 + 4 = 6 (vertical segment as the y-coordinate is different).CD = 2 - (-1) = 2 + 1 = 3 (vertical segment as the y-coordinate is different).BC = 3 - (-1) = 3 + 1 = 4 (horizontal segment as the x-coordinate is different).The perimeter of a polygon is the sum of the lengths of all the outer sides of the polygon, hence:
P = AB + CD + BC + AD.
The perimeter in this problem is of 18 units, hence the length of AD is given as follows:
18 = 6 + 3 + 4 + AB
13 + AB = 18
AB = 5 units.
What is the missing information?The figure is missing and is given by the image at the end of the answer.
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4Use algebra to solve the following equation. Round decimal to two places.400 (1.065)t = 850
We need to solve the equation
[tex]400(1.065)t=850[/tex]In order to do so, we can first divide both sides of the equation by 400:
[tex]\begin{gathered} \frac{400}{400}(1.065)t=\frac{850}{400} \\ \\ (1.065)t=2.125 \end{gathered}[/tex]Now, to isolate the variable t on the left side and find its value, we can divide both sides by 1.065:
[tex]\begin{gathered} \frac{\mleft(1.065\mright)}{1.065}t=\frac{2.125}{1.065} \\ \\ t=1.9953\ldots \\ \\ t\cong2.00 \end{gathered}[/tex]Therefore, rounding to two decimal places, the answer is 2.00.
Which of the following graphs shows a system of equations with the same end behavior for both functions? Thanks!
Solution
The answer is given in the graph below
Graph the linear equation
y=4x-1
A line is uniquely defined by two points. So, we only need to find two points that lie on the line.
[tex]x=1 \implies y=4(1)-1=3\\\\x=2 \implies y=4(2)-1=7[/tex]
So, you can draw the line through (1, 3) and (2, 7).
Find an anti derivative for each function when C = 0
Given:
[tex]\frac{9}{8}\sqrt[8]{x}[/tex]You can find the antiderivative by integrating it:
1. Set up:
[tex]\int\frac{9}{8}\sqrt[8]{x}\text{ }dx[/tex]2. You can rewrite it in this form:
[tex]=\frac{9}{8}\int x^{\frac{1}{8}}dx[/tex]3. Apply this Integration Rule:
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}[/tex]Then, you get:
[tex]=\frac{9}{8}(\frac{x^{\frac{1}{8}+1}}{\frac{1}{8}+1})+C[/tex][tex]=\frac{9}{8}(\frac{x^{\frac{9}{8}}}{\frac{9}{8}})+C[/tex]4. Simplify:
[tex]=\frac{9}{8}(\frac{x^{\frac{1}{8}+1}}{\frac{1}{8}+1})+C[/tex][tex]=\frac{9}{8}(\frac{8\sqrt[8]{x^9}}{9})+C[/tex][tex]=\sqrt[8]{x^9}+C[/tex]Remember this Property for Radicals:
[tex]\sqrt[m]{b^n}=b^{\frac{n}{m}}[/tex]You can rewrite the expression in this form:
[tex]=\sqrt[8]{x\cdot x^8}+C[/tex]Applying this Property for Radicals:
[tex]\sqrt[n]{b^n}=b[/tex]You get:
[tex]=x\sqrt[8]{x}+C[/tex]5. Knowing that:
[tex]C=0[/tex]You obtain:
[tex]=x\sqrt[8]{x}[/tex]Hence, the answer is:
[tex]=x\sqrt[8]{x}[/tex]two mechanics worked on a car the first mechanic worked for 10 hours in the second mechanic worked for 15 hours together they charged a total of $2,450 what was the rate charge per hour by each mechanic if the sum of the two rates was $185 per hour
wo mechanics worked on a car the first mechanic worked for 10 hours and the second mechanic worked for 15 hours together they charged a total of $2,450 what was the rate charge per hour by each mechanic if the sum of the two rates was $185 per hour
Let
x -----> the rate of the first mechanic
y -----> the rate of the second mechanic
we have that
x+y=185 -------> equation A
10x+15y=2,450 ------> equation B
Solve the system of equations by graphing
see the attached figure
therefore
the rate of the first mechanic is $65 per hour the rate of the second mechanic is $120 per hourWhat is the solution to the equation below? Round your answer to two
decimal places.
7x = 77
Answer:
x = 11
Step-by-step explanation:
divide both sides by 7
x = 11
help meeeeeeeeeeeeeee
Answer:
Rose.
Step-by-step explanation:
Because the number is positive, it does not symbolize a withdrawal, it shows. deposit.
I hope this helps!
P.S, Brainliest if correct, thanks!
11. In how many different ways can the letters of the word MATH be rearranged to form a four-letter code word (i.e. it doesn't have to be a word in English)?
The number of letters in the word MATH IS
[tex]=4[/tex]To rearrange a letter with n letters to form a four-letter code will be
[tex]\begin{gathered} n! \\ \text{Where n=4} \end{gathered}[/tex]Hence,
The number of ways of rearranging the words will be
[tex]\begin{gathered} =4! \\ =4\times3\times2\times1 \\ =24\text{ ways} \end{gathered}[/tex]This problem is a bit different. Instead of choosing one item from each of several different
categories, we are repeatedly choosing items from the same category (the category is: the
letters of the word MATH) and each time we choose an item we do not replace it, so there is
one fewer choice at the next stage: we have 4 choices for the first letter (say we choose A),
then 3 choices for the second (M, T, and H; say we choose H), then 2 choices for the next
letter (M and T; say we choose M) and only one choice at the last stage (T). Thus, there are
4 · 3 · 2 · 1 = 24 ways to spell a code word with the letters MATH.
Hence,
The final answer = 24 ways
What’s the correct answer answer asap for brainlist
Answer:
B
Step-by-step explanation:
Musicologists generally define the Classical period of music as ranging from 1730 to 1820. Classical era music followed the late Baroque period of music.
What is 3/8 of 4/5??
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{3}{8}\ of\ \dfrac{4}{5}}[/tex]
[tex]\mathsf{= \dfrac{3}{8}\times \dfrac{4}{5}}[/tex]
[tex]\mathsf{= \dfrac{3\times4}{8\times5}}[/tex]
[tex]\mathsf{= \dfrac{12}{40}}[/tex]
[tex]\mathsf{= \dfrac{12\div4}{40\div4}}[/tex]
[tex]\mathsf{= \dfrac{3}{10}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{3}{10}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Two friends are both pregnant, and find out they are each expecting twins!
Let A be the event that one friend is pregnant with identical twins, and note that P(A)=0.0045.
Let B be the event that the other friend is pregnant with fraternal twins, and note that P(B)=0.01.
A and B are independent events. What is the probability that one friend is pregnant with identical twins, and one friend is pregnant with fraternal twins?
Give your answer as a percent, rounded to four decimal places if necessary.
The probability that one friend is pregnant with identical twins, and one friend is pregnant with fraternal twins is 0.000045.
What is the probability?From the information illustrated,
Let A = event that one friend is pregnant with identical twins, and note that P(A)=0.0045.
Let B = event that the other friend is pregnant with fraternal twins, and note that P(B)=0.01.
Therefore, the probability will be gotten by using the multiplication for two independent events. This will be:
= P(A) × P(B)
= 0.0045 × 0.01
= 0.000045
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