After 22 s, the car has velocity
[tex]v=\left(1.7\dfrac{\rm m}{\mathrm s^2}\right)(22\,\mathrm s)=36.4\dfrac{\rm m}{\rm s}[/tex]
In this time, it will have traveled a distance of
[tex]\dfrac12\left(1.7\dfrac{\rm m}{\mathrm s^2}\right)(22\,\mathrm s)^2=411.4\,\mathrm m[/tex]
Over the next 29 s, the car moves at a constant velocity of 36.4 m/s, so that it covers a distance of
[tex]\left(36.4\dfrac{\rm m}{\rm s}\right)(29\,\mathrm s)=1055.6\,\mathrm m[/tex]
so that after the first 51 s, the car will have moved 1467 m.
After the 29 s interval of constant speed, the car's negative acceleration kicks in, so that its velocity at time [tex]t[/tex] is
[tex]v(t)=36.4\dfrac{\rm m}{\rm s}+\left(-5.8\dfrac{\rm m}{\mathrm s^2}\right)t[/tex]
The car comes to rest when [tex]v(t)=0[/tex]:
[tex]36.4-5.8t=0\implies t=6.3[/tex]
That is, it comes to rest about 6.3 s after the first 51 s. In this interval, it will have traveled
[tex]\left(36.4\dfrac{\rm m}{\rm s}\right)(6.3\,\mathrm s)+\dfrac12\left(-5.8\dfrac{\rm m}{\mathrm s^2}\right)(6.3\,\mathrm s)^2=114.2\,\mathrm m[/tex]
so that after 57.3 s, the total distance traveled by the car is 1581.2 m, or about 1.6 km.
Simplify: (7a − 9c) − (−12a − 33c) − (−21a + 10c)
Answer:
The answer is 40a+14c
Step-by-step explanation:
Step 1: Open the brackets
7a-9c+12a+33c+21a-10c
Step 2: Group all the like terms
Like terms are terms with similar variables, for example;
(7a, 12a, 21a) are all like terms since they have a common variable (a)
(-9c, 33c,-10c) are also like terms since they have a common variable (c)
Step 2: Solve
(7a+12a+21a)+(33c-10c-9c)=40a+14c
The answer is 40a+14c
the following shows the result of a random survey about favorite seasons. you decide to display the information as a pie chart. what percentage would represent each season? round to the nearest tenth. show or explain your work.
Answer:
The answer is below
Step-by-step explanation:
Data
Winter = 234
Spring = 673
Summer = 843
Fall = 425
Total = 2175
Then
Winter 2175 ------------------------- 100%
234 ----------------------- x
x = 234(100)/2175 = 10.8 %
Spring 2175 ------------------------ 100%
673 ----------------------- x
x = 673(100)/2175 = 30.9 %
Summer 2175 ------------------------ 100%
843 ------------------------ x
x = 843(100) /2175 = 38.8 %
Fall 2175 ------------------------ 100%
425 ---------------------- x
x = 425(100)/2175 = 19.5%
Total = 10.8 + 30.9 + 38.8 + 19.5 = 100%
You have purchased a new warehouse. To finance the purchase, you’ve arranged for a 25-year mortgage for 75 percent of the $4,200,000 purchase price. The monthly payment on this loan will be $18,300.
What is the APR on this loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Final answer:
Explanation on how to calculate the APR for a mortgage loan based on provided information.
Explanation:
To calculate the APR on the loan, we first need to determine the total amount paid over the life of the loan. The total payment per month is $18,300, and the loan term is 25 years. So, the total payment over 25 years would be $18,300 x 12 months x 25 years = $5,220,000.
Next, calculate the total interest paid by subtracting the loan amount from the total payments: $5,220,000 - 75% of $4,200,000 = $5,220,000 - $3,150,000 = $2,070,000.
Finally, use the formula for APR: APR = (Total Interest Paid / Loan Amount) x 100%. Therefore, APR = ($2,070,000 / $3,150,000) x 100% ≈ 65.71%. So, the APR on this loan is approximately 65.71%.
Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 40 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 6 minutes?
Answer:
30 parts
Step-by-step explanation:
We are given that machine produces 100 parts twice as fast as machine B does.
Machine produces 100 parts in 40 minutes.
We have to find number of parts produces by machine A in 6 minutes.
According to question
Machine A takes time to produce 100 parts =[tex]\frac{40}{2}=20 minutes[/tex]
Machine A and machine B produces parts at constant rate.
Machine A produces parts at the rate=[tex]\frac{100}{20}=5 parts /minute[/tex]
In one minute,Machine A produces =5 parts
In 6 minutes , machine B produces =[tex]5\times 6=30[/tex] parts
Hence, machine A produce parts in 6 minutes=30
Square EFGH stretches vertically by a factor of 2.5 to create rectangle E′F′G′H′. The square stretches with respect to the x-axis. If point H is located at (-2, 0), what are the coordinates of H′ ? A. (-5, 0) B. (-2, 0) C. (0.5, 0) D. (-2, 2.5)
Answer:
The coordinates of point H' are (-2 , 0) ⇒ answer B
Step-by-step explanation:
* Lets revise the vertical stretch
- A vertical stretching is the stretching of the graph away from the
x-axis
- If k > 1, then the graph of y = k • f(x) is the graph of f(x) vertically
stretched by multiplying each of its y-coordinates by k
* Lets solve the problem
- Square EFGH stretches vertically by a factor of 2.5 to create
rectangle E′F′G′H′
∴ k = 2.5
- The square stretches with respect to the x-axis
∴ The square stretches vertically
∴ The y-coordinates of each vertex of the square EFGH are
multiplied by 2.5 to get the vertices of the rectangle E'F'G'H'
∵ Point H located at (-2 , 0)
∵ The image of point (x , y) after stretched vertically by k is (x , ky)
∴ Point H' located at (-2 , 0 × 2.5) ⇒ (-2 , 0)
∴ The coordinates of point H' are (-2 , 0)
∴ Point H' located at (-2 , 0)
Answer:
B. (-2, 0)
Step-by-step explanation:
If you give siri 0 cookies and she has 0 cookies but then gives you back a cookie where did she get the cookie from? if You and her had 0 cookies ?
Answer:
Maybe she borrowed a cookie from somone? or maybe bought a cookie?
A gym charges a $25 sign-up fee plus $25 per month. You have a $200 gift card for the gym. When does the total spent on your gym membership exceed the amount of your gift card?
Answer:
After 7 months
Step-by-step explanation:
DATA:
⇒ Sign-up fee = $25
⇒ Monthly fee = $25
⇒ Number of months = y
⇒ Gift card = $200
Form an equation to calculate when the total spent on gym would exceed the amount of the gift card
Sign-up fee + (monthly fee x number of months) = Gift card amount
25 + 25y = 200
25y = 200-25
25y = 175
y = 7
Therefore, the total spent on your gym membership exceeds the amount of your gift card after 7 months.
Jessica wants to buy a new team jacket that costs $35. If Jessica saves $5 a week for 4 weeks and $4 a week for 3 weeks, will she have enough money to buy the team jacket? Explain
No, Jessica he will not have enough to buy the jacket. She would have saved $32, not $35.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Lets x represent the number of weeks it will take to save enough money. If she saves $11 each week, then in x weeks she will save 11x dollars.
Also, Add this to the 107 she has already saved, and at the end of 11 weeks she will have 11x + 107 dollars.
We want the amount saved to be equal to the price of the bike, so our equation;
11x + 107 = 173
Now we solve the equation.
Subtract 107 from both sides ;
11x = 66
Divide both sides by 11;
x = 6
No, Jessica he will not have enough to buy the jacket. She would have saved $32, not $35.
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I move east a distance of 4km, south a distance of 2 km, and then west a dostance of 1km. What is the cartesian cordinates relative to my starting point ?
Answer:
In x: 4-1=3
In y: -2
Cartesian coordinates: (3,-2)
Step-by-step explanation:
If we move horizontally we must consider only the x axis, if we move to east it is positive, and if we move to west it is negative.
f we move vertically we must consider only the y axis, if we move to north it is positive, and if we move to south it is negative.
What is the slope for 3x + 2y = 8
Answer:
[tex] -1 \frac{1}{2} = m[/tex]
Step-by-step explanation:
3x + 2y = 8
-3x - 3x
___________
2y = -3x + 8
___ _______
2 2
y = -1½x + 4
↑
rate of change [slope]
I am joyous to assist you anytime.
What is the place value of 2 in 24,398,407,268
Answer:
20,000,000,000 or 200
Step-by-step explanation:
depending on which 2 you are asking for
The place value of 2 in the number 24,398,407,268 is 20 billion, as it is in the ten billion place.
The place value of 2 in the number 24,398,407,268 refers to the position of 2 in the number and its corresponding value. In this case, the 2 is in the ten billion place. To find the value of 2 in that position, we multiply it by 10 billion (109). Therefore, the place value of 2 in this number is 20 billion (2 x 10^9).
The probability that an American industry will locate in Shanghai, China, is 0.7, the probability that / / 60 Chapter 2 Probability it will locate in Beijing, China, is 0.4, and the probability that it will locate in either Shanghai or Beijing or both is 0.8. What is the probability that the industry will locate (a) in both cities? (b) in neither city?
Answer:
A) 0.3
B) 0.2
Step-by-step explanation:
We are given the following in the question:
P(Industry in Shanghai) = P(A) = 0.7
P(Industry in Beijing) = P(B) = 0.4
P(Industry in Shanghai or Beijing) = P(A∪B) = 0.8
a)We need to find the probability that the industry is located in both Shanghai and Beijing that is we need to find P(A∩B)
Formula:
P(A∪B) = P(A) + P(B) - P(A∩B)
Putting the values we get,
0.8 = 0.7 + 0.4 - P(A∩B)
P(A∩B) = 0.3
Thus, the probability that the industry is located in both Shanghai and Beijing is 0.3.
b)Now, we need to find the probability that it is not in either cities
Probability = 1 - Probability(Industry in Shanghai or in Beijing)
= 1 - P(A∪B)
= 1 - 0.8
= 0.2
The probability that the industry will locate in both Shanghai and Beijing is 0.3, while the probability that it will locate in neither of the cities is 0.2.
Explanation:This problem is solved using the concept of probability in Mathematics. Let's denote A as the event that an industry with locate in Shanghai and B is the event that it will locate in Beijing.
The probability of A, P(A), is given as 0.7 and the probability of B, P(B), is given as 0.4. The probability it will locate in either of the cities, P(A U B), is given as 0.8.
We know, P(A U B) = P(A) + P(B) - P(A ∩ B), where P(A ∩ B) represents the probability the industry will locate in both cities. Using the given probabilities:
0.8 = 0.7 + 0.4 - P(A ∩ B), so P(A ∩ B), the probability the industry will locate in both cities, is equal to 0.3. (a)
The probability the industry will not locate in either of the cities, denoted as P'(A U B), is equal to 1 - P(A U B) = 1 - 0.8 = 0.2. (b).
This means there is a 30% chance the industry will locate in both Shanghai and Beijing, and a 20% chance it will locate in neither city.
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A ball is dropped from a height of 600 feet. The height of the ball, H, after t seconds can be modeled by the function rule, ()=−4.92+600. What would be the independent quantity?
Answer:
the independent quantity is "t" (time in seconds)
Step-by-step explanation:
The problem statement tells you the function rule gives you H (the dependent quantity) as a function of t seconds. "t seconds" is the independent quantity.
if (fx)=5x, what is f^-1(x)
Answer:
x/5
Step-by-step explanation:
To get the inverse function you need to leave the x alone and then switch variables ( f(x) = y)
f(x) = 5x
y = 5x
y/5 = x
Now that x is alone you switch the x for y and the y for x and you get:
x/5 = y
And this new y is the inverse function of f(x) ( f^-1(x))
f^-1(x) = x/5
Someone please help me
Answer:
14. 61.2 mi N, 49.8 mi W
15. 7.3 ft
Step-by-step explanation:
14. The components in the different directions are found using the sine and cosine functions. (Draw yourself a diagram to help see this.)
north distance = (78.9 mi)cos(39°10') ≈ 61.2 mi
west distance = (78.9 mi)sin(39°10') ≈ 49.8 mi
__
15. Let d represent the distance from the observation point to the door. Then ...
8.8 ft = d·tan(56°)
x = d·tan(51°)
Dividing the second of these equations by the first cancels d and gives ...
x/(8.8 ft) = tan(51°)/tan(56°)
Multiplying by 8.8 ft, we can find x:
x = (8.8 ft)(tan(51°)/tan(56°)) ≈ 7.3 ft
Graph f(x) = x2 + 2x - 3, label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry
The given function : [tex]f(x)=x^2+2x-3[/tex]
Using completing the squares, we have
[tex]f(x)=x^2+2x+1-1-3[/tex] [∵ [tex](x+1)^2=x^2+2x+1[/tex]]
[tex]f(x)=(x+1)^2-4[/tex] (1)
Comparing (1) to the standard vertex form [tex]f(x)=(x-h)^2+k[/tex] , the vertex of function is at (h,k)=(-1,-4)
For x-intercept, put f(x)=0 in (1), we get
[tex]0=(x+1)^2-4\\\\\Rightarrow\ (x+1)^2=4[/tex]
Square root on both sides, we get
[tex]x+1=\pm2\\\\x+1=-2\ or\ \ x+1=2\\\\=x=-3\ \ or\ x=1[/tex]
∴ x intercepts : x= (-3,0) and (1,0)
For y-intercept put x=0 in (1), we get
[tex]f(1)=(1)^2-4=1-4=-3[/tex]
∴ y intercept : (0,-3)
Axis of symmetry : [tex]\dfrac{-b}{2a}[/tex]
In [tex]f(x)=x^2+2x-3[/tex] , a=1 and b=2
Axis of symmetry=[tex]\dfrac{-2}{2(1)}=-1[/tex]
A graph of the quadratic equation [tex]f(x) = x^2 + 2x - 3[/tex] with its key features is shown on the coordinate plane in the image below.
What is the graph of a quadratic function?In Mathematics and Euclidean Geometry, the standard form of a quadratic function is represented by the following equation;
[tex]y = ax^2 + bx + c[/tex]
Where:
x and y represents the data points on the graph.a represents the leading coefficient.Since the leading coefficient (value of a) in the given quadratic function [tex]f(x) = x^2 + 2x - 3[/tex] is positive one (1), we can logically deduce that the parabola would open upward and the solutions are the x-intercepts. Furthermore, the key features of this quadratic function include the following;
The vertex is (-1, -4).The mininum value is equal to -4.The axis of symmetry is x = -1.x-intercepts: (-3, 0) and (1, 0)The parabola opens upward.The y-intercept is (0, -3).Read more on quadratic functions here: brainly.com/question/29499209
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Complete Question;
Graph [tex]f(x) = x^2 + 2x - 3[/tex], label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry
Please please help me out with this
Answer:
y = [tex]\frac{3}{4}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ( = (0, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line
m = [tex]\frac{5-2}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]
Note the line crosses the y- axis at (0, 2) ⇒ c = 2
y = [tex]\frac{3}{4}[/tex] x + 2 ← equation of line
OMG HELP A GIRL OUT !!HELP ME PLEASE I NEED A 70%
1. Translate and solve: What number is 408% of 568? Round to the nearest hundredth.
2.In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the total percent decrease.
3.A cash box of $1 and $5 bills is worth $45. The number of $1 bills is three more than the number of $5 bills. How many of each bill does it contain?
4.Marquese is making 10 pounds of trail mix from raisins and nuts. Raisins cost $3.45 per pound, and nuts cost $7.95 per pound. How many pounds of raisins and how many pounds of nuts should Marquese use for the trail mix to cost him $6.96 per pound?
Answer:
#1. 408% of 568
We get two equations from this
408% = x
568 = 100%
568/x=100%/408%
Solve and you'll get
408% of 568
=2317.44
2. New - Original = % change
712500 - 950000 = -237500
3. 10 at $1, 7 at $5
4. 2.2 lb. of raisins, 7.8 lb. of nuts
As per the given conditions we have
1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).
2. Total decrease in percentage of the population of Detroit is equals to 25%.
3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.
What is equation?
" Equation is defined as the relation between the variables using sign of equality."
What is percentage?" Percentage is defined as the hundredth part of the given number."
According to the question,
1. 'x' represents the number
As per given condition,
x = 408% of 568
⇒ [tex]x= \frac{408}{100} (568)[/tex]
⇒ [tex]x = 2317.44[/tex]
Therefore, the number which is 408% of 568 is equals to 2317.44.
2. Total population of Detroit = 950,000
Population after 10 years = 712,500
Decrease in population = 950,000 - 712,500
= 237,500
Total percentage decrease in population = [tex]\frac{237500}{950,000}(100)[/tex]
= 25%
Therefore, total decrease in percentage of the population of Detroit is equals to 25%.
3. 'x' represents the bill of $1
'y' represents the bill of $5
As per the condition given equation we have,
$1x + $5y = $45 ______(1)
x = y + 3 ______(2)
Substitute the value of equation (2) in (1) we get,
[tex]1(y + 3) + 5y = 45\\\\\implies 6y = 45-3\\\\\implies y \frac{42}{6} \\\\\implies y = 7[/tex]
Substitute the value y in (2) we get,
[tex]x= 7 + 3\\\\\implies x =10[/tex]
Therefore , cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. 'x' represents the pounds of raisins
'10- x ' represents the pounds of nuts
Cost of trail mix from raisins and nuts per pound = $6.96
Therefore,
Cost of 10 pounds of trail mix of raisins and nuts = $(6.96 ×10)
= $69.6
Cost per pound of raisins = $3.45
Cost per pound of nuts = $7.95
Equation formed as per given condition we get,
[tex]3.45x + 7.95(10-x) = 69.6\\\\\implies 3.45x + 79.5 -7.95x = 69.6\\\\\implies -4.5x = 69.6 - 79.5\\\\\implies-4.5x= -9.9\\\\\implies x =\frac{9.9}{4.5}\\ \\\implies x = 2.2 pounds[/tex]
Pounds of raisins = 2.2pounds
Pounds of nuts = 10 - 2.2
= 7.8 pounds
Therefore, pounds of raisins is equals to 2.2 and pounds of nuts is equals to 7.8 for the trail mix.
Hence, As per the given conditions we have
1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).
2. Total decrease in percentage of the population of Detroit is equals to 25%.
3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.
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The scale on a map of Virginia shows that 1 inch represents 15 miles. The actual distance from Richmond, VA, to Washington, D.C., is 110 miles. On the map, how many inches are between the two cities? Enter your answer as a mixed number with the fraction in simplest form.
The distance on the map is __ in.
Answer:
The answer to your question is: 7 1/3 inches
Step-by-step explanation:
Data
1 inch --------- 15 miles
Distance from Richmond to Washington = 110 miles
Use a rule of three to solve it
1 inch ----------------- 15 miles
x -------------------- 110 miles
x = 110x 1 /15
x = 110 / 15 simplify dividing by 5
x = 22/3
Convert it to a mix number
22/3 = 7 1/3 inches
Final answer:
On the map, 7.6 inches are between the two cities
Explanation:
To find out how many inches are between two cities on a map given the scale and the actual distance. The scale here is that 1 inch represents 15 miles. Therefore, for an actual distance of 110 miles, we simply divide the actual distance by the scale factor to obtain the distance on the map.
By setting up the proportion:
1 inch / 15 miles = x inches / 110 miles, we cross-multiply and solve for x,
which is the number of inches on the map. The calculation would be:
(1 inch / 15 miles) * 110 miles = 110 inches / 15 = 7 3/5 inches or 7.6 inches.
A test consists of 10 true/false questions. To pass the test a student must answer at least 88 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? Round to three decimal places.
Answer:
The probability that the student is going to pass the test is 0.0545
Step-by-step explanation:
The variable that says the number of correct questions follows a Binomial distribution, because there are n identical and independent events with a probability p of success and a probability 1-p of fail. So, the probability of get x questions correct is:
[tex]P(x)=\frac{n!}{x!(n-x)!} *p^{x} *(1-p)^{n-x}[/tex]
Where n is equal to 10 questions and p is the probability of get a correct answers, so p is equal to 1/2
Then, if the student pass the test with at least 8 questions correct, the probability P of that is:
P = P(8) + P(9) + P(10)
[tex]P=(\frac{10!}{8!(10-8)!}*0.5^{8}*(0.5)^{10-8})+(\frac{10!}{9!(10-9)!} *0.5^{9} *(0.5)^{10-9})+(\frac{10!}{10!(10-10)!} *0.5^{10} *(0.5)^{10-10})[/tex]
P = 0.0439 + 0.0097 + 0.0009
P = 0.0545
Order the function from the least steep slope to the steepest slope.
The functions ordered from the least steep slope to the steepest slope are: logarithmic (log(x)), linear (x), quadratic (x²), exponential (eˣ), and cubic (x³).
Explanation:To compare the steepness of the slopes for different types of functions, we consider the growth or decay rates of each function. The order is determined by the behavior of the functions as x increases.
1. Logarithmic function (log(x)): It grows slowly and approaches infinity as x increases, making it the least steep slope.
2. Linear function (x): It has a constant slope, making it steeper than logarithmic but less steep than quadratic, exponential, and cubic functions.
3. Quadratic function (x²): It increases faster than linear but slower than exponential and cubic functions.
4. Exponential function (eˣ): It grows at an increasing rate, making it steeper than quadratic but less steep than cubic.
5. Cubic function (x³): It has the steepest slope as x increases, making it the most rapidly increasing function.
This order is based on the general behavior of each function type and their rates of growth or decay. Understanding the characteristics of these functions helps in comparing and ordering them in terms of steepness.
Answer: here’s the correct answer
A vase contains 7 red flowers, 3 white flowers, and 5 yellow flowers. If George selects a flower from the vase for his wife, what is the probability that he will select a red one.
Answer:
The answer to your question is: P(A) = 0.47
Step-by-step explanation:
Data
7 red flowers
3 white flowers
5 yellow flowers
Probability that he select a red one
Formula
P(A) = Number of favorable cases of A / total number of outcomes
Number of favorable cases = 7
Total number of outcomes = 7 + 3 + 5 = 15
Substitution
P(A) = 7 / 15
P(A) = 0.47
Sarah begins at a negative position along the x-axis. Sarah moves in the positive x-direction, turns around and then moves in the negative x-direction. Her final position is more negative that her initial position. Is the magnitude of Sarah's displacement greater than, less than, or equal to the distance she travels?
Answer:
he magnitude of Sarah's displacement is less than the distance she travels
Step-by-step explanation:
Hi!
The magnitude of her displacement is just the difference between her final and initial state, however the distance she traveled is two times the distance she moved in the positive x-direction until she turned around, since she had to move back, plus her displacement.
So:
[tex]displacement = |x_{final} -x_{initial}| \\distanceTraveled = 2|x_{return}-x_{initial}| + displacement\\[/tex]
Since all the terms are positive:
[tex]x_{displacement}<x_{traveled}[/tex]
Have to bake a lot of brownies to sell! You have plenty of flour, cocoa, milk, and oil, but you only have 6 1/2 sticks of butter. You need to know how many batches of brownies you can bake, based on your limited amount of butter. You can cook partial batches in order to use up every bit of butter, which will also help you to bake the most brownies possible. Each batch needs 3/4 of a stick of butter.
Answer: 8 + 2/3 batches of brownies you can bake.
Step-by-step explanation:
6 1/2 butter = 6 + 1/2 = (2·6 + 1)/2 = 13/2 sticks of butter, we have this
Since we have 13/2 sticks of butter and each batch of brownies needs 3/4 of a stick of butter, we have to divide the amount of butter we have between the amount of butter we use to bake a batch of brownies.
13/2 butter ÷ 3/4 butter/batch = 13·4/2·3 batches = 52/6 batches = 8 + 2/3 batches
Answer: 8 + 2/3 batches of brownies you can bake.
[tex]\textit{\textbf{Spymore}}[/tex]
By dividing the total amount of butter (13/2 sticks) by the amount required per batch (3/4 stick), we find that it's possible to make 8 full batches of brownies with 6 1/2 sticks of butter, with some butter left over.
To determine how many batches of brownies you can bake with 6 1/2 sticks of butter, you have to divide the total amount of butter you have by the amount required for one batch. Since each batch requires 3/4 stick of butter, you calculate as follows:
Total sticks of butter: 6 1/2
Required per batch: 3/4
Now convert 6 1/2 to an improper fraction: 6 1/2 = 13/2.
Next, calculate the number of batches by dividing the total butter by the butter per batch:
Number of batches = (13/2) / (3/4) = (13/2) * (4/3) = 52/6
When you simplify 52/6, you get 8 with a remainder, meaning you can make 8 full batches of brownies, and you will have some butter left over.
A 3-gallon container of laundry detergent costs $20.76. What is the price per quart?
The price per quart of a 3-gallon container of laundry detergent is $1.73.
Explanation:To find the price per quart, we need to convert the 3-gallon container into quarts. Since there are 4 quarts in a gallon, there are 4 x 3 = 12 quarts in a 3-gallon container
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Final answer:
The answer calculates the price per quart of laundry detergent from a 3-gallon container and provides estimated costs for 40 oz. and 90 oz. sizes. All calculations are based on the given information and formula.
Explanation:
Price of 3-gallon container: $20.76
Price per quart: $20.76 / 12 quarts = $1.73 per quart
If the detergent were sold in a 40 oz. size: Estimated cost = $1.73 x 3.33 = $5.76
If the detergent were sold in a 90 oz. size: Estimated cost = $1.73 x 7.5 = $12.98
19. While serving, the shuttlecock must land within JLMN, the service box. Find the probability that a shuttlecock will land in the service box, relative to the court. (JUSTIFY)
Answer:
HI! I'M TAKING THE TEST FOR IT! SO I HOPE THIS IS RIGHT! IF NOT, FORGIVE ME! SO THE ANSWER IS 25.094
Step-by-step explanation:
I attached the step by step, so look at it for me!
PLEASE HELP!!!
The area of a triangle is given by the
formula A = 1/2bh Solve this for h.
Answer:
h = [tex]\frac{2A}{b}[/tex]
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex] bh
Multiply both sides by 2 to clear the fraction
2A = bh ( isolate h by dividing both sides by b )
h = [tex]\frac{2A}{b}[/tex]
Answer: h = 2a/b
Step-by-step explanation:
Which word best completes this definition? Two lines are _____ if and only if they lie in the same plane and do not intersect. A parallel B perpendicular C bisectors D transversals
Answer:
Parallel
Step-by-step explanation:
All of the other answers give examples of lines that intersect at some point.
Answer:
transversal
Step-by-step explanation:
The line is called transversal. A transversal is a line which intersects two or more parallel lines
Is it possible for a linear system to have a unique solution if it has more equations than variables? If yes, give an example. If no, justify why it is impossible.
Answer:
Yes
Step-by-step explanation:
Yes it is possible, if the equations are equivalent. For example in one variable, we have x=2 and if we add the equation 2x=4 both considered on the Real numbers, then the system has two equations and one variable, more equations than variables and yet the solution is unique x=2.
Answer:
Yes, it's possible.
Step-by-step explanation:
We know that a linear system has a unique solution if it has the same number of equations than variables (but remember that you musn't have a linear combination of equations).
So it is possible to create a system with more equations than variables, with a unique solution.
Example:
1) X + Y + Z = 3
2) 2X + 2Y + 2Z = 6
3) X + Y = 2
4) X + Z = 2
This is a 4 equation and 3 variable system. Pay attention to equation number 1) and 2). They are a linear combination (number 2 is the number 1 multiplied by 2). So, for this system you can basically ignore one of them.
If you do that, you will have 3 equations and 3 variables, with a unique solution. In this case solution is X = 1, Y = 1, Z = 1.
Now, let's see if equation number 2 satisfies:
2x1 + 2x1 + 2x1 = 6
6 = 6
With this simple example we proved that you can have a linear system with a unique solution if it has more equations than variables.
You are driving home from school steadily at 95 km/h for 180 km. It then begins to rain and you slow to 65 km/h. You arrive home after driving 4.5 h. (a) How far is your hometown from school? (b) What was your average speed?
Answer:
(a) 349.34
(b) 77.63 km/h
Step-by-step explanation:
Distance you covered before it rain S = 180 km
Speed v = 95/km
Time taken to cover 180 km = [tex]\frac{S}{v}[/tex]
= [tex]\frac{180}{95}[/tex]
= 1.89473 hrs.
Total time to cover the distance between school to home T = 4.5 hrs.
Remaining time t = T - t
= 4.5 - 1.89473
= 2.60527 h.
Velocity after travel 180 km. v' = 65 km/h
Distance traveled in this velocity S' = v'(t)
= 2.60527 × 65
= 169.34 km
(a) distance of hometown from school = 169.34 + 180 = 349.34 km.
(b) Your average speed V = [tex]\frac{S}{T}[/tex]
= [tex]\frac{349.34}{4.5}[/tex]
= 77.63 km/h