Answer:
8 bags
Step-by-step explanation:
The area of the path is equal to the area of the overall square minus the area of the garden.
Area of a square is the side length squared:
A = s²
The overall square has a side length of 11 feet. The side length of the garden is 11 - 2 - 2 = 7 feet. So the area of the path is:
A = 11² - 7²
A = 121 - 49
A = 72
The area of the path is 72 ft². If one bag of gravel covers 9 ft², then the number of bags needed is:
72 ft² × (1 bag / 9 ft²) = 8 bags
Solve the right triangle
Answer:
Step-by-step explanation:
To start with a = 12 (given)
Tan(50) = b / 12
Tan(50) = 1.192
1.192 = b / 12 Multiply both sides by 12
1.192 * 12 = b
b = 14.301
=================
Cos(50) = 12/c
Cos(50) = 0.4628
0.4628 = 12 / c Multiply both sides by c
0.4628 * c = 12 Divide by 0.4628
c = 12/ 0.4628
c = 18.67
Someone help
Rick is driving to his uncle's house in Greenville, which is 120 miles from Rick's town. After covering x miles, Rick sees a sign stating that Greensville is 20 miles away. Which equation, when solved, will give the value of x? A. x + 120 = 20 B. x × 120 = 20 C. x + 20 = 120 D. x × 20 = 120
Answer:
c
Step-by-step explanation:
The equation which represents the total distance is x + 20 = 120. The correct option is C.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Rick is driving to his uncle's house in Greenville, which is 120 miles from Rick's town. After covering x miles, Rick sees a sign stating that Greensville is 20 miles away.
The expression will be written as,
x + 20 = 120
Therefore, the equation which represents the total distance is x + 20 = 120. The correct option is C.
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Need help with math question
Answer:
48
Step-by-step explanation:
[tex] y = \frac{96}{2} = 48 \\ [/tex]
Which trig function and ratio would you use to solve the following?
tan 30 = x4
sin 30 = 4x
cos 30 = x4
cos 30 = 4x
Have you found the answer to this??
Answer:
[tex]cos(30)= \frac{4}{x}[/tex]
Step-by-step explanation:
WE use the given triangle to solve for x
Given triangle is right angle triangle , so we use trigonometric rations
WE know
sin = opposite side / hypotenuse
cos = adjacent side / hypotenuse
tan= opposite side / adjacent side
For angle 30 degree, the hypotenuse is x
adjacent side have side length 4
we know the hypotenuse and adjacent side so we use cos
[tex]cos(30)= \frac{adjacent}{hypotenuse}[/tex]
[tex]cos(30)= \frac{4}{x}[/tex]
What is the absolute deviation for 15 in the data set?
{20, 20, 30, 15, 40}
A. 5
B. 10
C. 15
D. 25
Final answer:
The absolute deviation of 15 in the data set {20, 20, 30, 15, 40} is the absolute value of (15 minus the mean 25), which is 10. So, the correct answer is B. 10.
Explanation:
To calculate the absolute deviation of a number in a data set, you subtract the number from the mean of the data set and take the absolute value of the result. The mean of the data set {20, 20, 30, 15, 40} is (20 + 20 + 30 + 15 + 40) / 5, which equals 125 / 5 or 25. The absolute deviation for the number 15 would be the absolute value of (15 - 25), which is the absolute value of -10 or simply 10. Therefore, the correct answer is B. 10.
2) Write an equation that represents Boyle’s law (the volume of air varies inversely with the pressure). Use k for the variation constant.
3) Solve for k utilizing the fact that you have 4 quarts of air in your lungs when the pressure is 3 atm and 6 quarts of air in your lungs when the pressure is 2 atm. Rewrite your inverse variation equation from Question #2 using your new value for k.
4) Using your equation from Question #3, construct a table relating the volume of air in your lungs to the pressure. The values for the pressures are 1 atm, 2 atm, and 3 atm.
5) Write an equation relating volume to depth. (Hint: Replace P in your equation from Question #3 with an expression in terms of d. You do not need to simplify your equation.)
Answer:
Step-by-step explanation:
2) Boyle's law says volume varies inversely with pressure:
V = k / P
3) V = 4 when P = 3:
4 = k / 3
k = 12
4) [tex]\left[\begin{array}{cc}P&V\\1&12\\2&6\\3&4\end{array}\right][/tex]
5) Since P = d/33 + 1:
V = 12 / (d/33 + 1)
6) [tex]\left[\begin{array}{cc}d&V\\0&12\\33&6\\66&4\\99&3\end{array}\right][/tex]
The sum of two numbers is -1. If one number is subtracted from the other, their difference is 11. Find the numbers.
Answer:
the solution is (5, -6)
Step-by-step explanation:
Let the numbers be x and y. Then x + y = -1 (meaning that either x or y is negative), and x - y = 11.
Solve the system:
x + y = -1
x - y = 11
-------------
2x = 10, or x = 5. If x = 5, then x - y = 11 becomes 5 - y = 11, or y = -6.
Then the solution is (5, -6).
Is the sum of 5 and -6 equal to -1? YES.
If -6 is subtracted from +5, is the difference 11? Yes.
Final answer:
The two numbers in the system of equations are 5 and -6. By adding the equations x + y = -1 and x - y = 11, we find x = 5, and substituting back, we find y = -6.
Explanation:
Let's define the two unknown numbers as x and y. According to the question, we have two equations. The first one, x + y = -1, tells us the sum of the two numbers is -1. The second one, x - y = 11, tells us the difference between the two numbers is 11.
To solve this system of linear equations, we can use the method of substitution or elimination. However, adding both equations is the simplest approach here:
Adding both equations, we get:
2x = 10
Now we can solve for x by dividing both sides by 2:
x = 5
Substituting the value of x into one of the original equations to find y:
5 + y = -1
Solving for y gives us:
y = -1 - 5
y = -6
So the two numbers are 5 and -6.
A group of hikers buys 8 bags of mixed nuts. Each contains 3 and 1/2 cups of mixed nuts. The mixed nuts are shared evenly among 12 hikers. How many cups of mixed nuts will each hiker receive?
Hello There!
1 bag = 3.5 cups, then 8 bags = 8 x 3.5 = 28 cups of trail mix
28 cups/12 people = 2.33 cups/person
One canned juice drink is 15% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 5L that is 13% orange juice?
Answer:
3 liters of 15% and 2 liters of 10%
Step-by-step explanation:
You can set up a table that says the number of liters multiplied by the percent juice equals total percent of juice in L liters:
L * % juice = %L
That is the main set up for the table. We will put in values for the percent juice right away, because they were given to us. Remember that percentages need to be expressed as decimals in order to use them in equations.
L * % juice = %L
15% .15
10% .10
___________________________________
13% .13
Easy enough so far. We know that the 15% juice canned juice contains 15% juice. No secrets there at all. We also made a row for the mixture that needs to be 13% juice. Next we know that the total amount of the mixture has to be 5 liters. If we mix one juice with another and the total has to be 5 liters, then we have an unknown amount of one juice, and 5 - that unknown amount of the other juice. Filling in we have:
L * % juice = %L
15% x .15
10% 5 - x .10
______________________________
13% 5 .13
Our equation tells us that we have to multiply the L times the % to fill in that last column:
L * % juice = %L
15% x * .15 = .15x
10% 5-x * .10 = .10(5 - x)
__________________________________
13% 5 * .13 = .65
We are told from the problem we are adding the 2 juices to get the mixture, so we will add the rows in the last column and set it equal to .65:
.15x + .10(5 - x) = .65
Let's multiply everything by 100 to get rid of all those decimals:
15x + 10(5 - x) = 65
Distributing and combining like terms:
15x + 50 - 10x = 65 and
5x = 15
x = 3
That means that we need 3 liters of the canned juice that is 15% juice.
5 - 3 = 2...and 2 liters of the canned juice that is 10% juice to get the correct number of liters of 13% juice.
The question is to determine the volumes of two types of orange juice with different concentration percentages required to mix to get another juice with a specified concentration. Using the concept of weighted averages, a mathematical equation can be set up and solved to get the desired volumes.
Explanation:To solve this problem, we'll use the concept of weighted averages in mathematics. The method is to set up an equation based on the volume and percentage of orange juice. We'd consider the volume of the 15% juice as 'x' liters and that of the 10% juice as '5 - x' liters (since the total volume must be 5 liters).
The equation would be: 0.15x + 0.10(5 - x) = 0.13 * 5
Solving this equation gives the volume of the 15% juice (x) and 5 - x gives the volume of the 10% juice.
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Please help me out with this
For this case we have that by definition, the point-slope equation is of the form:
[tex]y-y_ {0} = m (x-x_ {0})[/tex]
Where:
m: It's the slope
[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passes
We find the slope of the line according to the given points:
[tex](x1, y1) :( 7, -21)\\(x2, y2): (- 4,23)[/tex]
[tex]m = \frac {y2-y1} {x2-x1} = \frac {23 - (- 21)} {- 4-7} = \frac {44} {- 11} = - 4[/tex]
So:
[tex]m = -4\\(x_ {0}, y_ {0}) :( 7, -21)[/tex]
Substituting:
[tex]y - (- 21) = - 4 (x-7)\\y + 21 = -4x + 28[/tex]
Answer:
[tex]y + 21 = -4x + 28[/tex]
Answer:
y = - 4x + 28
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (7, - 21) and (x₂, y₂ ) = (- 4, 23)
m = [tex]\frac{23+21}{-4-7}[/tex] = [tex]\frac{44}{-11}[/tex] = - 4
Using m = - 4 and (a, b ) = (7, - 21), then
y + 21 = - 4(x - 7) ← in point- slope form
Distribute right side and simplify
y + 21 = - 4x + 28 ← in slope- intercept form
Roy is twice as old as Joan, and in 3 years the sum of their ages will be 21 years. Find their present ages.
Answer:
Roy is 10 years old at present and Joan is 5 years old at present
Step-by-step explanation:
Let
x----> Roy's age
y----> Joan's age
we know that
x=2y ----> equation A
(x+3)+(y+3)=21 ----> equation B
substitute equation A in equation B
(2y+3)+(y+3)=21
solve for y
3y+6=21
3y=21-6
3y=15
y=5 years
Find the value of x
x=2y ----> x=2(5)=10 years
therefore
Roy is 10 years old at present
Joan is 5 years old at present
Answer:
Roy is 10 and Joan is 5
Step-by-step explanation:
What does it mean for an event to have a probability of 1?
A.
There is a 100% chance that the event will not occur.
B.
There is a 100% chance that the event will occur.
C.
The event might occur.
D.
There is not enough information to determine
Answer:
Step-by-step explanation:
B.
There is a 100% chance that the event will occur.
There is a 100% chance that the event will occur is the correct answer.
Think that you have 6 blue balls in a bags what is the odd of you getting a blue ball when you take one out of the bag?
6/6 easy right.
What does 6/6 equal to?
1 that means if something has a probability of 1 it will always happen
if something has a probability of 0 it is impossible
Tammy says the quotient of 793 ÷ 6 is 132 r1. Use multiplication to check Tammy's answer. × 6 + 1 = Tammy's answer is .
To find the answer, we should multiply 132 by 6.
132*6=792
792+1=793
Tammy’s answer is correct.
An organization of berry farmers releases a study reporting that people who eat blueberries every day have a lower cholesterol level.
Which statement describes the best conclusion to draw from the study?
Answer:
Step-by-step explanation:
The study doesn't prove any causation. The only conclusion is that people with lower cholesterol levels are more likely to eat blueberries.
Answer:
There may be a correlation between eating blueberries and a lower cholesterol level.
Step-by-step explanation:
An organization of berry farmers releases a study reporting that people who eat blueberries every day have a lower cholesterol level.
The statement that describes the best conclusion to draw from the study is :
I would say that the study reveals that there may be a correlation between eating blueberries and a lower cholesterol level.
A laptop computer is purchased for $2250 . After each year, the resale value decreases by 35% . What will the resale value be after 3 years?
[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &2250\\ r=rate\to 35\%\to \frac{35}{100}\dotfill &0.35\\ t=\textit{elapsed time}\dotfill &3\\ \end{cases} \\\\\\ A=2250(1-0.35)^3\implies A=2250(0.65)^3\implies A\approx 617.91[/tex]
The invoice date is November 15. The terms are 4.5/10 EOM. What is the discount rate and the last day to pay in full?
A. 4.5%; November 25
B. 4.5%; December 30
C. 4%; December 25
D. 4.5%; December 20
Answer:
A. 4.5%; November 25
Step-by-step explanation:
4.5/10 EOM is a type of payment term you will see on an invoice. The 4.5 stands for discount percentage and the 10 is a number of days. 4.5/10 means the payment on the invoice is due in 10 days. EOM stands for end of the month. So if the amount is paid within 10 days, the customer gets a discount of 4.5%. Which means the last day to pay in full is November 25. After that there is no discount.
which of the following is an accurate statement of an acceleration value. a 3 meters per second b 3 meters per second 3 square meters per second .
Answer:
The answer would be c
Step-by-step explanation:
The accurate statement about the value of acceleration is 3 meters per second squared.
Given data:
Acceleration is a fundamental concept in physics that describes the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction.
It can be expressed as:
a = Δv / Δt
where Δv represents the change in velocity and Δt represents the change in time.
So, the denominator of the acceleration expression has the square of time.
Hence, the statement 3 meters per second squared determines the acceleration.
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The complete question is attached below:
Which of the following is an accurate statement of an acceleration value, translated from symbols into words?
A) 3 meters per second
B) 3 meters per second squared
C) 3 square meters per second
D) 3 meters in 3 seconds
Given: f (x ) = 4x⁴ - 15 and g (x ) = 2x + 11
What is the value of g (f (x )) ?
64x^4+1408x^3+11616x^2+ 42592x+ 58549
In Mr. Huanabe’s class, students are split into groups of 8. Each group member measured the length of his or her hair. Veronica had the longest hair in her group, with a length of 42 inches. The other seven group members had hair lengths measuring 13, 23, 24, 5, 5, 13, and 8 inches. Find the mean, median and mode without and with Veronica’s hair length, and explain the changes.
Neeeeed Help..
Answer:
With Veronica's hair
Median: 13
Mean: 17.9
Mode: 13,5
Without
Mean :13.8
median: 13
mode: 13,5
Step-by-step explanation:
If secx = -2, then in which quadrants do the solutions lie?
A. I, II
B. I, III
C. II, III
D. III, IV
ANSWER
C. II, III
EXPLANATION
The secant ratio is negative in the second and third quadrants but positive in the first and fourth quadrants.
The given secant ratio is
[tex] \sec(x) = - 2 = - \frac{2}{1} [/tex]
Since the secant ratio is negative, its solution must lie in the third and second quadrant.
The correct answer is C
Two angles of a triangle measure 48° and 97°. If the longest side is 12 cm, find the length of the shortest side to the nearest tenth.
A) 5.8 cm
B) 6.9 cm
C) 8.1 cm
D) 9.0 cm
Answer:
B) 6.9 cm
Step-by-step explanation:
The remaining angle is the smallest, 180° -48° -97° = 35°. The shortest side is opposite this angle. The Law of Sines tells you its length is ...
short side = (longest side)·(sin(smallest angle)/sin(largest angle))
= (12 cm)sin(35°)/sin(97°) ≈ 6.9 cm
The shortest side is about 6.9 cm.
A mutual fund has a market value of $40,000,000 and 4,000,000 outstanding shares. What is the value per share?
1
10
100
1,000
Answer:
Option B. $10.00
Step-by-step explanation:
Market value of a mutual fund = $40,000,000
Total outstanding shares = 4,000,000
To find out per share value we use this formula
[tex]\frac{\text{Market value of the shares}}{\text{total number of shares}}[/tex]
[tex]\frac{40,000,000}{4,000,000}[/tex] = $10/share
The value of per share is $10.00
PLEASE HELP I AM VERY CONFUSED AND WANT TO UNDERSTAND!!!! WILL MARK BRAINLIEST!!!
Answer:
with?
Step-by-step explanation:
Can someone pease help
Consider the sequence below.
Complete the recursively defined function to describe this sequence.
ANSWER
[tex]f(1) = - 34[/tex]
[tex]f(n) = f(n - 1) + 13[/tex]
EXPLANATION
The given sequence is;
-34,-21,-8,5,....
The first term of the sequence is
[tex]f(1) = - 34[/tex]
The common difference is
[tex]d = 5 - - 8[/tex]
[tex]d = 5 + 8 = 13[/tex]
The recursive definition is given by;
[tex]f(n) = f(n - 1) + d[/tex]
[tex]f(n) = f(n - 1) + 13[/tex]
for n=2,3,4,...
Answer:
I just took the test and got it right.
Step-by-step explanation:
A quadratic function and an exponential function are graphed below. Which graph most likely represents the quadratic function?
*PIC*
f(x), because an increasing exponential function will eventually exceed an increasing quadratic function
g(x), because an increasing quadratic function will eventually exceed an increasing exponential function
g(x), because an increasing exponential function will always exceed an increasing quadratic function until their graphs intersect
f(x), because an increasing quadratic function will always exceed an increasing exponential function until their graphs intersect
Answer:
The right answer for the question that is being asked and shown above is that: "f(x), because an increasing exponential function will always exceeds an increasing quadratic function until their graphs intersect." The points of f(x) compared to g(x) is more increasing.
hope this help
The graph which most likely represents the quadratic function is f(x), because an increasing exponential function will eventually exceed an increasing quadratic function.
What is a quadratic function ?A quadratic function is the function in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic function is,
f(x)=ax²+bx+c
Here,(a,b, c) is the real numbers and (x) is the variable.
Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
An increasing exponential function is eventually exceed an increasing quadratic function.
Thus, the graph which most likely represents the quadratic function is f(x), because an increasing exponential function will eventually exceed an increasing quadratic function.
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40 POINTS HELP FAST!!
Ori needs to find how many 1/4th sections are in a half an apple.Use the fraction bars to model 1/2 divided by 1/4 Then solve the division problem.
A.1/2
B.1
C.2
D.3/4
Answer:
The answer is C.
Step-by-step explanation:
1/2 x 4/1 = ?
We begin by multiplying the numerators:
1 x 4 = 4
And then we multiply the denominators:
2 x 1 = 2
The answer has a numerator of 4 and a denominator of 2. In other words:
1 x 4/2 x 1 =4/2
This fraction can be reduced to lowest terms:
4 ÷ 2/2 ÷ 2 =2/1 = 2
Two cars started moving in opposite directions from the same point at the same moment of time. If the speed of one car is 50 mph, and the other car goes at a speed of 60 mph, how soon the distance between them will become 1320 miles?
<---------------------------||----------------------------------------->
A B
50 mph 60 mph
so let's recall that d = rt, distance = rate * time.
both cars start out at the same time, say "t" hours.
after "t" hours car A has covered say "d" miles, since there's a total of 1320, then car B must surely had covered the slack, or 1320 - d.
[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ A&d&50&t\\ B&1320-d&60&t \end{array}\qquad \implies \begin{cases} ~\hfill \boxed{d}=50t\\ 1320-d=60t \end{cases} \\\\\\ 1320-\boxed{50t}=60t\implies 1320=110t\implies \cfrac{1320}{110}=t\implies 12=t[/tex]
Huang, José, and Sam ran a 100-m dash. José did not come in second; Huang did not come in third. José’s time was 2 seconds faster than that of the oldest boy in the race. In what order did the boys finish the race?
a. José, Huang, Sam
b. José, Sam, Huang
c. Sam, José, Huang
d. Sam, Huang, José
Answer:
A. José, Huang, Sam
Explanation:
José’s time is faster than the oldest boy, so he came in 1st or 2nd. It is given that José did not come in second, so he came in first. The remaining places are second and third. It is stated that Huang did not come in third, so Huang came second and Sam came third. The order is José, Huang, and then Sam.
A. josé ,Huang ,Sam
The sequence is shown below what is the sum of the sequence?
Answer:
1.875
Step-by-step explanation:
1+ 0.5 = 1.5
1.5+0.25 = 1.75
1.75+0.125 = 1.875
Answer:
1.875
Step-by-step explanation:
Find the equation of the graph in function notation. Name your function "f" and use x as your variable.
Answer:
[tex]f(x)=\frac{1}{2}x-1[/tex]
Step-by-step explanation:
The equation of the graph can be obtained using the formula:
[tex]\frac{x}{x-intercept}+\frac{y}{y-intercept}=1[/tex]
From the graph, the y-intercept is -1 and the x-intercept is 2
We substitute these values to get:
[tex]\frac{x}{2}+\frac{y}{-1}=1[/tex]
[tex]\frac{x}{2}-y=1[/tex]
This implies that;
[tex]\frac{x}{2}-1=y[/tex]
Or
[tex]y=\frac{1}{2}x-1[/tex]
The function notation is
[tex]f(x)=\frac{1}{2}x-1[/tex]