let's say each restaurant has a container of soup which is the same size, let's say there is a total of "s" amount of soup in the container of each restaurant, so 5/4 of that much will just be (5/4)s and 7/4 of "s" is just (7/4)s.
well, one restaurant makes 20 servings from 5/4 of it and the other makes 25 from 7/4 of it,
[tex]\bf \cfrac{5}{4}s\div 20\implies \cfrac{5}{4}s\div \cfrac{20}{1}\implies \cfrac{~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{4}s\cdot \cfrac{1}{\underset{4}{~~\begin{matrix} 20 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \boxed{\cfrac{1}{16}}s \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{4}s\div 25\implies \cfrac{7}{4}s\div \cfrac{25}{1}\implies \cfrac{7}{4}s\cdot \cfrac{1}{25}\implies \boxed{\cfrac{7}{100}}s[/tex]
now, which one is larger? well, we can simply put both fractions with the same denominator by multiplying one by the other's denominator,
[tex]\bf \cfrac{1}{16}\cdot \cfrac{100}{100}\implies \boxed{\cfrac{100}{1600}}\qquad \qquad \qquad \stackrel{\textit{\Large larger}}{\cfrac{7}{100}\cdot \cfrac{16}{16}\implies \boxed{\cfrac{112}{1600}}}[/tex]
45-2×(15-3) Please Help me figure this out because my calculator says the answer is 21 but I don't know why
Answer:
see explanation
Step-by-step explanation:
Following the order of operations as set out in PEMDAS
Given
45 - 2 × (15 - 3) ← evaluate parenthesis
= 45 - 2 × 12 ← evaluate multiplication
= 45 - 24 ← evaluate subtraction
= 21
If f(x) = 2x2 – 5 and g(x) = -x + 3, what is the value of f(g(4))?
Answer:
-3
Step-by-step explanation:
f(x) = 2x2 – 5 and g(x) = -x + 3,
g(4) = -4+3=-1
f(g(4)) = f(-1) = 2(-1)² -5 = -3
In ΔOPQ, the measure of ∠Q=90°, OQ = 39, QP = 80, and PO = 89. What is the value of the tangent of ∠P to the nearest hundredth?
The given question is about a right triangle (ΔOPQ) where the value of the tangent of ∠P is being calculated. Using the lengths of the sides, tang P is calculated as 80/39 which is equal to 2.05 to the nearest hundredth.
Explanation:In ΔOPQ, which is a right triangle with ∠Q being 90°, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the student wants to find the value of the tangent of ∠P.
The side opposite ∠P is QP and the side adjacent to ∠P is OQ. Given that QP = 80 and OQ = 39, we can calculate tan P as follows:
tan P = QP/OQ = 80/39 = 2.05Therefore, to the nearest hundredth, the value of the tangent of ∠P in ΔOPQ is 2.05.
Learn more about Tangent of an angle here:https://brainly.com/question/23185930
#SPJ12
To find the value of the tangent of angle P in triangle OPQ, we can use the trigonometric function tangent, which is the ratio of the length of the opposite side to the length of the adjacent side. By substituting the given lengths into the formula, we can calculate the value of tangent to be approximately 0.8989.
Explanation:In triangle OPQ, we are given that angle Q is a right angle (90 degrees), OQ is 39 units, QP is 80 units, and PO is 89 units. To find the value of the tangent of angle P, we need to use the trigonometric function tangent, which is defined as the ratio of the length of the opposite side to the length of the adjacent side.
Tan(P) = Opposite/Adjacent
In this triangle, the opposite side of angle P is QP and the adjacent side is OP. Therefore, we can substitute the given lengths into the formula:
Tan(P) = 80/89
To find the value of tangent, we can divide 80 by 89 using a calculator or decimal approximation.
Tan(P) ≈ 0.8989 (rounded to the nearest hundredth)
Learn more about Tangent of an angle here:https://brainly.com/question/23185930
#SPJ12
In 6th grade, the ratio of boys to girls is 4 to 5. If there are 145 girls,how many boys are there
Step-by-step explanation:
whrn you have a proble. you can tell me thank you have a nice day
To solve, find how many groups of 5 are in 145 girls (145 ÷ 5 = 29 groups of girls). Then, find how many boys are in these groups by multiplying the number of groups by the boys' ratio (4), thus 29 x 4 = 116 boys in the 6th grade.
Explanation:To determine the number of boys in the 6th grade, we will make use of the ratio provided, 4:5. This ratio means that for every 4 boys, there are 5 girls. To translate this into actual numbers, take the total number of girls (145) and calculate how many groups of 5 you have, because that's how many groups of boys you would have also. To determine the number of boys, you multiply the number of groups by 4.
First, Divide 145 by 5 to find out how many groups of girls there are: 145 ÷ 5 = 29. These equate to groups of students based on the ratio. Second, Multiply the number of groups by the boys’ ratio number (4) to find the number of boys. So, 29 x 4 = 116. That's the total number of boys in the 6th grade.
Learn more about Ratio here:
https://brainly.com/question/32531170
#SPJ2
The circumference of a circle is 32 centimeters. Which is closest to the radius? A. 10.2 centimeters B. 5.1 centimeters C. 16 centimeters D. 5.3 centimeters
Answer:
B.5.1 cm
Step-by-step explanation:
Hello, I think I can help you with this
the circumference of a circle is given by:
[tex]s=2*\pi *radius[/tex]
Step 1
Let
s=32 cm
radius=?
isolate the radius from the equation
[tex]s=2*\pi *radius\\\frac{s}{2\pi } =radius\\s=32,so\\radius=\frac{32}{2\pi } \\radius=5.1\ cm[/tex]
5.1 cm ⇔B.
I hope it helps ,Do not hesitate to ask me any questions about it. Have a fantastic day
Which equation represents the slope-intercept form of the line below?
y-intercept = (0, -6)
slope = -5
Answer:
y = - 5x - 6
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 )
Here m = - 5 and c = - 6, thus
y = - 5x - 6 ← equation in slope- intercept form
The slope intercept form is y = -5x-6
What is the required equation of line ?
Given, y-intercept = (0, -6) & slope of the line = -5
The general form of an equation of line is, y = mx+c
where, m is the slope of the line & c is the y intercept
So, when x = 0 , y = -6
So, the line above passes through the point (0, -6)
Therefore, The slope intercept form is, y = -5x-6
Learn more about equation of line here :
https://brainly.com/question/27885940
#SPJ2
Mr. Hermans's class is selling candy for a school fundraiser. their goal is to raise $500 by selling C boxes of candy. for every box of candy they sell, they earn $2.75. Write and equation that the students could solve to figure out how many boxes they need to sell. Please answer quickly.
The equation to solve how many boxes of candy Mr. Hermans's class needs to sell to reach their goal of $500 is 2.75C = 500. To solve for C (number of boxes), divide 500 by 2.75.
Explanation:In order to figure out how many boxes of candy Mr. Hermans's class needs to sell, you can create an algebraic equation using your known values. Here you know that for each box of candy sold, the class earns $2.75 (represented in our equation as 2.75C) and that their fundraising goal is $500. This sets up the equation as 2.75C = 500. To solve this equation and find the number of boxes needed (represented by 'C'), you would divide each side of the equation by 2.75, which gives you C = 500 / 2.75.
Learn more about Algebraic equations here:https://brainly.com/question/953809
#SPJ12
The perimeter P of a square whose side length is n… is this direct variation?
The perimeter of a square is four times the side, since you have to sum all sides, and they're all the same length:
[tex]P=n+n+n+n=4n[/tex]
This is direct variation, because we have
[tex]P=4n \iff \dfrac{P}{n}=4[/tex]
and if the ratio between two variables is constant (in this case, 4), then the two variables are in direct variation.
The perimeter of a square is directly proportional to its side length, therefore it's an example of direct variation.
Explanation:Yes, the perimeter (P) of a square with side length (n) is an example of direct variation. In this case, P is directly proportional to n. To understand this, think of a square. A square has four equal sides. Thus, its perimeter (P) is n times 4, or P = 4n. If n is increased, the perimeter also increases proportionally, which supports that it's a direct variation relationship. A change in one quantity leads to a proportional change in the other one.
Learn more about Direct Variation here:https://brainly.com/question/9775007
#SPJ3
The question: A parallelogram has vertices at (0,0), (0,6), (4,4), and (4, -2). Which transformation maps the parallelogram to itself?
Answer:
C
Step-by-step explanation:
Consider all options.
A. A reflection across the line x=2 gives us the parallelogram A'B'C'D' (see first attached diagram) with vertices A'(4,0), B'(4,6), C'(0,4) and D'(0,-2). As you can see this is not the same parallelogram as parallelogram ABCD.
B. A reflection across the line y=2 gives us the parallelogram A''B''C''D'' (see first attached diagram) with vertices A''(0,4), B''(0,-2), C''(4,0) and D''(4,6). As you can see this is not the same parallelogram as parallelogram ABCD.
C. A rotation of 180° about the point (2,2) gives us the same parallelogram ABCD (see second attached diagram), because the image of A is C, the image of B is D, the image of C is A and the image of D is B.
D. A rotation of 180° about the point (0,0) gives us the parallelogram A'''B'''C'''D''' (see second attached diagram) that differs from parallelogram ABCD.
Answer:
c
Step-by-step explanation:
7 divided by 4,088 in long division
Answer:584
Step-by-step explanation:
Final answer:
To simplify 2.4 times 10¹³ divided by 8 times 10⁷, subtract exponents to get 2.4 times 10⁶, or adjust the numerator and divide by 8 to find 3 times 10⁵ as the result to perform the calculation mentally.
Explanation:
When dealing with the division of expressions involving powers of ten, using exponent subtraction is often useful to simplify the problem. For the expression 2.4 times 10¹³ divided by 8 times 10⁷, one approach is to directly subtract the lower exponent from the higher one, yielding 2.4 times 10¹³⁻⁷, which simplifies to 2.4 times 10⁶. However, to perform in my head, an alternative way is to adjust the numerator by dividing it by 8, which results in 0.3 times 10¹³. Moving the decimal point in the numerator gives 3 times 10¹², and then dividing by 10⁷ gives a final result of 3 times 10⁵.
-1+3m=2m+4
what is the answere to that?
Write the equation of the line that passes through the points (8,1) and (2,-5) in standard form, given the the point- slope for is y+1=2/3(x-8)
first off, those two points above do not give that point-slope form, however, the issue is just what's the standard form.
keeping in mind that standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]\bf y+1=\cfrac{2}{3}(x-8)\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y+1)=3\left( \cfrac{2}{3}(x-8) \right)}\implies 3y+3=2(x-8) \\\\\\ 3y+3=2x-16\implies 3y=2x-19\implies -2x+3y=-19 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 2x-3y=19~\hfill[/tex]
The equation of the line that passes through the points (8,1) and (2,-5) in standard form is 2x - 3y = 13.
Explanation:To find the equation of the line that passes through the given points we need to understand the slope (rise over run) and the y-intercept. The provided equation, y + 1 = 2/3(x - 8), is in point-slope form (which is y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the line). To transform to the standard form, we distribute the 2/3 on the right side, subtract 1 from both sides to move y to the left side.
Following these steps, we get: 2x - 3y = 13, as the equation of the line in the standard form.
Learn more about Lines Equation here:https://brainly.com/question/30600659
#SPJ3
Trevor spent $27 and now has no money left. What did he have before his purchase
Answer:$27
Step-by-step explanation:
x-27=0
0+27=27
27-27=0
What is the sum of the polynomials?
17m-12n-1+4-13m-12n
[tex]\text{Hello there!}\\\\\text{Combine like terms:}\\\\17m-12n-1+4-13m-12n\\\\4m-12n-1+4-12n\\\\4m-24n-1+4\\\\\boxed{4m-24n+3}[/tex]
Final answer:
The sum of the given polynomials is 4m - 24n + 3.
Explanation:
The sum of the polynomials 17m-12n-1+4-13m-12n can be found by combining like terms. To combine like terms, we group the terms containing the same variable and their coefficients.
Here’s how you can solve this:
Combine the terms with m: 17m and -13m to get 4m.Combine the terms with n: -12n and -12n to get -24n.Combine the constant terms: -1 and 4 to get 3.After combining like terms, the sum of the polynomials is 4m - 24n + 3.
Given the functions f(x) = 3x2, g(x) = x2 - 4x + 5, and h(x) = -2x2 + 4x + 1, rank them from least to greatest based on their axis of symmetry.
f(x), g(x), h(x)
f(x), h(x), g(x)
g(x), h(x), f(x)
g(x), f(x), h(x)
Answer:
If we rant their axis of symmetry from least to greatest, it would be:
f(x),h(x), g(x)
Step-by-step explanation:
Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror like reflection of either side of the object.
We can find axis of symmetry with the help of formula:
x = -b/2a
We know that the quadratic equation is written like:
ax^2+bx+c
where a,b are coefficients: c is constant term and x is variable
Now look at the function f(x)= 3x^2
For this function we have a= 3, b =0 , c=0
Put the values in the above mentioned formula:
x = -b/2a
x = - (0)/2(3)
x = 0/6 = 0
Thus the axis of symmetry for f(x) = 0
Now g(x) = x2 - 4x + 5
a = 1 , b = -4 , c =5
x = -b/2a
x = -(-4)/2(1)
x = 4/2
x = 2
Axis of symmetry for g(x) = 2
h(x) = -2x2 + 4x + 1
a = -2 , b =4 , c=1
x = -b/2a
x = -(4)/2 (-2)
x = -4 /-4
x = 1
Axis of symmetry for h(x) = 1
So if we rant their axis of symmetry from least to greatest, it would be:
f(x),h(x), g(x)
How can I Factor the expression below 9x2-1
Answer:
Step-by-step explanation:9×2=18
18-1=17
Anwser 17
Answer:
(3x – 1)(3x + 1)
Step-by-step explanation:
A recipe uses 5 cups of water, 3 cups of rice, and 1 cup of black beans. What is the ratio of cups of rice to cups of water?
I believe it is 5:3:1. I'm not completely sure, but that's what I think it is.
The ratio of cups of rice to cups of water in the recipe is 3:5, as there are 3 cups of rice for every 5 cups of water.
To find the ratio of cups of rice to cups of water from the recipe that calls for 5 cups of water and 3 cups of rice, you can simply compare the two quantities directly. The question asked does not require considering additional batches or conversions, so we look at the given amounts.
For every 3 cups of rice, there are 5 cups of water. This can be written as 3:5 or as a fraction \\(\frac{3}{5}\\).
Therefore, the ratio of cups of rice to cups of water is 3:5.
If you buy 15 bags of grass seed which cost $8.29 each, what is the total cost? $87.05 $82.90 $127.50 $124.35
Answer:124.35
Step-by-step explanation: if you times 8.25 by 15 you will get the answer of 124.35
In order to get the answer to this question you could rather multiply $8.29 by 15 or you could add 8.29 15 times.
[tex]1b=8.29[/tex]
[tex]15\times8.29=124.35[/tex]
[tex]=124.35[/tex]
Therefore your answer would be the fourth option "$124.35."
Hope this helps.
A swimming pool has 500 gallons of water in it and is leaking. The change in the amount of water in the pool is -3 gallons per hour. How many gallons of water will the pool contain after 6 hours?
Answer:it will be -18 gallons
Step-by-step explanation:
Answer:
482 gallons
Step-by-step explanation:
if the total amount in the pool is 500 gallons and it is leaking at -3 gallons per hour then we can solve for how much it has lost in 6 hours by using this equation:
-3(amount loss per hour) x 6(number of hours)= -18
Now we do 500(total)-18(amount lost in 6 hours)= 482 gallons
Which means there are 482 gallons of water left after 6 hours.
-3.3m=-1.1 please include how you solved it
Answer:
1/3
Step-by-step explanation:
-3.3m = -1.1
Divide both sides by -3.3
m = -1.1
-3.3
The solution to the equation -3.3m = -1.1 is m = 1/3 or approximately 0.33. This was determined by dividing both sides of the equation by -3.3.
Explanation:The problem -3.3m = -1.1 is a simple one-step equation which can be solved by isolating the variable. Here the variable is m. Dividing both sides of the equation by -3.3, we get m = (-1.1/-3.3). This simplifies to m = 1/3 ≈ 0.33. So, the solution to the equation is m = 0.33.
What we did here is an application of the principle that whatever you do to one side of an equation, you should do to the other side as well. This principle is essential in solving mathematical equations.
Learn more about Solving Equations here:https://brainly.com/question/18322830
#SPJ2
What is the range of this function?
Whats the place and value of each underlined digit for example whats the place and value of 5,291
I do not see the underlined digit, but I will do this for you. The 5 in the thousands place is worth 5000, the 2 in the hundreds place is worth 200, the 9 in the tens place is worth 90, and the 1 in the ones place is worth 1.
Hope this helped!
Nate
Final answer:
In the number 5,291, the digit 5 is in the thousands place (value of 5,000), the digit 2 is in the hundreds place (value of 200), the digit 9 is in the tens place (value of 90), and the digit 1 is in the ones place (value of 1).
Explanation:
The place value of a digit in a number indicates the value of the digit based on its position relative to the other digits. For example, in the number 5,291, the digit 5 is in the thousands place, which means its value is 5,000. Similarly, the digit 2 is in the hundreds place, so its value is 200; the digit 9 is in the tens place, so its value is 90; and the digit 1 is in the ones place, which means its value is simply 1.
The speed of a moving object equals
distance divided by time. If a bicycle
rider averages 7.5 mph for 6 h, how
far did he ride?
Answer:
45 Miles
Step-by-step explanation:
Speed = Distance / Time
Distance = Speed * Time
= 7.5 * 6 = 45 Miles
Final answer:
To find the distance traveled by the bicycle rider, multiply the average speed of 7.5 mph by the time of travel of 6 hours, resulting in a total distance of 45 miles.
Explanation:
Calculating Distance Traveled
To calculate the distance traveled by the bicycle rider, we use the formula that relates average speed, distance traveled, and time of travel:
Average speed = Distance traveled / Time of travel
In this scenario, the bicycle rider's average speed is given as 7.5 mph, and the time of travel is 6 hours. Therefore, the distance traveled can be calculated by multiplying the average speed by the time of travel:
Distance traveled = Average speed × Time of travel
Distance traveled = 7.5 mph × 6 h = 45 miles
Therefore, the bicycle rider traveled a total of 45 miles.
Which ordered pair (c,d) is the solution to the given system of linear equations?
-C+2d=13
|-9c-4d=-15
Answer:
(-1, 6)
Step-by-step explanation:
{-c + 2d = 13
{-9c - 4d = -15
-⅑[-9c - 4d = -15]
{-c + 2d = 13
{c + 4⁄9d = 1⅔ >> New equation
______________
2 4⁄9d = 14⅔
______ _____
2 4⁄9 2 4⁄9
d = 6 [Plug this back into both equations to get the c-value of -1]; -1 = c
I am joyous to assist you anytime.
Answer:
(-1,6)
Step-by-step explanation:
We are given that system of linear equations
[tex]-c+2d=13[/tex]
[tex]-9c-4d=-15[/tex]
We have to find the value of ordered pair (c,d).
Equation first multiply by 2 then add to equation second
We get
[tex]-9c-4d-2c+4d=26-15[/tex]
[tex]-11c=11[/tex]
[tex]c=\frac{11}{-11}=-1[/tex]
Substitute the value of c in equation first then, we get
[tex]-(-1)+2d=13[/tex]
[tex]1+2d=13[/tex]
[tex]2d=13-1=12[/tex]
[tex]d=\frac{12}{2}=6[/tex]
Hence, the ordered pair (-1,6) is the solution of given system of linear equations.
x² - y² = z²
Express y in terms of x and z.
Answer:
y² = x² - z²
Step-by-step explanation:
x² - y² = z²
Transpose y the other side
x² - z² = y²
or
y² = x² - z²
Answer:
y= ± [tex]\sqrt{x^2-z^2}[/tex]
Step-by-step explanation:
Given
x² - y² = z² ( isolate y² by subtracting x² from both sides )
-y² = z² - x² ( multiply through by - 1 )
y² = x² - z² ( take the square root of both sides )
y = ± [tex]\sqrt{x^2-z^2}[/tex]
A small transport truck can carry about 200 pounds of fruits and vegetables. How many ounces of fruits and vegetables can the truck carry? (1 pound = 16 ounces) A. 12.5 ounces B. 25 ounces C. 200 ounces D. 1,600 ounces E. 3,200 ounces
Answer:
All you have to do is convert the pounds into ounces by doing 200 x 16! That equals 3,200! So therefore your answer would be “The truck can carry 3,200 ounces of fruits and vegetables or 200 pounds!” AKA E.
Idk idk idk idk help pls
Answer:
shade in 7 rectangles, than shade in 70 cubes
Step-by-step explanation:
Step-by-step explanation:
color 7 rectangles then 7 squares
0.2(x – 4.5) + 1.7 = 9.6
Answer:
44
Step-by-step explanation:
3dgenuity said so
5-0.852. What's is the answer
Answer:
4.148
Step-by-step explanation:
20 POINTS¡!!!!!
At top speed, the Spirit of Australia boat can cover 1,533 kilometers in 3 hours. At what unit rate does the boat travel during this time frame?
The boat travels at a unit rate of ____ kilometers per hour during the given time frame.