Evan's mother used 1/3 pound of beef, 1/2 pound of shrimp, and 3 pounds of pasta to make dinner for 4 people.
Use this information to answer ALL FOUR PARTS below.
Question:
Part A:
Each person will receive an equal share of beef with none left over. What is the amount, in pounds, of each serving of beef?
Part B:
Each person will receive an equal share of shrimp with none left over. What is the amount, in pounds, of each serving of shrimp?
Part C:
Each person will receive an equal share of pasta with none left over. What fraction represents the amount, in pounds, of each serving of pasta?
Part D:
Evan only ate 1/2 of the pasta that he received. What is the amount, in pounds, of pasta did Evan eat? Explain how you got this answer step-by-step using math vocabulary.
The area of a rectangle playgrond is 78 square meters. If the length of the playground is 13 meters, what is its width?
Answer:
6 meters.
Step-by-step explanation:
Let w represent width of the rectangle.
We have been given that the area of a rectangle playground is 78 square meters. The length of the playground is 13 meters.
We know that area of a rectangle is width times length of rectangle. We can represent our given information in an equation as:
[tex]\text{Area of rectangle}=\text{Length}\times \text{Width}[/tex]
[tex]78\text{ m}^2=13\text{ m}\times \text{Width}[/tex]
[tex]13\text{ m}\times \text{Width}=78\text{ m}^2[/tex]
[tex]\frac{13\text{ m}\times \text{Width}}{13\text{ m}}=\frac{78\text{ m}^2}{13\text{ m}}[/tex]
[tex]\text{Width}=6\text{ m}[/tex]
Therefore, the width of the rectangle is 6 meters.
A wooden disk is shaped like a cylinder with a radius of 20.2 millimeters, and a height of 3.9 millimeters. What is the surface area of the wooden disk to thenearest whole millimeter?
A candy wrapping robot can wrap 434 pieces of candy in five minutes. How many pieces of candy can it wrap in any number of minutes
-4x-15y=-17
-x+5y=-13
[tex] - 4x - 15y = - 17 \\ - x + 5y = - 13[/tex]
Edwin needs to buy a car, a truck, and a motorcycle for his shipping business. He wants the car to be red or yellow; the truck to be black, white, or silver; and the motorcycle to be green, blue, or orange.
How many different combinations of vehicles does Edwin have to choose from?
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What is the trigonometric ratio for sin C ?
Enter your answer, as a simplified fraction, in the boxes.
Answer:
The trigonometric ratio for [tex]\sin C[/tex] is [tex]\frac{9}{41}[/tex]
Step-by-step explanation:
Given : A right triangle ABC with ∠B = 90° and AC = 82 and BC = 80
We have to find the value of [tex]\sin C[/tex]
Since, Sine is defined as the ratio of perpendicular to its hypotenuse.
Mathematically written as [tex]\sin\theta=\frac{Perpendicular}{Hypotenuse}[/tex]
For the given triangle ABC, we have
Using Pythagoras theorem, For a right angled triangle, sum of square of base and perpendicular is equal to the square to its hypotenuse.
[tex](AC)^2=(AB)^2+(BC)^2[/tex]
Substitute, we get,
[tex](82)^2-(80)^2=(AB)^2\\\\ 6724-6400=(AB)^2\\\\ 324=(AB)^2\\\\ \Rightarrow AB =18[/tex]
[tex]\theta=C[/tex]
So, perpendicular = AB and Hypotenuse = AC
[tex]\sin C=\frac{AB}{AC}[/tex]
[tex]\sin C=\frac{18}{82}=\frac{9}{41}[/tex]
Thus, The trigonometric ratio for [tex]\sin C[/tex] is [tex]\frac{9}{41}[/tex]
What is the volume of a cube with an edge length of 3.2 meters? Enter your answer, as a decimal, in the box.
A standard coffee mug has a capacity of 16 fluid ounces. If Annie needs to fill 12 mugs mugs with coffee, how many quarts of coffee does she need?
Vote for the best representation of 7 95/125 what’s the answer ??
Given is a mixed number i.e. [tex] 7\frac{95}{125} [/tex].
We can solve it as given below :-
[tex] 7\frac{95}{125} \\\\
=\frac{(125*7)+95}{125} \\\\
=\frac{875+95}{125} \\\\
=\frac{970}{125} \\\\
=\frac{194}{25} \\\\
=7\frac{19}{25} \;\;or\;\; 7.76 [/tex]
Hence, [tex] \frac{194}{25} \;or\; 7\frac{19}{25} \;or\; 7.76 [/tex] would be better representation of given mixed number i.e. [tex] 7\frac{95}{125} [/tex].
Hope, this helps! :)
If there is a 30% increase in the operation charge for using a service,$82.70 remains to be paid.how much is the original bill ?
a photograph measuring 4 inches wide and 5 inches long is enlarge to make a wall mural. If the mural is 120 inches wide, how long is the mural?
If f=6 and g=8, what does h equal
The value of h in this given alphabetical series is 10.
What is an arithmetic sequence?The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the. sequence. The nth term of an arithmetic sequence is given by. aₙ = a + (n – 1)d
Given, f=6 and g=8
Since, there is no additional data is given I will assume this is the question of Alphabetic sequence.
In Alphabet Series section, a string of alphabets, either in a single file or in combination form a sequence. This sequence comes together following a definite rule. The candidate is expected to detect this rule and answer the questions at the end.
So,
the value of f = 6 and g = 8
Since, Alphabetic order after f and g is h, i ,j, k, l, .....
And common factor is 2
Thus,
The value of h = 8+2 = 10
The value of i = 10+2 = 12
The value of j = 12 +2 =14
And so on
Learn more about arithmetic sequence here:
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Determine the volume of a cylindrical bucket if the diameter is 8.5 in. and the height is 11.5 in.
A. 652.2 in3
B. 2608.9 in3
C. 306.9 in3
D. 882.4 in3
We know that the volume,V of a cylinder is given by:
[tex] V=\pi r^2h [/tex]
where r is the radius, h is the height of the cylinder.
Now, it has been given to us that the diameter of the cylinder is 8.5 in. Therefore, the radius of the cylinder will be half it's diameter and will be, [tex] r=\frac{1}{2}\times 8.5=4.25 [/tex] in.
The height, h=11.5 inches
Therefore, applying the formula we will get:
Volume, V=[tex] \pi (4.25)^2(11.5)\approx652.57 in^3 [/tex]
Thus, out of the given options, Option A is the correct option.
Carlos and Maria drove a total of 233 miles in 4.4 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.
Answer:
Time of driving of Maria = 1.8 hours
Step-by-step explanation:
Let a be time drove by Carlos and b be the time drove by Maria.
Carlos and Maria drove a total of 233 miles in 4.4 hours.
Total time = 4.4 hours
a + b = 4.4 ------------------eqn 1
Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour.
Speed of Carlos = 55 miles per hour
Speed of Maria = 50 miles per hour
Total distance = 233 miles
That is
55 a + 50 b = 233----------------------eqn 2
eqn 1 x 50
50 a + 50 b = 220---------------------------eqn 3
eqn 3 - eqn 2
55 a + 50 b - 50 a - 50 b = 233 - 220
5a = 13
a = 2.6
Substituting in eqn 1
2.6 + b = 4.4
b = 1.8
Time of driving of Maria = 1.8 hours
A shopper buys cat food in bags of 3 lbs. Her cat eats 3/4 lb each week. How many weeks does one bag last?
Final answer:
To find out how many weeks a 3 lb bag of cat food will last for a cat that eats 3/4 lb per week, divide the total weight of the bag by the weekly consumption. One 3 lb bag lasts for 4 weeks.
Explanation:
The question asks how many weeks a bag of cat food will last if the cat eats 3/4 lb each week and the bag is 3 lbs. To find the answer, we need to divide the total weight of the bag by the amount eaten each week.
Here's the step-by-step calculation:
Total weight of cat food per bag: 3 lbsThe amount of cat food the cat eats per week: 3/4 lbNumber of weeks one bag lasts = Total weight of cat food per bag \/ The amount of cat food the cat eats per weekNumber of weeks one bag lasts = 3 lbs / 3/4 lb = 4 weeksTherefore, one bag of cat food will last for 4 weeks.
A sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7 : 6. The store donates 24 soccer balls. How many basketballs does the store donate
The store donates __ basketballs
what does this mean? and can gove answer
2 - 4x = 14 A) -4 B) -3 C) 0 D) 3 Eliminate
Derek uses a $50 gift card to purchase 3 books for $12 each and a calendar for $9.What is the amount left on the card ?
the fish tank in Paul's bedroom has a pump that will recirculate 75 gallons of water in 1/4 of an hour. Find the unit rate in gallons per hour.
a. 5 gallons per hour
b. 18.75 gallons per hour
c. 300 gallons per hour
d. 187.5 gallons per hour
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Graph the two lines
2x + 3y = 18
3x -4y > 16.
Give the Domain and Range, Slope, and Y-intercept for each line. Graph each equation above on the graph below and show all work. Give the Domain and Range, Slope, and Y-intercept for each line. Explain in detail how you got each answer.
2x + 3y = 18 3x -4y > 16
Slope-Intercept Form: Slope-Intercept Form:
Domain: Domain:
Range: Range:
Slope: Slope:
Y-intercept: Y-intercept:
Answer:
For Equation 1:
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]Y-intercept: 6For Equation 2:
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\frac{3}{4}[/tex]Y-intercept: -4Step-by-step explanation:
We are given two lines - one is an equation and one is an inequality.
Neither are in slope-intercept form (y = mx + b), so we need to make these adjustments.
Slope-intercept form has two key parts to the equation: m, which is the slope of the line and b, which is the y-intercept of the line.
Equation 1
[tex]\displaystyle2x+3y=18\\\\3y = -2x + 18\\\\y = -\frac{2}{3}x+6[/tex]
With this, we can now determine the domain, range, slope, and y-intercepts for this line.
For Equation 1, because our equation is in slope-intercept form, we can find the slope and the y-intercept.
Our equation is [tex]y=-\frac{2}{3}x+6[/tex]. Therefore, our m is [tex]-\frac{2}{3}[/tex] and our b is 6.
Because the equation is linear, there is no instance in which the line will not meet an x- or y-value. Therefore, our domain and range is all real numbers, or [tex]\mathbb{R}[/tex].
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]Y-intercept: 6Equation 2
[tex]\displaystyle3x-4y>16\\\\-4y>-3x+16\\\\y < \frac{3}{4}x-4[/tex]
Now that we have solved the inequality, we can determine our slope, the domain, and the range of the function.
We can use the same tactic as before - m is our slope and b is our y-intercept. Therefore, [tex]\frac{3}{4}[/tex] is our slope and -4 is our y-intercept.
Because the inequality represents a line, our domain is all real numbers, or [tex]\mathbb{R}[/tex]. If we were to plug in any number for x, y would be true for that value. Therefore, our range is also all real numbers, or [tex]\mathbb{R}[/tex].
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\frac{3}{4}[/tex]Y-intercept: -4a jope rope is 9 feet long how long is the jump rope in yards
Increasing a number by 10% is the same as multiplying it by y. What is the value of y? Express your answer as a decimal to the nearest tenth.
The table shows data for a random sample of 20 students out of middle school. Use the sample to draw an inference about each measure. Explain your reasoning.
|-2x+6|=-8 absolute value equations
Picture is attached need help fast thanks
1) Given that lines L and M are parallel, which of the statements is true? A) ∠ DEF ≅ ∠ EBC B) ∠ ABC ≅ ∠ DEF C) ∠ ABC ≅ ∠ EBC D) ∠ BEF ≅ ∠ ABC
Rachael is a nurse. She earns 12 vacation days after working 768 hours. How many hours does Rachael need to work to earn 1 vacation day? Remember to include units! (Example: 12 hours)
Question 4 options:
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Identify the following numbers as Irrational (I) or Rational (R).
a. ¾ ______
b. 1/3 ______
c. 4√4 ______
d. .3333 ______
e. 0.3¯0.3¯ _____
f. ππ _____
g. -3/4 ______
h. -4.32 _____
i. 12−−√12 _____