Answer:
Option A is correct
5 feet is the length of the actual picnic table
Step-by-step explanation:
Proportion states that two ratios or fractions are equal.
As per the statement:
A blueprint for a picnic table has a scale of 1 : 20.
The table in the blueprint is 3 in. long.
Let x be the length of the actual picnic table.
By definition of proportion;
[tex]\frac{1}{20} = \frac{3}{x}[/tex]
By cross multiply we have;
[tex]x = 20 \cdot 3 = 60[/tex]
⇒x = 60 inches
Use conversion:
1 inches = [tex]\frac{1}{12}[/tex] feet
then;
60 inches = [tex]\frac{60}{12} = 5[/tex] feet
Therefore, the length of the actual picnic table is, 5 feet
Two sides of a triangle are equal in length, and the third side is 5 inches. If the perimeter is 17 inches, how long are the two equal sides?
A trinket company has a warehouse that contains 50,000 trinkets. At the end of each day, a truck picks up 4,000 trinkets to deliver to the trinket store. When the warehouse drops below 15,000 trinkets, the company will begin producing more trinkets to restore the inventory. 1) Write an equation for the number of trinkets in the factory after days. 2) After how many days will the factory begin producing trinkets?
Let x be a random variable with pareto distribution with parameter α . determine the probability distribution function of the random variable y = ln ( x ) . what kind of distribution does y have?
a rectangular fish pond is 21 ft squared in area. if the owner can surround the pond with a 20 ft fence what are the dimensions of the pond
THE ANSWER IS 41 FEET
A human hair was measured to be 8.0×10−4 inch thick. A cat hair was measured to be 4.0×10−1 inch thick. How much greater is the thickness of the cat hair than the human hair? Write the answer in standard form.
Human hair: 8.0 x 10-4 = 0.00080
Cat hair: 4.0 x 10-1 = 0.40
Subtracting: 0.40 - 0.00080 = 0.3992
Using rules of precision, the answer becomes 0.40
Answer:
time 4learning answer is 500
Step-by-step explanation:
In Marissa's Calculus course, attendance counts for 5% of the grade, quizzes count for 10% of the grade, exams count for 60% of the grade, and the final exam counts for 25% of the grade. Marissa had 100% average for attendance, 93% for quizzes, 86% for exams, and 85% on the final exam. Determine Marissa's course average.
Marissa's course average is calculated by weighting each grade by its importance and then summing. This results in an overall average grade of 87.15%.
Explanation:To calculate Marissa's course average given the percentage weight of each grading category and her averages in each category, we multiply each of her grades by the respective weight, then add the weighted grades together.
So, the calculation would be as follows:
Attendance grade: 100% * 0.05 = 5
Quiz grade: [tex]93 * 0.10 = 9.3[/tex]
Exams grade: [tex]86 * 0.60 = 51.6[/tex]
Final exam grade: [tex]85 * 0.25 = 21.25[/tex]
Adding these up, we get [tex]5 + 9.3 + 51.6 + 21.25 = 87.15[/tex]
So, Marissa's course average is 87.15%
Learn more about Average Grade Calculation here:https://brainly.com/question/36719766
#SPJ11
The owner of a bike shop sells unicycle and bicycles and keeps inventory by counting seats and wheels. One day she counts 20 seats and 28 wheels. The equation representing the total number of seats is u+b=20 where u is the number of unicycles and b is the number of bicycles. Select the equation representing the number of wheels.
The equation u+2b=28 represents the number of wheels, which is correct option(C).
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
The owner of a bike shop sells unicycles and bicycles and keeps inventory by counting seats and wheels. One day, she counts 20 seats and 28 wheels.
u is the number of unicycles and b is the number of bicycles.
There are total 20 seats
⇒ u+b=20
unicycle has 1 wheel and bicycle has 2 and total there are 28 wheels
⇒ u+2b=28
Hence, this equation represents the number of wheels.
Learn more about equation here:
brainly.com/question/10413253
#SPJ5
how can you find x in the equation ax-bx+y=z
Which situation CANNOT be represented by this equation? −14x+14=8
A hot-air balloon has a 14-foot diameter that each 14 of an hour gets steadily smaller.At what rate, x, does the balloon have to shrink per hour before it has shrunk to a diameter of 8 feet?
A hot-air balloon has a 14-foot diameter that is getting smaller at a rate of 14 foot per minute. How many minutes, x, will it take before the balloon has shrunk to a diameter of 8 feet?
A hot-air balloon has an 8-foot diameter that is changing at a rate of 14 foot per minute. How long in minutes, x, will it take until the balloon has a diameter of 14 feet?
Answer:
The third option is the answer.
Step-by-step explanation:
[tex]-14x+14=8[/tex]
A hot-air balloon has an 8-foot diameter that is changing at a rate of 14 foot per minute. How long in minutes, x, will it take until the balloon has a diameter of 14 feet?
The equation in this case will be : [tex]8-14x= 14[/tex]
where do the graphs Of linear equations 2x+3y=4 and 5x+6y=7 intersect
The graphs of the linear equations 2x+3y=4 and 5x+6y=7 intersect at the point (2, 0).
Explanation:The graphs of linear equations 2x+3y=4 and 5x+6y=7 intersect at a single point. To find the point of intersection, we can solve the two equations simultaneously.
Start by rearranging the equations to solve for y in terms of x:Now, set the two expressions for y equal to each other:Therefore, the graphs of the two equations intersect at the point (2, 0).
Kyle bought a pair of socks for $6. Last month, his friends bought the same socks for $5. What is the percent increase in the price of the socks?
Nayati wants to swim 50 miles this school year. She plans to swim 1/4 mile each day. How many days will it take her to swim 50 miles. Show your work.
what fraction of the letters in the word MUSHROOM are not vowels? show me how you got the answer please
A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches. What is the ratio of the area of the school banner to the area of the sign? $$
Answer:
2916/289 = 10 26/289 ≈ 10.09
Step-by-step explanation:
The ratio of areas of similar figures is the square of the scale factor. Here, the scale factor is the ratio of lengths, so is ...
k = banner/sign = 54/17
The ratio of areas is k² = (54/17)² = 2916/289 = 10 26/289 ≈ 10.09
The ratio of the area of the school banner to the area of the sign is approximately 3.36:1. This was calculated by first finding the areas of both the banner and the sign, and then dividing the area of the banner by the area of the sign.
Explanation:The subject of this question falls under Mathematics, and it deals with the concept of ratio and similar figures. In this case, the figures are a school banner and a sign, both of which are rectangular in shape. The ratio of their areas can be determined by calculating the areas of both figures and then finding the ratio of the two values.
Firstly, let's calculate the area of the school banner. The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the school banner = 54 inches (length) * 36 inches (width) = 1944 square inches.
Next, the sign's width isn't given, but because the two shapes are similar, the ratio of the banner's length to its width is equal to the ratio of the sign's length to its width. So, if we let 'w' be the width of the sign, then 54/36 = 17/w. Solving this for 'w', the width of the sign = [tex](17 * 36) / 54 = 17*2 = 34[/tex] inches. The area of the sign, then, is 17 inches (length) * 34 inches (width) = 578 square inches.
To get the ratio of the school banner's area to the sign's area, divide 1944 by 578, which equals approximately 3.36. Therefore, the ratio of the areas is 3.36:1. Meaning for every square inch of the sign, there are approximately 3.36 square inches of the school banner.
Learn more about Ratio and Proportions here:https://brainly.com/question/26974513
#SPJ11
Angle ABC is formed by two tangents intersecting outside of a circle. If minor arc AC = 110°, what is the measure of angle ABC?
Answer:
Step-by-step explanation:
Given that two tangents to a circle intersect at a point B outside the circle
A and C are points of contact.
By theorem on circles we have angle ABC is equal to 1/2 the difference of intercepted arcs.
Angle of minor arc =110 and hence major arc [tex]= 360-110 = 250[/tex]
Difference = [tex]250-110 =140[/tex]
Measure of angle ABC 1/2 of 140 = 70 degrees.
In questions 1-5, help the developer name the streets if the entrance street is y=2/3x-7, by using the patterns you discovered in the opening activity and the chart you filled in for the closing questions. All the streets that run parallel to the entrance street ( Oak Street) were given tree names, while all those that run perpendicular to the entrance street were given flower names. If it is neither parallel nor perpendicular to the main street, then the street was labeled with an animal name.
1. Street equation: y=-3/2x-2
weeping willow street
hibiscus street
oak street
Panther street
2.Street equation: y=2/3x+4
weeping willow street
hibiscus street
oak street
gray squirrel
3. Street equation: y=8/12x-7
silver maple street
hibiscus street
oak street
raccoon street
4. Street equation: y=-2/3x-16
elm street
daffodil street
oak street
panther street
5. Street Equation: y=4/6 x+5/3
elm street
camilla street
oak street
brown bear street
Rosa has 5 pounds of apples how many pies with 8 ounces of apples can Rosa make
f(t)=5t−7 please help
lllll
find (g o f)(x) where f(x)= x^2-2, g(x)=5x-8
The composite function (g o f)(x) of f(x) and g(x) is 5x^2-18.
We have given that,
f(x)= x^2-2, g(x)=5x-8
What is the value of (g o f)(x)?The value of (g o f)(x)=g(f(x)
g(f(x)=5(f(x))-8
=5(x^2-2,)-8
=5x^2-10-8
=5x^2-18
Therefore the composite function of f(x) and g(x) is 5x^2-18.
To learn more about the composite function visit:
https://brainly.com/question/10687170
#SPJ2
Least to greatest 1/2, 2/5, 6/10
a proportion relationship is represented by the equation 2x=18y.If y=kx,where k is the constant of proportionlaity,then what is the value of K?
A.9
B.2
C.1/2
D.1/9
which scale facor would produce an expansion under a dilation of the original image
A pentagon has angle measures of 102°, 100°, 115° and 110°. What must the fifth angle measure?
A pentagon has angle measures of 102°, 100°, 115°, and 110°. Therefore, The fifth angle measures 113°.
What is the sum of angles in pentagon?The sum of all the angles of Pentagon angles is 540°.
A pentagon has angle measures of 102°, 100°, 115°, and 110°.
To find the fifth angle so we subtract all angles above from 540°
102 + 100 + 115 + 110 = 540
540 - 102- 100 - 115 - 110 = 113°
Therefore, The fifth angle measures 113°.
Learn more about pentagon here;
https://brainly.com/question/17054992
#SPJ2
A full bag of dog food weighs 5 1 2 pounds. How much dog food do you have if there are 3 3 4 bags in the cupboard
The dog food we have if there are 3 3 4 bags in the cupboard is 20 5/8 pounds
What are proper and improper fractions and how to convert mixed fractions to simple fractions?A fraction represents a part of a number or any number of equal parts.
There is a fraction, containing a numerator(upper value) and denominator(lower value). When the numerator is less than the denominator, the fraction is called a proper fraction, otherwise, it is called an improper fraction. A proper fraction is also called a fraction that is less than 1. And an improper fraction is ≥ 1. A mixed fraction contains a sum of whole numbers and a proper fraction.
We have been given that a full bag of dog food weighs [tex]5\dfrac{1}{2}[/tex] pounds.
First, we need to convert mixed fractions into simple fractions;
[tex]5\dfrac{1}{2}[/tex] = 11/2
Also, [tex]3\dfrac{3}{4}[/tex] = 15/4
Therefore, we know there are 3 and 3/4 bags in the cupboard, and each one of them weighs 5 and 1/2 lbs, thus the total amount in the cupboard is just their product.
[tex]5\dfrac{1}{2}[/tex] × [tex]3\dfrac{3}{4}[/tex]
11/2 × 15/4
= [tex]20\dfrac{5}{8}[/tex]
Hence, The dog food we have if there are 3 3 4 bags in the cupboard is 20 5/8 pounds.
Learn more about fractions;
https://brainly.com/question/729654
#SPJ2
In △DEF, DF = 17 and m∠F=32. Find DF to the nearest tenth.
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Please explain how you got the answer.
What is the equation of the line that is parallel to the line y = x + 4 and passes through the point (6, 5)?
y = x + 3
y = x + 7
y = 3x – 13
y = 3x + 5
Answer:
b
Step-by-step explanation:
The equation of the line parallel to y = x + 4 passing through the point (6, 5) is y = x - 1, which has the same slope as the given line but a different y-intercept, determined by the given point.
Explanation:The question asks for the equation of a line that is parallel to y = x + 4 and passes through the point (6, 5). Since the line we are looking for must be parallel, it will have the same slope as the given line, which in this case is 1 (since the coefficient of x is 1 in the given equation). The general form of the line we're looking for is y = x + b, where b is the y-intercept. To find the specific equation, we substitute the point (6, 5) into the equation to solve for b:
5 = (1)(6) + bThus, the equation of the line that meets the conditions is y = x - 1, which is not represented in the options given. Since none of the options match, it's possible that there might have been a mistake in the options provided or an error in the transmission of the question. However, based on the information given, this is the correct equation for the line parallel to y = x + 4 that passes through (6, 5).
A tee box is 48 feet above its fairway.
Rami sold concessions during a concert. He sold bottled water for $3.50 each and bags of trail mix for $4 each. By the end of the evening, Rami sold 400 items for a total of $1,475. How many bottles of water and how many bags of trail mix did Rami sell?
Rami sold 250 bottles of water and 150 bags of trail mix at the concert, totaling $1,475 in sales.
To solve the problem of how many bottles of water and bags of trail mix Rami sold, we need to set up and solve a system of linear equations based on the given information.
Let's define the variables:
- [tex]\( x \)[/tex] = the number of bottles of water sold
- [tex]\( y \)[/tex] = the number of bags of trail mix sold
From the problem, we have two pieces of information that we can turn into equations:
1. The total number of items sold is 400.
2. The total revenue from the items sold is $1,475.
We can write these two statements as equations:
1. [tex]\( x + y = 400 \)[/tex]
2. [tex]\( 3.50x + 4y = 1475 \)[/tex]
We now have a system of linear equations:
[tex]\[\begin{cases}x + y = 400 \\3.50x + 4y = 1475\end{cases}\][/tex]
Step 1: Solve the first equation for [tex]\( y \)[/tex]
[tex]\[y = 400 - x\][/tex]
Step 2: Substitute [tex]\( y \)[/tex] in the second equation
Replace [tex]\( y \)[/tex] in the second equation with [tex]\( 400 - x \)[/tex]:
[tex]\[3.50x + 4(400 - x) = 1475\][/tex]
Step 3: Simplify and solve for [tex]\( x \)[/tex]
Expand and simplify the equation:
[tex]\[3.50x + 1600 - 4x = 1475\][/tex]
Combine like terms:
[tex]\[3.50x - 4x + 1600 = 1475\][/tex]
[tex]\[-0.50x + 1600 = 1475\][/tex]
Subtract 1600 from both sides:
[tex]\[-0.50x = 1475 - 1600\][/tex]
[tex]\[-0.50x = -125\][/tex]
Divide both sides by -0.50:
[tex]\[x = \frac{-125}{-0.50} = 250\][/tex]
So, Rami sold 250 bottles of water.
Step 4: Find [tex]\( y \)[/tex] using the value of [tex]\( x \)[/tex]
Substitute [tex]\( x = 250 \)[/tex] back into the first equation:
[tex]\[y = 400 - 250 = 150\][/tex]
So, Rami sold 150 bags of trail mix.
Conclusion
Rami sold:
- 250 bottles of water
- 150 bags of trail mix
To verify, we check the total revenue:
[tex]\[3.50 \times 250 + 4 \times 150 = 875 + 600 = 1475\][/tex]
The numbers match the given total revenue, confirming our solution is correct.
Please help me pleaseee