Answer:
A. What is the weight of each type of fruit in decimal form?
Grapes in decimal form = 0.8181 pounds
Bananas in decimal form = 1.75 pounds
Apples in decimal form = 2.8333 pounds
B. Does the weight of each type of fruit in decimal form represent a rational number? Explain.
Of course, each of the weights of the fruits in decimal form represent a rational number. The weights can be expressed as a fraction where both the numerator and the denominator in the fraction are integers, like we checked with 9/11, 1 3/4 and 2 5/6. The denominator in a rational number cannot be zero.
Step-by-step explanation:
1. Let's check the information provided to us to answer the questions correctly:
Janis purchased:
9/11 pounds of grapes
1 3/4 pounds of bananas
2 5/6 pounds of apples
2. What is the weight of each type of fruit in decimal form?
Grapes in decimal form = 0.8181 pounds
Bananas in decimal form = 1.75 pounds
Apples in decimal form = 2.8333 pounds
3. Does the weight of each type of fruit in decimal form represent a rational number? Explain.
Of course, each of the weights of the fruits in decimal form represent a rational number. The weights can be expressed as a fraction where both the numerator and the denominator in the fraction are integers, like we checked with 9/11, 1 3/4 and 2 5/6. The denominator in a rational number cannot be zero.
Stretch thinking Rewrite this sentence using the word fewer. Carey reads 10more pages than Lucey.
Answer:
Lucey reads 10 pages fewer than Carey.
given the 5th term is 103 and the come differences is -6 2/3 what is the 6th term?
Answer:
102 1/3
Step-by-step explanation:
To find the 6th term, add the common difference to the 5th term:
103 + (-6 2/3) = 102 1/3
Solve the equation:
5*4 / 10 + 4 =
Answer:
6
Step-by-step explanation:
5 times 4 is 20
20 divided by 10 is 2
2 plus 4 is 6
5 * 4 / 10 + 4
20 / 10 + 4
2 + 4
6
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Three different ways to put 6(3x + 8) + 32 + 12x
Answer:
Writing 6(3x + 8) + 32 + 12x in 3 different ways:
w₁ = 18x + 48 + 32 + 12x∵ 6(3x + 8) = 18x +48 as distribute law suggests that a(b + c) = ab + ac
w₂ = 18x + 80 + 12x ∵ 48 + 32 = 80 w₂ = 30x + 80 ∵ 18x + 12x = 30xStep-by-step explanation:
As the expression is 6(3x + 8) + 32 + 12x, and we have to write it in three different ways. Using the properties of operations we can write it in three different ways,
Let way one be denoted as w₁
Let way two be denoted as w₂
Let way three be denoted as w₃
So, lets write 6(3x + 8) + 32 + 12x in 3 different ways:
w₁ = 18x + 48 + 32 + 12x∵ 6(3x + 8) = 18x +48 as distribute law suggests that a(b + c) = ab + ac
w₂ = 18x + 80 + 12x ∵ 48 + 32 = 80 w₂ = 30x + 80 ∵ 18x + 12x = 30xKeywords: operation properties, distributive law
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The monthly salary of a show room attendant is the sum of a fixed
salary of $600 plus 8% of all monthly sales. What should the monthly
sales be so that her monthly salary reaches $1,800?
Answer:
Monthly sales = $15000
Step-by-step explanation:
Let x be the monthly sale.
Given:
The monthly salary of a show room attendant is the sum of a fixed salary of $600 plus 8% of all monthly sales.
8% of monthly sale = [tex]\frac{8}{100}\times mothly\ sale[/tex]
8% of monthly sale = [tex]\frac{8}{100}\times x[/tex]
So, the monthly salary of attendant is.
[tex]Monthly\ salary = 600+8\ percent \ of\ monthly\ sales[/tex]
[tex]Monthly\ salary = 600+\frac{8}{100}\times x[/tex]
Monthly salary is given.
[tex]1800 = 600+\frac{8}{100}\times x[/tex]
[tex]1800 - 600 = \frac{8}{100}\times x[/tex]
[tex]1200 = \frac{8}{100}\times x[/tex]
[tex]x=\frac{1200\times 100}{8}[/tex]
[tex]x=\frac{120000}{8}[/tex]
[tex]x=15000[/tex]
Therefore, the monthly sale is $15000
The base of a 40-foot ladder is 8 feet from the wall. How high is the ladder on the wall (round to the nearest foot)?
Answer:
Around 39.2
Step-by-step explanation:
To do this question, you use the pythag theorem, a^2 + b^2 = c^2. You have the hypotenuse of the triangle, 40 feet in length, and you have a because it's 8 feet from the wall. You now have b^2 = 1600-64. b^2 = 1536. Take the square root, and you have the height of the latter on the wall is equal to 39.1918 or 39.2 rounded
Which value of x would make NO || KJ?
1
6
8
10
Answer:
x = 8
Step-by-step explanation:
If NO is parallel to KJ then the sides LK and LJ are in proportion, that is
[tex]\frac{KN}{NL}[/tex] = [tex]\frac{JO}{OL}[/tex], substitute values
[tex]\frac{x+2}{x-3}[/tex] = [tex]\frac{x}{x-4}[/tex] (cross- multiply )
x(x - 3) = (x + 2)(x - 4) ← expand factors on both sides
x² - 3x = x² - 2x - 8 ( subtract x² - 2x from both sides )
- x = - 8 ( multiply both sides by - 1 )
x = 8
Answer:
8
Step-by-step explanation:
A teacher handed out 10 notebooks in packs with 5 notebooks in each pack. How many packs were there?
Answer:
2 packs
Step-by-step explanation:
Since there is 10 packs just divided it by how many notebooks were in the pack.
How do you wire 0.52 in words
Answer: fifty-two hundredths
Step-by-step explanation:
Romi opened a gift shop in 1995 and closed it in 2000. In 1995, her inventory of stuffed animals was 350. In 2000 her inventory of stuffed animals was 0. Let x represent the number of years since 1995. Write an equation, in slope-intercept form, that represents that data
Answer:
y=-70x+350
Step-by-step explanation:
Since x is the number of years since 1995, this means that at 1995, x=0. This also means that in 2000, x=5. The values of the stuffed animals were 350 in 1995 and 0 in 2000. The formula for slope is rise over run, so we can find the answer using this mathematical expression: y2-y1/x2-x1. Plugging in our values, we get 0-350/5-0 which simplifies into -350/5. This further simplifies into -70. Our slope is -70. The definition of y-intercept is the value of y when x=0. We know that x=0 at 1995 and the value for the stuffed animals was 350 at that time. This tells us that the y-intercept is 350. Slope-intercept form is y=mx+b, so plugging in our information, we get y=-70x+350.
The equation representing the data of Romi's stuffed animal inventory is y = -70x + 350
The given problem involves finding an equation in slope-intercept form to represent the data of Romi's stuffed animal inventory from 1995 to 2000. Let's first find the slope and y-intercept of the equation using the given data. We know that the inventory in 1995 was 350 and in 2000 was 0. We can use these two points to find the slope and y-intercept.
Slope (m) = (change in y)/(change in x) = (0 - 350)/(2000 - 1995) = -350/5 = -70
Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values
y = -70x + b
To find the value of b, we can substitute one of the given points into the equation. Let's use the point (0, 350).
350 = -70(0) + b
350 = b
Substituting the value of b back into the equation, we have the final equation:
y = -70x + 350
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24. A bag contains 6 red marbles, 5 yellow marbles, and
7 green marbles. How many additional red marbles
must be added to the 18 marbles already in the bag so
that the probability of randomly drawing a red marble
is
?
F. 12
G. 16
A. 18
J. 24
K. 36
Answer:
the answer is a 18 because that would mean there are more red than any color in the bag
To make the probability of drawing a red marble 1/2 with the current bag of marbles, you would need to add 12 more red marbles.
Explanation:To answer the question about how many additional red marbles must be added to the 18 marbles already in the bag so that the probability of randomly drawing a red marble is 1/2, we first need to understand how the probability of an event is calculated. Probability is calculated by dividing the number of ways an event can occur by the total number of outcomes. In this case, the event is drawing a red marble and the total number of outcomes is the total number of marbles in the bag.
Currently, there are 6 red marbles and 18 total marbles in the bag, so the probability of drawing a red marble is 6/18 = 1/3. We want this probability to increase to 1/2, so we need to add more red marbles. Let's represent the number of red marbles we need to add as x. To find x, we need to solve the following equation: (6 + x) / (18 + x) = 1/2.
Solving for x, we get x = 12. Therefore, you need to add 12 more red marbles to the bag to make the probability of drawing a red marble 1/2.
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ABCD IS A PARALLELOGRAM. IF SIDE AB=6X-10, SIDE BC=4X-5, AND SIDE CD= 3X+5, FIND THE VALUE OF X
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
we know that
In a parallelogram opposite sides are parallel and congruent
In this problem
AB and CD are opposite sides
so
AB=CD
substitute the given values
[tex]6x-10=3x+5[/tex]
solve for x
[tex]6x-3x=10+5[/tex]
[tex]3x=15[/tex]
[tex]x=5[/tex]
21. What method can be used to prove the
triangles below are congruent?
A. SSS
B. SAS
C. HL
D. Not Possible
Answer:
there is not a triangle
Step-by-step explanation:
but if is has all 3 sides the same it is sss, if there is two sides and an angle in between them it is sas, and if there is a hypotenuse and then a leg then it is hl, or if it is none it is d
The method that can be used to prove the triangles below are congruent is the SAS (Side-Angle-Side) criterion. To prove that two triangles are congruent using the SAS criterion, you need to show that two pairs of corresponding sides are congruent and the included angles between them are congruent. In the given options, B. SAS is the correct answer.
Explanation:The method that can be used to prove the triangles below are congruent is the SAS (Side-Angle-Side) criterion.
To prove that two triangles are congruent using the SAS criterion, you need to show that two pairs of corresponding sides are congruent and the included angles between them are congruent.
In the given options, B. SAS is the correct answer.
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Consider the formula S = sf/F
where
S represents sweetness of a cake,
• s represents the amount of sugar in a cake,
f represents the amount of frosting and
• F represents the amount of flour.
Select an appropriate measurement unit for sweetness of a cake,
SAY LETTER OR ANSWER
Answer:
D
Step-by-step explanation:
Answer:
D. (sugar * frosting)/Flour
Step-by-step explanation:
Given that
The formula for sweetness of a cake is represented by S = sf/F
where the
sweetness of a cake is denoted with S
amount of sugar in a cake, with A
amount of frosting, with f
amount of flour with F.
To get the appropriate unit, all we need to do is to substitute the letter representation of each unit with the original word.
So,
S = sf/F becomes
S = (sugar * frosting)/Flour
We arrive at this by replacing s with sugar; f with frosting and F with Flour
Discussion for Applications of Linear Systems
When solving a system of equations, how do you determine which method to use?
Step-by-step explanation:
There are certain methods for solving a system of equations. Some of which are:
Substitution MethodElimination MethodGraphing MethodSubstitution Method
Substitution method to solve a system of equations is suitable if a variable of a any equation seems isolated or could comfortably be isolated without any ration/fraction resulting.
For example, for the following system of equations
x - 2y = 11....[A]
x = 5 - y....[B]
substituting the value of x = 5 - y from equation [B] into equation [A], so that
(5 - y) - 2y = 11
5 - y - 2y = 11
3y = -6
y = -2
Elimination Method
Elimination method to solve a system of equations is suitable if both equation are in standard form, and just adding or subtracting the equations to determine an equation in one variable.
For example, for the following system of equations
2x + 7y = -5....[C]
5x - 7y = 12....[D]
Adding Equation [C] and Equation [D].
7x + 0 = 7
x = 1
Graphing Method
Sometimes graphing method may be used to solve the system of the equation and visualize the solution.
For example,
y = -2....[E]
y = 3x + 1....[F]
The solution for this system of equation is the point of intersection of both the lines, which is shown in attached figure. The point of intersection is (-1, -2).
Hence, the solution of this system of equations is (-1, -2), as shown in attached figure.
Keywords: system of equations, elimination method, substitution method, graphing method
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Each story in Will's apartment building is 9 feet tall. There are 10 stories in the building. How tall is the apartment building?
Answer:
the building is 90 feet tall
Step-by-step explanation:
each floor is 9 feet, there are 10 floors,
9 x 10 = 90 feet
A large bottle contains 1.3 liters of olive oil. A medium-sized bottle has 0.8 times the amount of olive oil as the large bottle.
How much more olive oil does the large bottle contain than the medium-sized bottle?
Answer: 0.236 Liters.
Step-by-step explanation:
First you multiply 1.3 and 0.8 you get 1.064.
You subtract 1.3 and 1.064 and you get your answer 0.236 Liters.
Emily's family loves to work together
in the garden. They have a.
preference for flowers as 80% of
their plants are flowers and the rest
are vegetables. They have 90 plants
in the garden. How many vegetable
plants do they have?
Answer:
They have 18 vegetable plants.
Step-by-step explanation:
Given:
Emily's family loves to work together in the garden.
They have a. preference for flowers as 80% of their plants are flowers and the rest are vegetables.
They have 90 plants in the garden.
Now, to find the number of vegetable plants.
Total plants in the garden = 90.
80% of the plants are flowers.
So, number of plants which are flowers = 80% of 90.
[tex]=\frac{80}{100} \times 90[/tex]
[tex]=\frac{7200}{100}[/tex]
[tex]=72\ plants.[/tex]
The number of flower plants = 72.
Total plants = 90 (given)
So, to get the number of vegetable plants we subtract:
[tex]90-72=18\ plants.[/tex]
Thus, vegetable plants = 18.
Therefore, they have 18 vegetable plants.
What is the sum of the digits in 18
Answer:
9
Step-by-step explanation:
1+8=9
Answer:
9
Step-by-step explanation:
1+8=9
When multiplying polynomials for a math assignment, Pat found the product to be -4x+8x^2-2x^3+5. He then had to state the leading coefficient of this polynomial. Pat wrote down -4. Do you agree with Pat’s answer? Explain your reasoning.
Answer:
I am not agree with him. Because -2 is the leading coefficient of this polynomial.
Step-by-step explanation:
Pat multiplied the polynomials for a math assignment.
Then he found the product is [tex]-4x+8x^2-2x^3+5[/tex]
Now Pat wants to find the leading coefficient to this polynomial.
Pat's answer was -4.
But I am not agree with him.
Because for a given polynomial we can calculate the leading coefficient when comparing with degrees of the polynomial.
Leading coefficient means that the coefficient whose degree is the highest.
When compared with the given polynomial we have [tex]x^3[/tex] is the highest degree, so that -2 is the leading coefficient to this polynomial.
is 3.456 a rational number
Answer:
Yes
Step-by-step explanation:
Answer:
yes it is
Step-by-step explanation:
3.456 could be written as a fraction, that means it is a rational number because rational number is any number that could be written as a fraction.
3.456=3456/1000
HELP PLEASEE!!!I DONT UNDERSTAND THIS
Answer:
Median
Step-by-step explanation:
Median, in geometry, is a line segment that is drawn from the vertex or the corner of the shape that extends to the middle or the midpoint of the side opposite of that corner.
When you say opposite the corner, that means it is the one across it. Look at the attached picture for emphasis.
Translate
Your grade must be at least 60 to pass this class
Answer:in Spanish: su calificación debe ser 60 para aprobar esta clase
Step-by-step explanation:
Answer:
That mean you must have 60 and above to pass and anything below that is failure
Step-by-step explanation:
What’s the pattern 788,778,768
Answer:
the tens place is going down one number each time
Step-by-step explanation:
To find the pattern of the data set we can subtract the 1st term to the 2nd term.
788 - 778 = 10
Now, multiply the 2nd term to the 3rd term to check.
778 - 768 = 10
Thus, the rule of the pattern is 10.
Best of Luck!
What is the slope of the line parallel to the line y = -5/3x + 5?
A) -5/3
B) -3/5
C) 3/5
D) 5/3
Answer:
C
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 )
y = - [tex]\frac{5}{3}[/tex] x + 5 ← is in slope- intercept form
with slope m = - [tex]\frac{5}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular }[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{5}{3} }[/tex] = [tex]\frac{3}{5}[/tex]
Answer:
5/3
Step-by-step explanation:
I need help please and thanks
FIND RATIOS
4. A string that is 75 inches long will be cut into two pieces in the ration of 4:11. Find the lengths
of the two pieces of string.
5. The ratio of two supplementary angles is 4:1. Find the measures of the two angles.
6. The ratio of the measures of the angles in a triangle is 3:5-7. Find the measure of each angle.
7. The ratio of the measure of the sides of a triangle is 5;7:8 and its perimeter is 40 inches. Find
the measure of each side.
Step-by-step explanation:
4. 4+11=15
to find the length of The first piece
4/15*75=20
to find the length of the second one
11/15*75=55
5. 4+1=5
to find the length of the first one
4/5*180=144
to find the length of the second one
1/5*180=36
7. 5+7+8=20
to find the length of the first one
5/20*40=10
to find the length of the second one
7/20*40=14
to find the length of the third one
8/20*40=16
4. The lengths of the two pieces are 20 inches and 55 inches.
5. The measures of the two angles are 144 degrees and 36 degrees.
6. The measures of the angles are 36 degrees, 60 degrees, and 84 degrees.
7. The lengths of the sides are 10 inches, 14 inches, and 16 inches.
4: A string that is 75 inches long will be cut into two pieces in the ratio of 4:11. Find the lengths of the two pieces of string.
The total length of the string is 75 inches.
The ratio given is 4:11.
First, find the total parts in the ratio by adding the two numbers: [tex]4 + 11 = 15[/tex].
Now, to find the length of each piece:
For the first piece: [tex](4/15) \times 75 = 20[/tex] inches.For the second piece: [tex](11/15) \times 75 = 55[/tex] inches.5: The ratio of two supplementary angles is 4:1. Find the measures of the two angles.
Supplementary angles add up to 180 degrees.
The given ratio is 4:1.
Find the total parts in the ratio: [tex]4 + 1 = 5[/tex].
Now, calculate the measures of the angles:
For the first angle: [tex](4/5) \times 180 = 144[/tex] degrees.For the second angle: [tex](1/5) \times 180 = 36[/tex] degrees.6: The ratio of the measures of the angles in a triangle is 3:5:7. Find the measure of each angle.
The sum of the angles in a triangle is 180 degrees.
The given ratio is 3:5:7.
Total parts in the ratio: [tex]3 + 5 + 7 = 15[/tex].
Now, calculate each angle's measure:
For the first angle: [tex](3/15) \times 180 = 36[/tex] degrees.For the second angle: [tex](5/15) \times 180 = 60[/tex] degrees.For the third angle: [tex](7/15) \times 180 = 84[/tex] degrees.7: The ratio of the measure of the sides of a triangle is 5:7:8 and its perimeter is 40 inches. Find the measure of each side.
The perimeter of the triangle is 40 inches.
The given ratio is 5:7:8.
Total parts in the ratio: [tex]5 + 7 + 8 = 20[/tex].
Now, calculate the length of each side:
For the first side: [tex](5/20) \times 40 = 10[/tex] inches.For the second side: [tex](7/20) \times 40 = 14[/tex] inches.For the third side: [tex](8/20) \times 40 = 16[/tex] inches.HELP
How would I find C? would I have to subtract 180 from 50??
Answer:
m∠C = 115°
Step-by-step explanation:
DE≈DF
ΔDEF is an isosceles triangle ∴ m∠DEF = m∠DFE = 1/2 (180-50) = 65
∴ m∠DFB = 180 -65 = 115
∵ DCBF is a parallelogram m∠DFB = m∠DCB = 115°
A, B, C are circular regions as shown below. There are 7 items in C and there are 20 items in A but 10 of those items are not in B. How many items are in B that are not in C
Answer:
3 items are in B that are not in C
Step-by-step explanation:
a: only in a, not count those in b or c
b: only in b, not count those in a or c
c: only in c, not count those in a or b
A = a + b + c = 20
c = 7
a + b = 20 - 7 = 13
10 not in b, of course not in c ∴ a = 10
b = 13 -10 = 3
The surface are of a cylinder is given by the formula SA=2pir^2+2pirh,where r is the radius of the base of the cylinder and h is the height of the cylinder. Solve the formula for h in the space given below.show all the steps.
Answer:
A = 2πr2 + 2πrh is the final answer
Step-by-step explanation:
Answer:
h = (x-2πr²)/2πr
Step-by-step explanation:
Given the surfaces area of a cylinder by the formula
SA = 2πr²+2πrh
To solve for h means making h the subject of the formula from the equation.
Let x be the surface area of the cylinder. The formula can be rewritten as;
x = 2πr²+2πrh
Subtracting 2πr² from both sides of the equation will give;
x-2πr² = 2πr²+2πrh-2πr²
x-2πr²= 2πrh
Dividing both sides by 2πr wikk results into;
(x-2πr²)/2πr = 2πrh/2πr
h = (x-2πr²)/2πr where x is the surface area of the cylinder.