how would you set up the equation: four executive integers whose sum is 30? (Ex: 3n + 3 = 144)
The required equation for the statement 'four executive integers whose sum is 30' is 4n + 6 = 30
In this question, we have been given a statement 'four executive integers whose sum is 30'
we need to write an equation for above statement.
Let n, n + 1, n + 2, n + 3 be four consecutive integers.
The sum of these four consecutive integers is 30.
⇒ n + n + 1 + n + 2 + n + 3 = 30
⇒ (n + n + n + n) + (1 + 2 + 3) = 30
⇒ 4n + 6 = 30
which is a required equation.
Therefore, the required equation for the statement 'four executive integers whose sum is 30' is 4n + 6 = 30
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The probability of rain in Nevada is 0.3. If it rains, the probability of the school bus being late is 0.4. If it does not rain, the probability of the school bus being late is 0.15. What is the probability that it will not rain? If it does not rain, the probability of the school bus bring on time is? What is the probability that it will rain and the school bus will be on time?
Form given information, the probability of rain in Nevada, the probability that it will not rain is 0.7
The probability that if it does not rain, the school bus will be on time is 0.85
The probability that it will rain and the school bus will still be on time is 0.6
In this question, we have been given the probability of rain in Nevada is 0.3
If it rains, the probability of the school bus being late is 0.4
If it does not rain, the probability of the school bus being late is 0.15
We need to find the probability that
a) it will not rain
b) If it does not rain, the school bus bring on time
c) it will rain and the school bus will be on time
The probability that it will not rain in Nevada:
= 1 - probability of rain in Nevada
= 1 - 0.3
= 0.7
The probability that if it does not rain, the school bus will be on time is:
= 1 - probability of the school bus being late if it does not rain
= 1 - 0.15
= 0.85
The probability that it will rain and the school bus will still be on time is:
= 1 - probability of the school bus being late if it rains
= 1 - 0.4
= 0.6
Therefore, the probability of rain in Nevada, the probability that it will not rain is 0.7
The probability that if it does not rain, the school bus will be on time is 0.85
The probability that it will rain and the school bus will still be on time is 0.6
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Ready
Linear Functions: Rate of Change and initial value
-Quiz-Level H
Joaquin's car has a full tank of gas at the start of a trip. The graph shows the amount of gas in the
tank, y, as a function of the distance traveled, x.
What is the initial value of the function?
Answer:
I can answer this is you provide a picture of the graph
Step-by-step explanation
The initial value of the graph is normally the y intercept of the graph. If you provide the graph linked to this question, I could answer it for you.
Answer:
10
Step-by-step explanation:
what is (2x-7)+(5x-15)
Katie is buying souvenir gifts for her big family back home. She wants to buy everyone either a key chain or a magnet. The magnets are on sale for 50 cents each and the key chains cost $1 each. She must purchase at least 24 gifts and spend no more than $20. Let represent the number of magnets and represent the number of key chains.
Model the scenario with a system of inequalities.
Graph the system of inequalities and choose an appropriate solution for the scenario. Use complete sentences to prove why the solution is appropriate.
The inequalities to represent the situation is given as: x + y ≥ 36 and 2 x + 0.6 y < 40
The magnets are on sale for 60 cents each.
The key chains cost $2 each.
Katie must purchase at least 36 gifts but has to spend less than $40.
Now let x represent the amount of key chains.
Let y represent the amount of magnets.
So, the system of inequalities that form are:
x + y ≥ 36
and
2 x + 0.6 y < 40
Therefore, the inequalities to represent the situation is given as: x + y ≥ 36 and 2 x + 0.6 y < 40
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What is the image of the point (-1,-4) after a rotation of 90 counterclockwise about the origin
The image of the point (-1,-4) after a rotation of 90 counterclockwise about the origin is (4,-1)
What is coordinate system?
A coordinate system can be defined as the method used to identifying the location of a point graphically. Most of the coordinate systems use two numbers generally x and y to define a coordinate and to identify location of any point. The center of graph or system is known as origin and generally pointed as zero (0).
what are various point representation in 2d coordinate system?The 2 coordinates is generally written as x and y. There are generally 4 quadrants in 2d coordinate system. These are :
Positive x and Positive y i.e. (x , y)Negative x and Positive y i.e. (-x , y)Positive x and Negative y i.e. (x , -y)Negative x and Negative y i.e. (-x , -y)Now in the given question the point is (-1,-4)
i.e. the point lie in 4th quadrant (-x,-y)
If the point is rotated 90 degree counterclockwise then the point becomes (y , -x)
Thus, point (-1,-4) becomes (4,-1)
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PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!
The predicted area of the circle is 49.67 cm²
Function and valuesGiven the expression that represents the least regression line as shown below:
log(Area) = 0.490 + 2.004log(time)
Given that the time after the stone is dropped is 4 seconds, the equivalent area is expressed as:
log(Area) = 0.490 + 2.004log(4)
log(Area) = 0.490 + 8.016
log(Area) = 1.6965cm
Area = 10^1.696
Area= 49.67 cm²
Hence the predicted area of the circle is 49.67 cm²
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3. A 6-ounce
package of fruit snacks contains 45
pieces. How many
pieces would you expect in a
10-ounce package?
Answer: 75 pieces
Step-by-step explanation:
The way to answer this question is through simple cross-multiplication.
oz/pieces = 6 oz/45 pieces = 10 oz/x pieces
Cross multiply to get: 6x=450
Simplify: x = 75
Emily knows that she can drive her car an average of 40 miles while using one gallon of gasoline. How many
gallons of gasoline will she need for at trip of 180 miles?
Answer:
4.5 gallons of gas
Step-by-step explanation:
180 ÷ 40= 4.5
Answer:
4.5 gallons
Step-by-step explanation:
Proportions:
40 miles ⇒ 1 gallon
180 miles ⇒ D gallons
D = 180miles * 1 gallon / 40 miles
D = 4.5 Gallons
2. You transfer into a college with 60 credits. How long will it take you to graduate if you can only take 8
credits per semester? The number of credits needed to graduate is 128. Write an equation for the
number of credits, C, accumulated as a function of the number of semesters, t, at the college.
the function as 17 / 2 = C t for the data given.
Credits we have = 60
credits needed to graduate = 128
Credits in 1 semester = 8
Let the number of semesters be t
Number of credits = C
So, we get the function as:
128 = 60 + 8 C t
128 - 60 = 8 C t
68 = 8 C t
17 / 2 = C t
Therefore, we get that, the function as 17 / 2 = C t for the data given.
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9. What is the smallest value of x that is not a
solution to 4x-26 < 4?
Answer:
Step-by-step explanation:
Help please picture attached
Answer:
(a) $878.24
(b) $848.30
(c) Amy would pay less for the golf clubs if she gets them directly from the distributor
Step-by-step explanation:
Part (a)
The wholesale price is $499. When the pro shop gets them from the distributor, it has to pay a mark-up of 10%. 10% expressed as decimal is 10/100 = 0.10
10% of 499 = 0.10 x 499 = 49.90
So total cost including markup for the pro shop is 499 + 49.90 = $548.90
We can compute this directly without computing mark-up cost using the formula
Cost = 499(1+0.10) = 499 x 1.1 = 548.90
The pro shop puts a mark up of 60% which in decimal is 60/100 = 0.6 on the above cost
So the price Amy pays = 548.90(1+0.6) = 548.90 (1.6) = $874.28
Part (b)
Wholesale price = $499
If Amy purchases directly from distributor there is a 70% markup on the wholesale price. 70% = 70/100 = 0.7
So the price Amy would have to pay = 499(1+0.7) = 499 x 1.7 = $848.30
Part (c)
Since the cost of purchasing directly from distributor is less than the cost of purchasing from pro shop the answer is
Amy would pay less for the golf clubs if she gets them directly from the distributor
Find the measures of the numbered angles in the figure, shown to the right. Name the theorem that justifies each answer.
Measure
m21-110
m22=110
m23-110
m24 110
Justification
angle whose measure is 70° and Linear Pair Theorem
21 and Alternate Interior Angles Converse
angle whose measure is 70° and Vertical Angles Theorem
21 and Corresponding Angles Converse
GEITS
#
70°
Answer:
interior angle is 70 so go answer my question pls
1. Explain, in detail, the differences between a line, a line segment, and a ray. In your own words
Answer:
A line is connected set of points that extends forever in both directions.
A line segment is a part of line with two end points.
A ray is a part of straight line that extends only in one direction from a fixed point.
Find the perimeter and the area of ABCD with vertices A(3, 5), B(6, 5), C(4, -1), and D(1, -1). Round your answer to the nearest hundredth place, if necessary. Perimeter: Area: units square units
The perimeter of the shape is determined as 19.91 units and the area is 20.87 sq. units.
What is perimeter?
The perimeter of an object or a shape is the distance around the edge of the shape.
Length of AB = √[(6 - 3)² + (5 - 5)²] = 3 units
Length of AC = √[(4 - 3)² + (-1 - 5)²] = 6.1 units
Length BD = √[(6 - 1)² + (5 - -1)²] = 7.81 units
Length CD = √[(1 - 4)² + (-1 - -1)²] = 3 units
Perimeter of the shape ABCD = 3 units + 6.1 units + 7.81 units + 3 units = 19.91 units.
Area of the shapeThe formula for area of a trapezoid will be used to determine the area of the shape as shown below;
A = ¹/₂(6.1 + 7.81) x 3
A = 20.87 sq. units
Thus, the perimeter of the shape is determined as 19.91 units and the area is 20.87 sq. units.
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Solve the equation for x.
the square root of the quantity x minus 6 end quantity plus 3 equals 10
Answer:
18
Step-by-step explanation:
u suck at life lololol
Units Sold to Break Even, Unit Variable Cost, Unit Manufacturing Cost, Units to Earn Target Income
Werner Company produces and sells disposable foil baking pans to retailers for $2.25 per pan. The variable cost per pan is as follows:
Direct materials $0.24
Direct labor 0.60
Variable factory overhead 0.73
Variable selling expense 0.17
Fixed manufacturing cost totals $115,117 per year. Administrative cost (all fixed) totals $15,698.
1. Compute the number of pans that must be sold for Werner to break even.
________ pans
2. Conceptual Connection: What is the unit variable cost? What is the unit variable manufacturing cost? Round your answers to the nearest cent.
Unit variable cost $ ______
Unit variable manufacturing cost $______
3. How many pans must be sold for Werner to earn operating income of $5,049?
______ pans
4. How much sales revenue must Werner have to earn operating income of $5,049?
$______
If Werner Company produces and sells disposable foil baking pans to retailers for $2.25 per pan, and the variable cost per pan are [Direct materials $0.24, Direct labor 0.60, Variable factory overhead 0.73, Variable selling expense 0.17] while, fixed manufacturing cost totals $115,117 per year and Administrative cost (all fixed) totals $15,698, then:
1. 256,000 Pans must be sold for Werner to break even.
2. The unit variable cost is $1.74, and the unit variable manufacturing cost is $1.57.
3. 266400 pans must be sold for Werner to earn an operating income of $5,049.
4. A sales revenue of $599,400 must Werner have to earn operating income of $5,049.
First, we have to calculate the number of pans that must be sold for Werner to break even.
Given, Fixed manufacturing costs $115,117
And, Fixed administrative costs $15698
Therefore, Total fixed costs $[tex](115,117+15,698)=130,815[/tex]
Also given, Selling price per unit $2.25
And, total Variable costs per unit $[tex](0.24+0.60+0.73+0.17)=1.74[/tex]
Contribution margin per unit = $[tex](2.25-1.74)=0.51[/tex]
[Since, contribution margin is the difference of the selling price and the variable costs]
Now, formula to calculate Break-even units goes as
(Total fixed costs / unit contribution margin).
Therefore, Break-even units in our case = [tex]\frac{130,815}{0.51}=256,000[/tex] units.
Secondly, we are required to calculate the unit variable cost and the unit variable manufacturing cost.
The unit variable cost is already calculated to be $1.74.
And, the unit variable manufacturing cost is the sum of all the variable costs excluding the variable selling expense, i.e., [tex](1.74-0.17)=1.57[/tex].
Thirdly, we will have to calculate the number of pans must be sold for Werner to earn an operating income of $5,049.
Already calculated, Total fixed costs are $130,815 and Contribution margin per unit $0.51.
Given, target operating income is $5049.
Now, formula to calculate Desired Units to earn profit goes as
(Total fixed cost + Target operating income)/(Contribution margin),
i.e., in our case, [tex]\frac{130815+5049}{0.51} = \frac{135864}{0.51}=266400[/tex] unit pans must be sold for Werner to earn an operating income of $5,049.
Lastly, We need to calculate the sales revenue must Werner have to earn operating income of $5,049.
Since, [Sales revenue = (Desired units * selling price)]
And desired units = 266400, while Selling price per unit, given as $2.25.
Therefore, Sales revenue = [tex](266,400*2.25)=599,400[/tex].
That is, a sales revenue of $599,400 must Werner have to earn operating income of $5,049.
Variable Cost: These are costs that change proportionally to the quantity of the goods or service that a business produces, changes.To learn more about Variable Costs, click on the link below.
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Give the first four terms of the arithmetic sequence
for which a₁ = 12 and d = -2.
A 12, 10, 8, 6
B 12, -24, 48, -96
C 12, 14, 16, 18
D 10, 8, 6, 4
An arithmetic sequence is a sequence of numbers which will have a constant common difference throughout the sequence.
The first term of the sequence is given as a₁ = 12 and
The common difference of the sequence is given as d = -2
We need to find the first four terms of the arithmetic sequence
So, the formula to find the first four terms of an arithmetic sequence is
a, a+d , a+2d, a +3d...
where a = 12
d = -2
Then, the arithmetic sequence of the first four-term is
= 12,12 + (-2) , 12 + 2(-2) , 12 + 3 (-2)
= 12 , 12-2 , 12 -4 , 12 - 6
= 12 , 10 , 8 , 6
So the arithmetic sequence of the first four-term is
12,10,8,6.
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the amount a person would have to deposit today to be able to take out 500$ a year for ten year from an amount earning 9%
The amount a person would have to deposit today to be able to take out 500$ a year for ten year from an amount earning 9% i
Calculating the amountThe formula for calculating amount is expressed as:
Amount = Principal + Interest
Determine the interest
Interest = 500*0.09 * 10
Interest = 5 * 90
Interest = $450
Principal= $500 - $450
Principal = $50
Hence the amount a person would have to deposit today to be able to take out 500$ a year for ten year from an amount earning 9% is $50
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A jar contains 360 beans. Of all the beans, 1/4 are white beans and the rest are black beans. What is the ration of white beans to black beans?
Explanation:
1/4 = 0.25
0.25*360 = 90
90 white beans, 360-90 = 270 black beans
The ratio of white to black is 90:270 which fully simplifies to 1:3 after dividing both parts by the GCF 90.
Find a rational number halfway in between the two numbers 7/9 and 1/4
Answer: You Can Search In Internet
Step-by-step explanation: There IS All Step By Step Explanation There Thank You!
There are 1,001 pennies lined up on a table.
Starting at one end of the line, I replace every
third coin with a dime. How much money on
the table?
Answer: 3998 cents, or $39.98
Step-by-step explanation: Hope it helps!
Please help me to solve this problem!
After plotting the line of the best fit, the estimated values of a and b are
(30,1.15) and the equation is M = 30L ₊ 1.15
Given, the values of L and M are plotted on the graph.
Then the line of best fit is created on the graph.
A line that most accurately depicts the relationship between data points on a scatter plot is called the line of best fit.
When data points appear to be in a straight line, the line of greatest fit is a straight line.
Therefore, we get the point on the line as (30,1.15)
The equation representing the relation:
M = aL + b
(a,b) from the graph is (30,1.15)
substitute the estimated the values,
M = 30L + 1.15
Hence the required values are estimated and plotted on the graph.
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Chloe has 500 marbles.
24% of them are red.
How many red marbles does she have?
Answer: 120
Step-by-step explanation: Since the equation is asking for 24% percent of 500 we will have to solve by putting them both as fractions. 24 percent automatically means the denominator will be 100 so we have 24/100. 500 is the denominator since that's the base number we are trying to solve for 24% of 500. So we put x over 500. The equation will be:
24/100 x/500
We multiply diagonally so 24*500=12000.
We then divide 500 by 100 which equals 120.
The reason why we didn't multiply 100 and x is because we are trying to solve for x so we had to simplify each side until we got what x was equal to.
Answer:
She has 120 Red Marbles
Step-by-step explanation:
1% of 500= 5 so you can do 5x24 which would be 120.
I hope it helps you!
~XxBellsAloneXx~
Find the surface area or volume of each rectangular prism. Show your work on a
separate sheet of paper.
Answer:
Formulas for a rectangular prism:
Volume of Rectangular Prism: V = lwh.
Surface Area of Rectangular Prism: S = 2(lw + lh + wh)
Space Diagonal of Rectangular Prism: (similar to the distance between 2 points) d = √(l2 + w2 + h2)
A coach asked her athletes if they enjoy running. Forty-five percent of the team do not like to run. Of those, 70% enjoy cycling, while 80% of those who enjoy running also enjoy cycling. The tree diagram shows how the athletes are divided into subgroups.
a tree diagram shows athletes branching off into two categories of enjoys running and does not enjoy running. Enjoys running branches off into two sub-categories of enjoys cycling and does not enjoy cycling. Does not enjoy running branches off into two sub-categories of enjoys cycling and does not enjoy cycling
What is the total percentage of the athletes who do not enjoy cycling?
50%
24.5%
13.5%
11%
Using proportions, the total percentage of the athletes who do not enjoy cycling is: 24.5%.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, the proportions of people who do not like cycling are:
0.30 of 0.45(do not like to run).0.2 of 0.55(enjoy running).Hence the total proportion is:
0.3 x 0.45 + 0.2 x 0.55 = 0.245.
Multiplying by 100% to convert from proportion to percentage, 24.5% of the athletes who do not enjoy cycling.
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There are 6000 registered voters in Roseville and
3/8
of these voters are registered Democrats. A survey
indicates that 2/3 of the
registered democrats are in favor of bond measure. And 3/5
of the other registered Democrats are in favor of this measure
How many of the voters are registered democrats
The number of voters who are registered democrats according to the description in the task content is; 2,250.
In order words, the total number of registered voters as democrats from the above is 2,250
What is the number of voters who are registered democrats?It follows from the task content that the number of voters who are registered democrats be determined.
On this note, since 3/8 of the total 6000 voters are registered democrats;
However, the number of registered democrats is;
(3/8) × 6000
= 2,250.
Ultimately, the total number of voters who are registered democrats from the above is; 2,250.
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PLEASE HELP ME WITH THIS QUESTION
f(x) = 5x³ + 2x² - 7x +4
g(x) = 3x - 7
Find (f + g)(x).
A. (f+g)(x) = 5x³ + 2x² - 4x + 3
B. (f+g)(x) = 5x³ + 2x² - 10x - 3
C. (f+g)(x) = 5x³ + 2x² - 4x - 3
D. (f+g)(x) = 5x³ + 2x² - 10x + 3
Answer:
Choice C
5x³ + 2x² - 4x - 3
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
So simply add the two terms together
5x³ + 2x² - 7x + 4
+ 3x - 7
--------------------------
5x³ + 2x² - 4x - 3
Please help will give brainliest
h = 9.3 - V/πr² is an equivalent expression to V = πr²(9.3 - h) for cylindrical grain cilo.
What is volume?Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.
Finding an object's volume can help us figure out how much of it will be needed to fill it, such as how much water will be needed to fill a bottle, aquarium, or water tank.
It is shown that Volume V = πr²(9.3 - h)
Lets divide both sides with πr²
V/πr² = πr²(9.3 - h)/πr²
= 9.3 - h
Now, subtract 9.3 from both sides
V/πr²- 9.3 = 9.3 - h - 9.3
= -h
Now multiply both sides with -1
-1(V/πr²- 9.3) = -1(-h)
-V/πr² + 9.3 = h
⇒ h = 9.3 - V/πr²
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