In Linear equation, The of sales/month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
What is linear equation?
An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.
The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.
Let x be # sales/month:
Plan A: $2500 + 6%•x
Plab B: $3000 + 4%•x
For Plan A to be better than Plan B: Plan A > Plan B
So inequality would be: $2500 + 6%•x > $3000 + 4%•x, then solve for x:
2%•x > $500 or x > $500/0.02
x > 25,000
Therefore, the of sales/month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
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In Linear equation, The of sales of the month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b.
To solve this system of linear equations, we can use the method of elimination or substitution.
Let x be sales of the month:
Plan A: $2500 + 6% × x
Plan B: $3000 + 4% × x
For Plan A to be better than Plan B: Plan A > Plan B
So inequality would be: $2500 + 6%×x > $3000 + 4%×x
then solve for x:
=> 2500+0.06x > 3000+0.04x
=> 0.06x-0.04x > 3000-2500
=> 0.02x > 500
=> x > 500/0.02
=> x > 25000
Therefore, the of sales of the month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
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The length of a rectangle is 4 meters less than 2 inches times width. The perimeter is 34 meters. Find the width
Answer:
7
Let's call the width = x
width : x
so (x + 2x-4)2 = 34 (perime formula of a rectangle) x+2x-4 = 7
3x = 21
x = 7
so x is 7
Is -4/3 perpendicular to 3/4
Answer:
no its not
Step-by-step explanation:
Using the slope-intercept form, the slope is Undefined. The slope of a perpendicular line to a vertical line is zero.
Pat's Pizza made
21
2121 cheese pizzas,
14
1414 veggie pizzas,
23
2323 pepperoni pizzas, and
14
1414 sausage pizzas yesterday.
Based on this data, what is a reasonable estimate of the probability that the next pizza made is not a cheese pizza?
Choose the best answer.\
Therefore , the solution of the given problem of probability comes out to be pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.
What exactly is probability?Any considerations technique's fundamental objective is to determine the likelihood that a claim is true or that a particular incident will take place. Any number range from one to one, when 0 traditionally signifies a percentage and 1 typically implies the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The total number of pizzas made yesterday can be determined using the information provided as follows:
2121 cheese pizzas total.
Pizzas with vegetables: 1414
2323 pepperoni pizzas total.
1414 sausage pizzas were consumed.
Total pizzas produced were
=>2121 + 1414 + 2323 + 1414 = 7272.
Therefore, there were 2121 cheese pizzas prepared yesterday out of a total of 7272 pizzas.
The likelihood that the following pizza will be a cheese pizza is calculated as follows:
=> 2121 / 7272
The likelihood that the next pizza prepared won't be a cheese pizza is thus:
=> 1 - (2121 / 7272) = 5151 / 7272
Therefore, a conservative estimate of the likelihood that the following pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.
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If sam can swin 10 laps in 20 minutes, what would be his expected time for 15 laps?
Asnwer: 30 minutes
Explanation:
10 laps in 20 minutes is 1 lap every 2 minutes.
So we get this:
1 lap = 2 minutes
But we want 15 laps, so multiply both sides by 15 to get:
15 laps = 30 minutes
The measure of DOT and TOU
The measure of ∠DOT is equal to 58°
The measure of ∠TOU is equal to 32°.
What is a complementary angle?In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).
Mathematically, a complementary angle can be calculated by using this mathematical equation:
Q + R = 90°
Where:
Q and R are measure of the angles subtended.
By substituting the given parameters into the complementary angle formula, the sum of the angles is given by;
(7x + 2) + 4x = 90.
11x + 2 = 90
11x = 90 - 2
x = 88/11
x = 8.
For the measure of ∠DOT, we have;
∠DOT = (7x + 2)
∠DOT = 7(8) + 2
∠DOT = 58°
For the measure of ∠TOU, we have;
∠TOU = 4x
∠TOU = 4(8)
∠DOT = 32°.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
NO LINKS!!! URGENT HELP PLEASE!!!
Express the statement as an inequality (Part 1a^2)
a. b is positive
1. b ≥ 0
2. b ≤ 0
3. b = 0
4. b > 0
5. b < 0
b. s is nonpositive
1. s ≤ 0
2. s = 0
3. s ≥ 0
4. s < 0
5. s > 0
c. w is greater than or equal to -8
1. w < -8
2. w = -8
3. w ≥ -8
4. w > -8
5. w ≤ -8
a. 4. b > 0
If b is positive, then we know it will be greater than 0.
b. 1. s ≤ 0
If s is nonpositive, this means it is negative or 0. We will use a less than or equal to symbol.
c. 3. w ≥ -8
If w is greater than or equal to -8, we will use a greater than or equal to symbol.
Please anwser the question i will reward brainlest.
Answer:
2((3(4) + 4(7) + 3(7)) = 2(12 + 28 + 21) = 2(61) = 122 square meters
100 Points! Algebra question, only looking for an answer to B. Photo attached. Please show as much work as possible. Thank you!
Apply the fraction rule:
[tex]\text{a}\times\dfrac{\text{b}}{\text{c}} =\dfrac{\text{a}\times\text{b}}{\text{c}}[/tex]
Answer:
[tex]\longrightarrow\boxed{\bold{\frac{\text{fx}}{\text{g}}}}[/tex]
Which phrase is represented by the expression 5x(36+9)
A. The product of 36 and 5, increased by 9
B. The product of 36 and 9, multiplied by 5
C. The sum of 36 and 9, multiplied by 5
D. The sum of 36 and 5, increased by 9
A person invested $840 in an account growing at a rate allowing the money to double every 10 years. How long, to the nearest tenth of a year would it take for the value of the account to reach $1,540?
It would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.
HOW CAN WE CALCULATE THE AMOUNT?To solve this problem, we can use the formula for exponential growth:
[tex]A = P * (1 + r)^t[/tex]
where:
A = final amount (in this case, $1,540)
P = principal amount (initial investment, in this case, $840)
r = rate of growth (as a decimal, in this case, the rate at which the money doubles every 10 years, or 1/10 = 0.1)
t = time (in years, which we need to find)
Plugging in the values:
[tex]1,540 = 840 * (1 + 0.1)^t[/tex]
Dividing both sides of the equation by 840:
[tex]1.83333... = (1.1)^tTaking the natural logarithm of both sides:ln(1.83333...) = ln((1.1)^t)Using the property of logarithms that ln(a^b) = b * ln(a), we get:ln(1.83333...) = t * ln(1.1)Finally, dividing both sides by ln(1.1) to solve for t:t = ln(1.83333...) / ln(1.1)[/tex]
Using a calculator, we can find that t ≈ 7.5 (rounded to the nearest tenth of a year).
So, it would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.
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If z is a standard normal variable, find P(z>.97)
Therefore, P(z > 0.97) = 0.166 using standard normal distribution table.
Standard normal distribution table explained.
A standard normal distribution table, also called a z-score table or a standard normal table, is a table that provides the area under the curve to the left of a specific z-score value in a standard normal distribution. A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.
The table usually includes positive z-score values in the right-hand column and the second decimal place in the top row. The intersection of a specific z-score value and decimal place provides the area under the curve to the left of that z-score value.
For example, if we want to find the area under the curve to the left of a z-score value of 1.32, we would locate the row with 1.3 in the top row and the column with 0.02 in the right-hand column. The intersection of this row and column gives the area under the curve to the left of 1.32, which is 0.9066.
Using a standard normal distribution table or calculator, we can find the probability of z being greater than 0.97 is approximately 0.166. Therefore, P(z > 0.97) = 0.166.
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A student randomly selects a marble from a bag with 3 red marbles , 4 blue marbles, 2 green marbles, and 5 yellow marbles. How many outcomes are in the sample space?
There are a total of 14 possible outcomes, one for each marble in the bag.
How many outcomes are in the sample space?The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is selecting a marble from the bag.
There are 14 marbles in the bag in total.
When the first marble is selected, there will be 13 marbles remaining in the bag, then 12, then 11, and so on.
Therefore, the number of outcomes in the sample space is:
3 + 4 + 2 + 5 = 14
There are 14 possible outcomes, one for each marble in the bag.
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Show that the circles touch each other internally.
This shows that the two circles intersect at a point P, and that the distance between their centers, OP1OP2, is less than the sum of their radii, r1 + r2. Thus, the two circles touch each other internally at point P.
How can you demonstrate how two circles internally contact one another?You must calculate each circle's radius and centre in order to accomplish this. The circles will externally touch if the total of the radii and the space between the centres are identical. The circles will internally touch if the variations in radii and the separation between their centres are equal.
Let C1 and C2 stand for the two circles, with O1 and O2 serving as their respective centres. Let r1 and r2 represent the radius of C1 and C2, respectively.
Let's say that point P is where the two circles converge. The Pythagorean Theorem thus gives us:
OP1² = r1²
OP2² = r2²
OP1² + OP2² = (r1 + r2)²
Simplifying the third equation, we get:
OP1² + OP2² = r1² + 2r1r2 + r2²
The left half of this equation can be rewritten as (OP1 + OP2)2 - 2OP1OP2. When we simplify the equation above and substitute this, we get:
(OP1 + OP2)² = (r1 + r2)² + 2OP1OP2
Since OP1 and OP2 are both positive, we have:
(OP1 + OP2)²> (r1 + r2)²
Therefore, we must have:
OP1OP2 < r1 + r2
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What is an equation of the line that passes through the points
(
5
,
−
6
)
(5,−6) and
(
−
5
,
−
4
)
(−5,−4)?
Answer:
y= -1/5x-5
Step-by-step explanation:
You can use the slope formula and the slope intercept form which is y=mx+b.
The diameter of a child's bicycle wheel is 12 inches. Approximately how many revolutions of the wheel will it take to travel 1,200 meters? Use 3.14 for π and round to the nearest whole number. (1 meter ≈ 39.3701 inches)
Answer:
First, we need to convert 1,200 meters to inches:
1,200 meters * 39.3701 inches/meter = 47,244.12 inches
Next, we need to find the circumference of the wheel:
Circumference = π * Diameter
Circumference = 3.14 * 12 inches
Circumference = 37.68 inches
To find the number of revolutions, we can divide the total distance traveled (47,244.12 inches) by the distance traveled per revolution (37.68 inches):
47,244.12 inches ÷ 37.68 inches/revolution ≈ 1,254 revolutions
Rounding to the nearest whole number, it will take approximately 1,254 revolutions of the wheel to travel 1,200 meters on a child's bicycle.
For the following sequence: 6,15,24,33,.....
a) Write an expression for the nth term
b) Find the 10th term.
Answer:
a) The common difference between consecutive terms is 9. Thus, the nth term can be expressed as:
n(9)+(-3)
b) To find the 10th term, we substitute n=10 in the expression we just found:
10(9) + (-3) = 87
Therefore, the 10th term of the sequence is 87.
Due tonight at 11 please help
Thus, the height of the cylinder for the given volume and radius is found to be 10 ft.
Explain about the solid cylinder:Objects in three dimensions are represented by solid shapes. Search the area! Solid shapes include any other three-dimensional object, such as a laptop, phone, ice cream cone, balls, etc.
On a three-dimensional plane, a cylinder is a solid shape. It maintains a set spacing between two circular, parallel bases that are connected by a curved surface (like a tube).
Given that:
volume of cylinder V = 502 cu. ftRadius r = 4 ftThe formula for the volume of cylinder V:
V = πr²h
Put the values:
502 = 3.14*4²*h
502 = 3.14*16*h
h = 502 / 50.2
h = 10 ft
Thus, the height of the cylinder for the given volume and radius is found to be 10 ft.
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Complete question:
Find the missing dimension of the given solid.
The figure is attached.
The function h(x) = 2|x| is a transformation of the absolute value parent function, f(x) = |x| which graph shows h(x)
The graph of the function h(x) is then added as an attachment
Selecting the graph that best shows the function h(x)From the question, we have the following parameters that can be used in our computation:
h(x) = 2|x|
Also, we have
f(x) = |x|
When the function f(x) = |x| is compressed by a factor of 2, we do the following
We multiply 2 to the function equation
So, we have
h(x) = |x| * 2
Evaluate
h(x) = 2|x|
This means that the transformed function is passes through (x, 2y) of the original function
The graph of the function h(x) is then added as an attachment
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If a 24-pound EP rib of beef costing $45.00 is purchased oven-ready, and 1/4 of it is lost during roasting, how much does a 6-ounce serving cost?
$15 is the cost of a 6-ounce serving cost.
What is the cost price?
The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.
Here, we have
Given: If a 24-pound EP rib of beef costing $45.00 is purchased oven-ready, and 1/4 of it is lost during roasting.
EP = 24 lb costing $45
1/4th lost during roasting.
Remaining = 24 lb - (1/4) of 24 lb
= 24 lb - 6 lb
= 18 lb
Now, this roast should match the cost of the original EP.
Cost per lb = (cost of beef originally)/(quantity of roasted beef)
= 45/18 dollar per lb
Cost of 6-ounce serving cost = (45/18)×6 = $15.
Hence, $15 is the cost of a 6-ounce serving cost.
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IREADYYYY...............................................
This is the equation that represents the situation: 3q + 7 = 40.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=). An equation states that two expressions have the same value, and it provides a way to find the unknown values of variables by manipulating the expression using algebraic operations. Equations are used in a variety of fields, including physics, chemistry, engineering, economics, and many others, to model relationships and solve problems.
Here,
Let's call the length of the fourth side "x".
Since the three sides of the quadrilateral are the same length, we know that they are each equal to "q".
The perimeter of a quadrilateral is the sum of all its sides, so we can write:
q + q + q + x = 40
Simplifying, we get:
3q + x = 40
We also know that the length of the fourth side is 7 inches, so we can substitute that in for "x":
3q + 7 = 40
This is the equation that represents the situation.
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what is the area in square centimeters, of the trapezoid below?
The area in square centimeters, of the trapezoid below is equal to 84.4 cm².
How to calculate the area of a trapezoid?In Mathematics and Geometry, the area of a trapezoid can be calculated by using this mathematical equation (formula):
Area of trapezoid, A = ½ × (a + b) × h
Where:
a and b represent the base areas of a trapezoid.
h represent the height of a trapezoid.
By substituting the given side lengths into the formula for the area of a trapezoid, we have the following:
Area of trapezoid, A = ½ × (7.9 + 13.2) × 8
Area of trapezoid, A = 84.4 cm².
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Is (-6, 8) a solution to this system of equations?
y = 8
7x + 4y = -10
yes
Or
no
Answer:
7(-6) + 4(8) = -42 + 32 = -10, so (-6, 8) is the solution to this system of equations.
The answer is Yes.
An area of land measures 735 metres by 756 metres. It is to be divided up into
square plots of equal size.
(a) What is the area of the largest squares that will fit on it?
(b) How many squares will fit on it?
Answer:
See below!
Step-by-step explanation:
Given:Length = 735 meters
Width = 756 meters
Finding the area:Area = length × width
Area = 735 × 756
Area = 555660 m²
Part a)To find the area of largest square, we first need to find the highest common factor of 735 and 756.
HCF of 735 and 756:
= 21
This means the length of largest square will be 21 m.
Now,
Area of largest square:= length × length
= 21 × 21
= 441 m²Part b)No. of squares = Total area / Area of largest square
No. of squares = 555660 / 441
No. of squares = 1260 squares[tex]\rule[225]{225}{2}[/tex]
Compare the values for the following, which is greater: sin 100° or sin 250°? Use the sin wave to approximate
each value and label it on the graph.
The value "Sin 100°" is greater than "sin 250°", that is, sin 100° > sin 250°
Which is greater, sin 100° or sin 250°?To compare the values of sin 100° and sin 250°, we need to understand the behavior of the sine function. The sine function oscillates between -1 and 1 over a period of 360°, with its maximum value of 1 at 90° and its minimum value of -1 at 270°.
Using the sine wave, we can see that sin 100° is located in the second quadrant, where the sine values are positive, while sin 250° is located in the third quadrant, where the sine values are negative. Therefore, sin 100° is greater than sin 250°, because sin 100° has a positive value closer to the maximum value of 1, while sin 250° has a negative value closer to the minimum value of -1.
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What is the measure of angle XYZ
The calculated measure of the arc XYZ is 83 degrees
Calculating the measures of the angle XYZFrom the question, we have the following parameters that can be used in our computation:
The circle
The angles created by secants and tangents that intersect outside a circle, which states that
The size of the angle formed by these two lines is equivalent to half the numerical difference between the measures of the arcs that they cut out from the circle.
So, we have
XYY = 1/2 * (166 - 0)
Evaluate
XYY = 83
Hence, the measure of the angle is 83 degrees
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Find the value of the annuity and the interest. Round to the nearest dollar.
Periodic Deposit: $100 at the end of each year
Rate: 4% compounded annually
Time: 9 years
The value of the annuity after 9 years is approximately $1,044.56. The interest earned on the annuity after 9 years is approximately $244.56.
What is annuity?A financial contract known as an annuity offers a series of recurring payments over a predetermined length of time. A monthly, quarterly, or annual payment schedule is available when buying an annuity from an insurance provider. The payments are made until the annuitant's death or for a predetermined amount of time.
Deferred annuities and immediate annuities are the two categories under which annuities fall. Deferred annuities are a particular kind of annuity where the payments are postponed for a predetermined amount of time, typically several years. On the other hand, an instant annuity starts paying out as soon as the annuity is bought.
The value of annuity is given by the formula:
[tex]A = P * ((1 + r)^n - 1) / r[/tex]
Substituting the given values we have:
[tex]A = $100 * ((1 + 0.04)^9 - 1) / 0.04\\A = $100 * (1.04^9 - 1) / 0.04[/tex]
A ≈ $1,044.56
Hence, the value of the annuity after 9 years is approximately $1,044.56.
Now, the interest is givn as:
Interest = A - (P * n)
Substituting the values we have:
Interest = $1,044.56 - ($100 * 9)
Interest ≈ $244.56
Hence, the interest earned on the annuity after 9 years is approximately $244.56.
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An object is thrown upward at a speed of 145 feet per second by a machine from a height of 2 feet off the ground. The height h of the object after t seconds can be found using the equation
When will the height be 230 feet?
seconds
When will the object reach the ground?
seconds
Answer:
Step-by-step explanation:
The equation for the height h of the object after t seconds is given by:
h = -16t^2 + 145t + 2
To find when the height will be 230 feet, we can set h = 230 and solve for t:
230 = -16t^2 + 145t + 2
We can simplify this equation by moving all the terms to one side:
16t^2 - 145t + 228 = 0
To solve for t, we can use the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 16, b = -145, and c = 228. Plugging in these values, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(228))) / 2(16)
t = (145 ± sqrt(21025 - 14592)) / 32
t = (145 ± sqrt(6433)) / 32
t ≈ 0.56 seconds or t ≈ 9.17 seconds
Therefore, the height of the object will be 230 feet at approximately 0.56 seconds or 9.17 seconds after it is thrown.
To find when the object will reach the ground, we can set h = 0 and solve for t:
0 = -16t^2 + 145t + 2
Again, we can simplify this equation by moving all the terms to one side:
16t^2 - 145t - 2 = 0
Using the quadratic formula again, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(-2))) / 2(16)
t = (145 ± sqrt(21249)) / 32
t ≈ 9.51 seconds or t ≈ 0.15 seconds
Therefore, the object will reach the ground at approximately 0.15 seconds or 9.51 seconds after it is thrown. However, since the negative solution does not make physical sense in this context, the object will reach the ground after approximately 9.51 seconds.
~~~Harsha~~~
Find the surface area for the figure ( on photo )
The surface area of the square pyramid given above would be = 400ft²
How to calculate the surface area of the given shape?The diagram above is a typical example of the square based pyramid which has four triangles connected to a vertex.
To calculate the surface area of the given figure, the formula that should be used would be = b² +2bs
where b = base length= 10ft
s = slant height= 15ft
Surface area = 100+2(10×15)
= 100+300
= 400ft²
Therefore the surface area of the square based pyramid given above would be = 400ft².
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A paperwight has height of 4cm and a volume of 38.4 cubic cm.
The calculated base area of the paperweight is 9.6 square cm.
Calculating the base areaTo calculate the base area of the paperweight, we can use the formula for the volume of a three-dimensional object:
Volume = Base area x Height
In this case, we know that the height of the paperweight is 4cm and the volume is 38.4 cubic cm.
So we can rearrange the formula and solve for the base area:
Base area = Volume / Height
Substituting the values we have:
Base area = 38.4 cubic cm / 4cm
Base area = 9.6 square cm
Therefore, the base area of the paperweight is 9.6 square cm.
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NO LINKS!! URGENT HELP PLEASE!!
Express the angle in terms of degrees, minutes, and seconds, to the nearest second.
350.5527°
Answer:
350° 33' 10".
Step-by-step explanation:
To convert the decimal degree 350.5527° to degrees, minutes, and seconds, we can use the following steps:
The whole number part of the decimal degree is the degree. So, the degree is 350.Multiply the decimal part by 60 to get the minutes.0.5527 x 60 = 33.162The whole number part of the minutes is the minutes. So, the minutes are 33.Multiply the decimal part of the minutes by 60 to get the seconds.0.162 x 60 = 9.72Round the seconds to the nearest second. The nearest second is 10.Therefore, 350.5527° is equivalent to 350° 33' 10".