The function () =
40+700
represents the average cost (in dollars) of making items. How
many items must be made for the average cost to fall to $5
The number of items must be made for the average cost to fall to $5 wil be; 900.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).
We are given that function = 40x +700 represents the average cost (in dollars) of making items.
Then the item made for function average cost to fall to $5.
= 40x + 700
= 40(5) + 700
= 200 + 700
= 900
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Graph the linear inequality y < 1/2x + 2 using slope-intercept form.
Given inequality:
y < 1/2x + 2To graph it first, consider line:
y = 1/2x + 2Find two points on the line.
Let them be x- and y-intercepts:
x = 0 ⇒ y = 1/2*0 + 2 = 2, so the point is (0, 2)y = 0 ⇒ 0 = 1/2x + 2 ⇒ 1/2x = - 2 ⇒ x = - 4, the point is (- 4, 0)Now, plot the two points.
Next, draw a dashed line trough the two points. Dashed line because the line is not included into solution set, due to '<' sign.
The last step, shade the area below the line. Below the line because 'y <' means 'y-values less than' which appears below the line.
Answer:
See attachment.
Step-by-step explanation:
Given linear inequality:
[tex]y < \dfrac{1}{2}x+2[/tex]
When graphing inequalities, temporarily replace the inequality sign for the equals sign:
[tex]\implies y=\dfrac{1}{2}x+2[/tex]
Find two points on the line by substituting two values of x into the equation:
[tex]x=0 \implies y=\dfrac{1}{2}(0)+2 =2\implies (0, 2)[/tex]
[tex]x=4 \implies \dfrac{1}{2}(4)+2=4 \implies (4,4)[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Therefore, to graph the given linear inequality:
Plot points (0, 2) and (4, 4).Draw a dashed straight line through the points.Shade under the dashed line.Find the slope of the line that passes through points 2, -8 and the origin using m=rise/run
Answer:
-4
Step-by-step explanation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-8)}{0-2}=\frac{8}{-2}=-4[/tex]
The slope of the line that passes through the points (2, -8) and the origin is calculated using the formula m = rise/run, which gives -4.
Explanation:In this Mathematics problem, we are asked to find the slope of the line that passes through two points using the formula m = rise/run, where 'm' is the slope. The points provided are (2, -8) and the origin, which is (0, 0).
To find the slope (rise/run), we can subtract the y-values (rise) and the x-values (run) of the two points, respectively. So, the formula becomes: m = (-8 - 0) / (2 - 0) => m = -8/2 = -4.
Therefore, the slope of the line that passes through the points (2, -8) and the origin is -4.
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how do write 3n - 6 as a phrase in words
Bismuth-214 has a half life of approximately 20 minutes. Find
the amount of bismuth-214 left from a 30-gram sample after 1 hour
One of the common terms for exponential decay is half-life, which refers to the period of time it takes for a quantity to fall by an exponential rate and halve its initial value.
What is meant by exponential decay function?In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. It can be written as [tex]y = a(1 - b)^x[/tex], where y represents the final amount, a represents the initial amount, b represents the decay factor, and x is the amount of time that has passed.
The exponential decay formula aids in determining the rapid decline over time, or exponential decline. The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay.
The time it takes for a quantity to drop by an exponential rate to halve its initial value is known as the half-life, which is one of the popular words used to describe exponential decay.
Each 20 minutes there is 1/2 as much one hour is 3 half lives :
start 30 then 15 then 7.5 then 3.75 gm
30(1/2)3 = 3.75 gm
The complete question is;
Write an exponential decay function to model each situation. Then find the value of the function after the given amount of time. Bismuth-214 has a half-life of approximately 20 minutes. Find the amount of bismuth-214 left from a 30-gram sample after 1 hour.
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Unit 11 volume and surface area homework 2 area of sectors
Answer:
2. KI = 20 ft 119 M K 4. YZ = 14.2 m 2 6. PO = 2.8 in R 311 8. WZ = 5.3 km w z 108
Step-by-step explanation:
Madeline spends all of her spare money on widgets, which cost $2 each, and gizmos, which cost $2 each. What is her opportunity cost if Madeline buys 12 widgets? opportunity cost:
The opportunity cost of Madeline based on the information would be 8 units of gizmos .
What is the opportunity cost of Madeline?The benefit or gain that a person might have obtained or earned if he or she had not chosen the current alternative is known as opportunity cost.
Madeline has spent $24 ($2 x 12) on the widgets in this question since she purchased 12 of them at a cost of $2 each. In this case, her opportunity cost would be the gadgets she could have purchased, which works out to $24 / $3 = 8 units.
Therefore, the opportunity cost is 8 units.
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Entry load and exit load are both calculated as a % of the
The "net asset value" is used to compute both entry load as well as exit load as a percentage.
Define the term Entry load and exit load?Entry load is the sum of money or fee that an investor must pay to join a scheme or a company as an investment.
Exit loads are fees or amounts collected from investors for quitting a plan or a corporation as a shareholder.
In other words, the per-unit cost would be 10.1 rupees if the NAV are 10 rupees or the entry load is 1%. Simply put, when units are allocated, the entry load is added to the NAV. The price at which the company is anticipated to be sold is known as the Exit Value (EV) or Terminal Value. This is typically computed using the Venture Capital technique as a multiple of a company's revenues during the year of sale.Thus, the "net asset value" is used to compute both entry load as well as exit load as a percentage.
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The tallest tree in the United States is the coast redwood and your deer Smith State Park in California. It is 321 feet tall suppose you are 5‘,8“ tall and cast a shadow that is 2 feet at a certain time of day about how long is the trees shadow at the same time of day convert five point 5‘8“ to feet
The shadow of the tree at the same time of day was 113.29 foot long.
What is foot?Foot, plural feet, any of numerous ancient, mediaeval, and modern linear measures based on the length of the human foot and used only in English-speaking countries, where it typically consists of 12 inches or one-third yard (typically 25 to 34 cm).
In most countries and all areas of science, the foot and its multiples and subdivisions have been largely replaced by the metre, the basic linear unit of the metric system. Since 1959, a foot in the US has been defined as exactly 30.48 centimetres.
We know that
1 feet = 12 inches
So, 5 feet 8 inches = 5[tex]\frac{2}{3}[/tex] feet
Now, lets find the shadow of tree
5[tex]\frac{2}{3}[/tex]/2 = 321/x
x = 113[tex]\frac{5}{11}[/tex]
x = 113.29
Thus, the tree's shadow at the same time of day was 113.29 foot long
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Determine if the scenario involves mutually exclusive events
You roll a fair six-sided die. The die shows an even number or a number less than three.
A) Not mutually exclusive
B) Mutually exclusive
2 is a common sample in the 2 events, therefore they are not mutually exclusive.
What is probability ?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will discover the likelihood of outcomes for a random experiment using this fundamental probability theory, which is also applied to the probability distribution.
Two occurrences are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, provide a clear illustration.
If we roll a dice which is fair
Events that we get to shw even are = {2, 4, 6}
Events that we get when getting less that 3 = {1, 2}
So, 2 is a common sample in the 2 events, therefore they are not mutually exclusive.
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What’s the tangents ratio for F?
5/4
5/3
4/3
3/4
The tangent ratio of F by using the rule from trigonometry is 4/3
What is the trigonometry ratio?Trigonometric ratios are ratios that represent the length of a triangle's sides. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the fundamental trigonometric ratios.
The sine of the trigonometry ratio is sin θ = opposite/hypotenuse. The cosine of the trigonometry ratio is cos θ = adjacent/hypotenuse. The tangent of the trigonometry ratio is tan θ = opposite/adjacent. From the image given. The opposite side is the line facing the angle F;
Thus, the opposite side = 8, and the adjacent is the smallest side, which is 6.
Therefore, the tangent ratio for F is:
tan θ = 8/6
This can be reduced to 4/3
Therefore, we can conclude that the tangent ratio of F is 4/3.
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[tex]\frac{1-5}{6-3} =\frac{-4}{3} =[/tex]
The value of the given fraction is -1.33.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Any number can be expressed as fractions.
Given is an expression in fractions of the form,
(1 - 5) / (6 - 3) = (-4) / 3
Actually we got an improper fraction here.
Improper fractions have larger value on the numerator than the denominator.
If we need the answer in decimal form, just divide the number 4 by 3 and give negative sign for the answer.
So here the given answer is -1.33.
Hence the decimal form of the fraction (-4)/3 is -1.33.
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Which expression is the least absolute value |-28| |-1| |6| |15|
Answer: |-1|
Step-by-step explanation:
So lets just solve all of this stuff so you can just look at it and get the answer. | - 28 | = 28, |-1| = 1, |6| = 6, |15| = 15. So we have 28, 1, 6, and 15. Put this in order we have: 28, 15, 6, 1 which means 1 is the least or your could say |-1| is the least. Have a good day ;)
Angles 3 and 4 are supplementary. The measure of angle 3 is
thirty-five more than one-fourth the measure of angle 4.
1. What is the measure of Angle 3?
2. What is the measure of Angle 4?
The values of ∠4 and ∠3 are 116 degrees and 64 degrees respectively.
Given ,
What are supplementary angles ?
The angles are said to be in supplementary if and only if the sum of two angles is 180 degrees .
Angles 3 and 4 are supplementary.
The measure of angle 3 is
thirty-five more than one-fourth the measure of angle 4.
So,
∠3 + ∠4 = 180 degrees.
∠3 = 180-∠4 - equation 1
∠3 = 35 + (1/4 ) ∠4 - equation2
As equation 1 and 2 are equal
hence,
180-∠4 = 35 + (1/4) ∠4
180-35 = ∠4 + (1/4) ∠4
145 = ((1/4)+1) ∠4
145 = (5/4) ∠4
∠4 = 145 * 4 / 5
∠4 = 29*4
∠4 = 116
∠3 = 180-116
∠3 = 64
Hence the values of ∠4 and ∠3 are 116 degrees and 64 degrees respectively.
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Can somebody please tell me how to Solve Systems by Elimination? I don't understand it at all and I'm staying up all night trying to figure it out. I especially don't understand the co-efficient part.
An example is:
2c+3d=12
5c-d=13
What would the answer be to that? Please provide an explanation!
Solving the example, hope it will help you with better understanding.
Given system:
2c + 3d = 125c - d = 13We need to eliminate one of the variables c or d. Let us eliminate d.
We see the first equation has 3d and the second equation has - d. The coefficients of d are 3 and - 1. If we multiply the second one by 3 it will become - 3, then if we add them up they will cancel, 3d - 3d = 0. By doing this we'll eliminate the variable d and left with variable c in the resulting equation.
Demonstrating how it works:
2c + 3d = 12, we leave it as is
5c - d = 13, we multiply all terms of this by 3, it becomes, 15c - 3d = 39
Now add up the two equations:
2c + 15c + 3d - 3d = 12 + 39, eliminated d17c = 51 solving for cc = 51/17c = 3Now we can find the value of d:
2c + 3d = 122*3 + 3d = 126 + 3d = 123d = 6d = 2Our solution is:
c = 3, d = 2During a series of plays in a football game, a running back carried the ball for the yardages given by 6, -3, 2, -1, 7,
-4, and -2. Find his total yards and his average yards per carry.
The total yards for the running back was
(Simplify your answer.)
Therefore ,As a result, the region's problem with the suggested solution is the playing field area measures 118 yards by 56 yards.
Define area.Add length and breadth together to calculate area. The calculation for area is L times B. Radius or area equals r2(=3.14) With the use of these techniques, it is also possible to determine the area of various quadrilaterals, a specific type of polygon with 4 sides and an angle smaller than 90 degrees. Application. Geometry has been based on the concept of area from its inception.
Here,
We find w = 56, which indicates that the parallelogram has a length of 56 yards.
Since the width is identical to 2w + 6, we can make the computation simpler by changing w to 56 to find the rectangle's length.
The rectangle's length is shown to be 118 yards.
The size of the playing area is accordingly 118 yard by 56 yards.
As a result, the proportions of the playing field—118 yards by 56 yards—are the answer to the dilemma at hand.
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Assistance is needed please thank you easy! simple interest problem
A. The interest Bianca earned for a period of 3 years is $382.50. The correct option is B. $382.50
B. The number of years Bianca kept the account open is 11 years
Calculating simple interestFrom the question, we are to calculate how much interest Bianca will earn for a period of 3 years
From the simple interest formula, we have that
S.I = PRT
Where S.I is the simple interest
P is the principal
R is the rate
and T is the time
From the given information
P = $3,000
R = 4.25% = 0.0425
T = 3
Therefore,
S.I = $3,000 × 0.0425 × 3
S.I = $382.50
B.
From the given information, Bianca receives $4,402.50 when she closes the account
Thus,
The simple interest = $4,402.50 - $3,000
Simple interest = $1402.5
We are to calculate how many years Bianca kept the account open. That is, T
Using the formula,
S.I = PRT
$1402.5 = $3000 × 0.0425 × T
$1402.5 = $127.5 × T
T = $1402.5/$127.5
T = 11
Hence, the time is 11 years
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Let me know if I got this right
What is the solution to the equation?
lnx−ln(4x−1)=ln5
Enter your answer in the box. Enter any fractions as simplified fractions.
Answer:
x = 5/19
Step-by-step explanation:
For left side, apply logarithm division property:
[tex] \displaystyle{ \ln a - \ln b= \ln \left( \dfrac{a}{b} \right)}[/tex]
Hence:
[tex] \displaystyle{ \ln \left( \dfrac{x}{4x - 1} \right) = \ln 5}[/tex]
Since both sides have same ln, we can cancel ln both sides:
[tex] \displaystyle{ \dfrac{x}{4x - 1} = 5}[/tex]
Solve the equation for x:
[tex] \displaystyle{x = 5(4x - 1)} \\ \\ \displaystyle{x = 20x - 5} \\ \\ \displaystyle{5 = 20x - x} \\ \\ \displaystyle{5 = 19x} \\ \\ \displaystyle{x = \dfrac{5}{19}}[/tex]
Therefore, x = 5/19
Kelly rolled scores of 254, 202, 284, 269, 151, 258 and 202 in a recent tournament. What was the mean, median and mode of her scores?
Answer:
See below!
Step-by-step explanation:
Data:254, 202, 284, 269, 151, 258, 202
Mean:The sum of data divided by the number of data is called mean.Mean of the data:
[tex]\displaystyle Mean= \frac{Sum \ of \ data}{number \ of \ data} \\\\Mean = \frac{254+202+284+269+151+258+202}{7} \\\\Mean=\frac{1620}{7} \\\\\boxed{Mean = 231.4}[/tex]
Median:The middle value of the data is median.Median of data:
Arrange the data in increasing order.
151, 202, 202, 254, 258, 269, 284
The middle value = 254
So,
Median = 254Mode:The frequently occurring value in the data is known as mode.Mode in data:
The mode, here, is 202. (occurring 2 times.)
So,
Mode = 2[tex]\rule[225]{225}{2}[/tex]
The linear function f is defined as f(x)= -2x+3 consider the graph y =f(x)
On solving the provided question, we can say that the linear function is f(x) = -2x +3 and by the graph y = f(x) = -1
What is linear function ?Two distinct but related concepts are referred to as linear functions in mathematics. A polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line. Any function that depicts a straight line on a coordinate plane is said to be linear. For instance, y = 3x - 2 is a linear function since it depicts a straight line on the coordinate plane. f(x) = 3x - 2 can be used to represent the function since f(x) can be linked to y.
here,
the linear function is f(x) = -2x +3
and by the graph y = f(x) = -2x +3 = -2(2) + 3 = -4+3 = -1
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Solve the following equation. 2(y +4) = 3(2y -4) SHOW YOUR WORK
Answer:
y = 5
Step-by-step explanation:
2(y + 4) = 3(2y - 4)
2y + 8 = 6y - 12
-4y = -20
y = 5
So far this semester, Franco is averaging a score of 70.7 points on math tests, which is 1% higher than his average last semester. What was the average of his scores last semester?
help me pleasee
Hurry - please help!!!!!!!!
Answer:
false
Step-by-step explanation:
I think it's false but I don't really remember, but I would go with someones else answer cause I'm not sure
Which is the mode for the data set? -1,0,3,4,-3,-1
Mode of data set -1, 0, 3 ,4, -3, -1 is - 1 with most often in data set.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The data set is,
⇒ -1, 0, 3 ,4, -3, -1
Now, We know that;
The mode is the value that appears the most often in the data set.
Here, In the data set - 1 is most often number.
So, The mode of data set = - 1
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Resolve F2 into components along the u and v axes determine the magnitudes of these components.
Resolving F2 into components along the u and v axes, the magnitudes of the components are determined as 150 N and 77.6 N.
According to the sine law, the side length of a triangle should be divided by the sine of the opposite angle. That is, when we divide side a by the sine of angle A, we get the same result as side b divided by angle B and side c divided by angle C.
For the given diagram, first, draw the vector components. Then, by sine law, we get,
[tex]\begin{aligned}\frac{F_u}{\sin 75^{\circ}}=\frac{F_2}{\sin 75^{\circ}}=\frac{F_v}{\sin 30^{\circ}}\end{aligned}[/tex]
Now, substitute the value of F₂, and we get,
[tex]F_u=F_2=\mathrm{150\;N}[/tex]
Now, solve for [tex]F_v[/tex], we get,
[tex]\begin{aligned}F_v&=\frac{F_2\sin 30^{\circ}}{\sin75^{\circ}}\\&=\mathrm{\frac{150\;N\times 0.5}{0.966}}\\&=\mathrm{77.64\;N}\end{aligned}[/tex]
The required answers are 150 N and 77.64 N.
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Use the drawing tool(s) to form the correct answer on the provided graph.
Using the information provided on the graph, draw the line the line that is perpendicular to line segment AB and passes through point P
The required equation of the line is given as y = 5x -6.
Given that,
To determine the equation of a line passing through the point P(9, -8) and perpendicular to the line AB y = 3x + 6.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the given line
y = 3x + 6.
m = 3
The equation of the perpendicular line is given as,
y - y₁ = -1/m (x - x₁)
Substitute the value in the above equation,
y + 8 = -1 / 3 (x - 9)
y = -x/3 + 3 - 8
y = -x/3 - 5
Thus, the required equation of the line is given as y = -x/3 - 5.
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Shawn found a deal for a kayak trip to see the bioluminescent
jellyfish in the Indian River Lagoon. The deal said it was 40%
of the regular price. Shawn paid $267 for 5 adults. What was
the regular cost of the kayak trip for 1 adult?
A. 32.04
B. $53.40
C. $89.00
D. $133.50
When the bargain was 40% off the standard price, the cost of the kayak trip for one adult was $53.40.
what is expression ?A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.
given
Shawn spent $267 on five persons,
$267 / five equals $53 (or 40%, or 40/100, or two out of five),
= $ 53.
When the bargain was 40% off the standard price, the cost of the kayak trip for one adult was $53.40.
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ILL GIVE BRAINLIEST IF CORRECT NEED HELP ASAP PLS
Answer: y=2x-15
Step-by-step explanation:
Answer:
y=1/2x + 15
Since,her original flight plan time is X and hence the flight will reach 2 times faster the X becomes X/2 and the additional time 15 minutes which has already been delayed.So,she will arrive her destination in(1/2X+15)min from 4:00 p.m.
*mark me brainliest
The points on the number line are opposite numbers. The tick marks represent
intervals of 1 unit.
Label 0 at the correct spot on the number line.
Label the point plotted to the right of 0.
Label the point plotted to the left of 0.
Picture will be inserted below
The points on the number line are opposite numbers, so that the required answer is as attached.
What is a number line?A number line is a straight line which extends from negative infinity to positive infinity on which the position of all directed numbers can be located.
Directed number are numbers with sign, which shows its direction i.e negative or positive.
In the given question since the points are opposite numbers, then we have single number but opposite in directions. Therefore there must be at equal distance to point 0 on the number line.
Considering the given conditions in the question, the opposite numbers are; -5 and +5. While the point 0 is the midpoint between -5 and +5.
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Which of the following are square roots of the number below? Check all that
apply.
529
A. 5291/2
B. 23
C. -23
D. 1058
E. -5291/2
The final statement is: The square roots of 529 are [tex]529^{1/2}[/tex] -23 and 23
What is Square Root?The square root of a number is defined as the value, which gives the number when it is multiplied by itself. The radical symbol √ is used to indicate the square root. For example, √16 = 4. The radical symbol is also called a root symbol or surds.
Given here: The number 529 and to find its square root equivalent.
We know 529=23² and (-23)²=529
Also √529= [tex]529^{1/2}[/tex]
Thus these are the square root equivalent of the number 529
Hence, The square roots of 529 are -23,23 and [tex]529^{1/2}[/tex]
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