Answer:
a) Domain: -∞ < x < ∞
b) Cost required to manufacture 3500 items is $15,900.
c) Number of items she can manufacture is 5208 if cost is kept at $20,000
Step-by-step explanation:
a) What is the reasonable domain of the function?
The function is C(x) = 7,500 + 2.4x
The domain of the function is the set of values for which the function is defined and valid.
In the given function there is no constraint or undefined points so domain is:
-∞ < x < ∞
b) What is the cost of 3,500 items?
We are given x = 3500 and we need to find the cost.
Putting values in the function given:
C(x) = 7,500 + 2.4x
C(x) = 7,500 + 2.4 (3500)
C(x) = 7500 + 8400
C(x) = 15,900
Cost required to manufacture 3500 items is $15,900.
c) If costs must be kept below $20,000 this month, what is the greatest number of items she can manufacture?
We are given cost, and we need to find x
C(x) = 7,500 + 2.4x
20,000 = 7500 +2.4x
20,000 - 7500 = 2.4x
12500 = 2.4 x
=> x = 12500/2.4
x= 5208.3 ≅ 5208
So, Number of items she can manufacture is 5208 if cost is kept at $20,000
Find the lateral area of the prism below. Round your answer to the nearest whole number. Need help asap easy geometry question
Answer:
LA = 322 meters squared
Step-by-step explanation:
LA = hp
= 26(2 + 5 + 5.39)
= 26(12.39)
= 322 meters squared rounded to the nearest whole number
The 4th choice
Answer:
It would be option D or option number 4.
In the figure, RQS QLK.
What is the value of x?
36
72
108
144
Answer:
x = 108
Step-by-step explanation:
∠RQS = ∠QLK = x ( corresponding angles )
∠QLK and ∠KLM form a straight angle and are supplementary, thus
∠QLK + ∠KLM = 180 ← substitute values
x + x - 36 = 180
2x - 36 = 180 ( add 36 to both sides )
2x = 216 ( divide both sides by 2 )
x = 108
Answer:
108
Step-by-step explanation:
For the function f(x) = x^2, what effect will multiplying f(x) by 1/4 have on the
graph?
Answer:
the graph will be vertically compressed i just answered apex
Step-by-step explanation:
Answer:
The graph will be compressed vertically.
Step-by-step explanation:
Solve 5x + 7 > 17.
{x | x < 2}
{x | x > 2}
{x | x < -2}
{x | x > -2}
Answer:
[tex]\large\boxed{\{x\ |\ x>2\}}[/tex]
Step-by-step explanation:
[tex]5x+7>17\qquad\text{subtract 7 from both sides}\\\\5x>10\qquad\text{divide both sides by 5}\\\\x>2[/tex]
Which distribution is likely to have a mean higher than the median?
Answer:
A distribution that is skewed to the right is likely to have a mean higher than the median.
Which of these numbers has the greatest absolute value? -43, -23, 0, 18 A) -43 B) -23 C) 0 D) 18
Answer:
A) -43
Step-by-step explanation:
The absolute value is the distance from 0... which means you take the number and if there's a negative sign in front of it, you remove it.
-43 becomes 43 as an absolute value... so it's bigger than the others (23, 0, and 18).
Answer is then A) -43
When solving the equation 12x^2 - 7x = 6-2(x^2 - 1). Evan wrote 12x^2 - 7x = 6 - 2x^2 + 2 as his first step. Which property
justifies this step?
a. subtraction property of equality
b. multiplication property of equality
c. associative property of multiplication
d. distributive property of multiplication over subtraction
Answer:
d. distributive property
Option D is correct, distributive property of multiplication over subtraction is the property used by Evan in first step.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
12x²- 7x = 6-2(x² - 1).
The first step written by Evan is 12x²- 7x = 6-2x² +2
We have to find the property which was used for the first step
In the equation splitted 2(x² - 1) using distributive property of multiplication over subtraction.
The distributive property of multiplication over subtraction is applied when we multiply a value by the difference of two numbers.
Hence, option D is correct, distributive property of multiplication over subtraction is the property used by Evan in first step.
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round 283,657 to the nearest thousand
284,000
(You would round up one because the number right before the thousands place is the hundred, which in our case, is above 4. As such, we are going to round up to 284,000.)
Hope I could help! :)
When rounding 283,657 to the nearest thousand, we look at the hundreds digit which is 6. Since it is greater than 5, we round up, resulting in a final rounded number of 284,000.
Explanation:To round 283,657 to the nearest thousand, we look at the hundreds place to decide whether to round up or down. Since the hundreds digit is a '6' (which is greater than 5), we round up to the next thousand. Therefore, 283,657 rounded to the nearest thousand is 284,000.
Rounding rules dictate that if the digit to the right of the target rounding place is 5 or greater, we round up the target digit by one. In this case, we're rounding to the nearest thousand, so we look at the hundreds place which is a 6. Since it is greater than 5, we add one to the thousands place, changing 283,000 to 284,000, and set all the following digits to zero, giving us our final rounded number.
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To the nearest 7739.5
Answer:
nearest whole = 7740
nearest ten = 7740
nearest hundred = 7700
nearest thousand = 8000
(HELP PLEASE)
Describe in your own words the characteristics of linear equations that determine whether a system of linear equations will be Intersecting, Parallel, or Coincident. (2 points, 0.5 for clarity of response, 0.5 for each type of system).
ANSWER
See below
EXPLANATION
Given the system of linear equation:
[tex]y = m_1x + b_1[/tex]
[tex]y = m_2x + b_2[/tex]
If
[tex] m_1 \ne \: m_2[/tex]
then the two equations, will intersect at one. The system has unique solution.
If
[tex]m_1 =m_2 \: and \: b_1 \ne \: b_2[/tex]
then, the two equations are parallel and the system will not have a solution.
If
[tex]m_1 =m_2 \: and \: b_1 = \: b_2[/tex]
Then, the two equations will coincide.
There is infinitely many solutions.
What would be the best method to use in order to solve the following quadratic equation? x^2-6x=0
Completing the square
Quadratic formula
Taking the square root
Factoring
Answer:
I think using factoring method would be the best because
Step-by-step explanation:
1) x^2-6=0
2) Factor out the X. x*(x-6)=0
3) x* (x - 6) =0 When the product of factors equal zero at least one factor is zero.
x=0
x-6=0
4)Solve for "x-6=0" for X. Move constant to the right by adding its opposite to both sides
x-6 +6 = 0 +6
Eliminate the opposites
x - 6 + 6 = 0 + 6
x= 0+6
x=6
5) the solutions are x1=0 and x2=6
if A/B and C/D are rational expressions, then which of the following is true?
Answer:
Option D. [tex]\frac{A}{B}*\frac{C}{D}=\frac{A*C}{B*D}[/tex]
Step-by-step explanation:
we have
[tex]\frac{A}{B}[/tex] and [tex]\frac{C}{D}[/tex]
we know that
To multiply fractions multiply the numerators of the fractions to get the new numerator and multiply the denominators of the fractions to get the new denominator
To divide two fractions, multiply the first fraction by the reciprocal of the second fraction
[tex]\frac{\frac{A}{B}}{\frac{C}{D}}=\frac{A}{B}*\frac{D}{C}[/tex]
and
[tex]\frac{A}{B}*\frac{C}{D}=\frac{A*C}{B*D}[/tex]
In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g. What percent of babies born in the United States are classified as having a low birth weight (< 2,500 g)? Explain how you got your answer.
Answer:
Sub into equation
Step-by-step explanation:
Answer: 2.775%
Step-by-step explanation:
Given: Mean : [tex]\mu=3,500\ g[/tex]
Standard deviation: [tex]\sigma=500\ g[/tex]
The formula to calculate z-score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 2,500g
[tex]z=\dfrac{2500-3500}{500}=\dfrac{-1000}{500}=-2[/tex]
The p-value of z = P(z<-2)=0.02275
In percent, [tex]0.02775\times100=2.775\%[/tex]
The percent of babies born in the United States are classified as having a low birth weight (< 2,500 g) = 2.775%
yvette measured the length of her driveway to be 5 meters long. Which of these is an equivalent measurement?
A. 0.07 mi
B. 15.5 yd
C. 16.4 ft
D. 585 in.
the answer is c. 16.4 feet in 5 meters
Answer:
16.4 ft
Step-by-step explanation:
We are given that Yvette measured the length of her driveway to be 5 meters long.
We have to find that which is equivalent to given length in given options.
Measurement of length = 5 m
We know that 1 meter =3.28 foot
1 meter=1.09 yard
1 meter =39.37 inches
5 m= [tex]5\times 3.28=16.4 ft[/tex]
5 m=[tex]5\times .109=5.45 yard[/tex]
5 m=[tex]5\times 39.37=196.85 inches[/tex]
Hence, measurement of length =5 m =16.4 ft
which word completes the law of detachment? if a conditional is true and its _ is true, then the conclusion is true. hypothesis conclusion conditional statement
Answer: hypothesis
Step-by-step explanation:
Answer:
The correct word is hypothesis.
Step-by-step explanation:
If a conditional statement is true and its HYPOTHESIS is true, then the conclusion is true.
The conditional statement is written in the following form -
If p is true, then q is true.
Here p is the hypothesis and q is the conclusion.
The opposite can be defined as - if the hypothesis is true and the conclusion is false, then the conditional statement is false.
Is the inverse a function
Answer:
Is not a function
Step-by-step explanation:
A relation is a function if each value of the input set (domain) is assigned only one value of the output set (range)
Given a function [tex]f(x)[/tex], the inverse of f denoted [tex]f ^ {- 1}(x)[/tex] is a function only if f(x) is a one-to-one function. This means that there are not in the domain of [tex]f(x)[/tex] two distinct values of x that produce the same value of y.
In the graph of f(x) you can see that the function is not one-to-one. Since [tex]f(x) = (-x)[/tex] for all x.
For example:
[tex]f(1) = f (-1)\\\\f (2) = f (-2)\\\\[/tex]
Observe the attached graph
In general, the inverse of a quadratic function f(x) is not a function
What is the measure of <4?
Answer:
90°
Step-by-step explanation:
Two lines intersect each other at a right angle, making them perpendicular. Thus, the resulting angles will all be 90°, making ∠4 = 90°.
Alternatively, we can use the supplementary angles equation.
Let's call the right angle marked in the picture ∠5.
∠4 + ∠5 = 180°, since the line is also a straight angle which measures 180°.
∠4 + 90° = 180°
∠4 = 90°
Either way, ∠4 = 90°
Hope this helps!
Dayton has 3 bags of frozen vegetables. Each bag has 5/8 pound of vegetables. He plans to make vegetable soup. Each pot of soup takes 1 pound of vegetables
Final answer:
Dayton has 3 bags of frozen vegetables, with each bag weighing 5/8 pound. He can make 1 pot of soup with 7/8 of another pot using these vegetables.
Explanation:
Dayton has 3 bags of frozen vegetables, and each bag contains 5/8 pound of vegetables. To find the total weight of the vegetables, we multiply the weight of one bag by the number of bags: (5/8) * 3 = 15/8 pounds. Since each pot of soup requires 1 pound of vegetables, we divide the total weight of the vegetables by 1 pound to find the number of pots of soup Dayton can make: (15/8) / 1 = 15/8 pots of soup. However, we can simplify this fraction to a mixed number: 15/8 = 1 and 7/8. So Dayton can make 1 pot of soup with 7/8 of another pot.
60 points
Please help answer, and If possible explain the questions. Thank you!
2. Which expression is not a polynomial?
A. X - 1
B. 4 + P
C. 5X^2 - √X
D. 8x - z^3
3. What is the degree of the polynomial?
3pq^4 - 2p^2q + q3
A.1
B.2
C.4
D.5
4. How many terms does the polynomial have?
p^3-4pq^2+q^2-3q
A.1
B.2
C.3
D.4
5. Which polynomial is written in standard form for the polynomial below?
-7x^2 - x^3 + x^5 +2
A. x^5+X^3+X^5+2
B. x^5 - x^3 + 7x^2+2
C. -7x^2 - x^3 + x^5+2
D. 7x^2 + x^3 + x^5+2
Answer:
2 is C. , 3 is C. , 4 is D.
Step-by-step explanation:
2
Square roots are not polynomials
3
The highest degree of one term in the polynomial is 4
4
Terms are separated by (+) or (-) signs. If you count them up there are 4
Answer:
C, D, D, B
Step-by-step explanation:
2. A polynomial has only integer exponents, no square roots. So C is not a polynomial.
3. The degree of the polynomial is the sum of the exponents of the highest term. p has an exponent of 1 and q has an exponent 4, so 1+4 = 5. D
4. Count the number of terms being added or subtracted. p^3, 4pq^2, q^2, and -3q. So there are 4 terms. D
5. Standard form of a polynomial is written from the highest exponent to the lowest. So the answer is B.
How many quarts of pure antifreeze must be added to 5 quarts of a 20% antifreeze solution to obtain a 30% antifreeze solution?
Answer:
5/7 quart
Step-by-step explanation:
Amount = concentration × volume
Amounts added = final amount
100% × x + 20% × 5 = 30% × (x+5)
Solving for x:
1.00x + 0.2×5 = 0.3×(x+5)
x + 1 = 0.3x + 1.5
0.7x = 0.5
x = 5/7
x ≈ 0.7
You should add 5/7 quart of pure antifreeze, or about 0.7 quart.
About 0.71 quarts of pure antifreeze should be added to 5 quarts of a 20% antifreeze solution to obtain a 30% antifreeze solution.
Explanation:To find out how many quarts of pure antifreeze must be added to 5 quarts of a 20% antifreeze solution to get a 30% antifreeze solution, we can set up the following equation:
0.2 * 5 + x = 0.3 * (5 + x) where x represents the amount of pure antifreeze to be added.
Solving this equation, we get:
1 + x = 1.5 + 0.3x,
This simplifies to 0.7x = 0.5,
So x = 0.5 / 0.7,
Therefore, About 0.71 quarts of pure antifreeze should be added to get a 30% solution.
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A scientist has a data set consisting of the temperature at which a chemical solution begins to evaporate. There are 500 measurements in the data set. He plans to estimate the standard error for the mean temperature by drawing a random sample from the data set consisting of 64 measurements.
What formula would produce an estimate for the standard error of the sample?
Divide the sum of all the measures by 500.
Divide the standard deviation of the sample measures by 8
Divide the sum of the sample measurements by 64
Calculate the sum of the squares of the deviations of the sample
Answer:
Divide the standard deviation of the sample measures by 8
Step-by-step explanation:
Given
measurements in data set=500
measurements in sample=64
Standard error of sample=?
As per the formula of standard error
Standard error= standard deviation/ square root of the number of measurements
= σ/√n
Here as we need to find standard error of the sample hence n=64
therefore √64= 8
The above equation will become:
standard error of the sample= σ/8 i.e. Divide the standard deviation of the sample measures by 8!
What are 5 ways that graph can be misleading ?
There are many ways that graphs can be misleading. Depending on how you set up your graph, the same set of data can look very different. It's important to understand that there are some common mistakes to avoid when making graphs. In addition, advertisers have been known to intentionally make their graphs misleading to make their data match their point.
In the image provided, this is a good example of a misleading graph.
First, notice that we know that the first bar is 10 and the second bar is 50. However, there are no labels on the horizontal or vertical axis so we don't know what the bars represent.
In addition, notice that there is no title on this graph. Since there is no title on the graph, we don't know anything about the data.
Further, look at the scale on the vertical axis. Notice that it's an uneven scale. The uneven scale makes it appear that the first bar is closer to the second bar than it actually is.
We could correct this graph by adding labels to the x and y-axis, adding a title to the graph, and making the scale on the vertical axis even.
Another way graphs can be misleading is using the wrong type to represent data. For example, a scatter plot might be better than a regular graph in some cases.
Lastly, graphs can be misleading by adding a wide range of numbers to show and increase or decrease relatively small to how it actually is.
A computer can sort x objects in t seconds, as modeled by the function
below:
t=0.003x^2 +0.001x
How many objects are required to keep the computer busy for exactly 7
seconds?
Round to the nearest whole object.
Answer:
48 objects
Step-by-step explanation:
we have
[tex]t=0.003x^{2}+0.001x[/tex]
where
t is the number of seconds
x is the number of objects
For t=7 sec
substitute in the equation and solve for x
[tex]7=0.003x^{2}+0.001x[/tex]
Solve the quadratic equation by graphing
The solution is x=48 objects
see the attached figure
select all the statements that are true for the given parabola
Answer:
A and C
Step-by-step explanation:
The graph has a minimum U at vertex (1, 5) → A is true
The x- intercepts, where the graph crosses the x- axis are not as given
The axis of symmetry has equation x = c where c is the value of the x- coordinate the axis passes through.
The axis of symmetry passes through the vertex with equation
x = 1 → C
The graph does not have a maximum vertex ∩
the distance between the points (12,9) and (0,4) is A) 14 units B) 13 units C) 15 units D) 16 units
Answer:
Option B 13 units is correct.
Step-by-step explanation:
The formula used to find distance between 2 points is:
[tex]d(P1,P2)=\sqrt{(x_{2} -x_{1})^2 + (y_{2} -y_{1})^2 }[/tex]
x₁ = 12 x₂ = 0 y₁= 9 and y₂=4
Putting values in the formula:
[tex]=\sqrt{(0-12)^2+(4-9)^2}\\=\sqrt{(-12)^2+(-5)^2}\\=\sqrt{144+25} \\=\sqrt{169} \\=13[/tex]
So, Option B 13 units is correct.
Answer:
B) 13 units
Step-by-step explanation:
1) Use the equation for solving the distance between points:
√(x2 - x1)²+(y2-y1)²
2) In this case, we would plug them into the equation:
√(12-0)²+(9-4)²
3) Now, we simplify:
√(12)²+(5)²
4) We simplify even further:
√144+25
5) We add the two:
√169
6) Take the square root of √169:
13.
85% expressed as a fraction in simplest form is
Hello There!
85% = 85/100
85/100 = 0.85
0.85/1 * 100/100
85/100
SIMPLIFIED IS 17/20
Percent are always out of 100 so...
[tex]\frac{85}{100}[/tex]
Simplifying:
[tex]\frac{85}{100}/\frac{5}{5}=\frac{17}{20}[/tex]
Hope this helped!
How do you convert 3x+2y=6 into slope intercept form?
pretty much by simply solving for "y".
[tex]\bf 3x+2y=6\implies 2y=-3x+6\implies y=\cfrac{-3x+6}{2} \\\\\\ \underset{\textit{distributing the denominator}}{y=\cfrac{-3x}{2}+\cfrac{6}{2}~\hfill }\implies y=-\cfrac{3}{2}x+3\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Answer:
y = -3/2 x +3
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
3x+2y = 6
Subtract 3x from each side
3x-3x+2y = -3x+6
2y = -3x+6
Divide each side by 2
2y/2 = -3x/2 +6/2
y = -3/2 x +3
This is in slope intercept form where the slope is -3/2 and the y intercept is 3
Simplify 12 to the 3rd over 12 to the 7th.
Answer
4.8/5
30
We are given 12 to the 3rd power over 12 to 7th power.
First we write given expression as exponent form and we get It looks ..
If base is same in division then their exponent subtract.
Thus, It would be 1 over 12 to the 4th.
help need to divide the fraction
Hello There!
So we divide fractions by multiplying by the reciprocal.
So let’s change 6/7 divided by 3/8 to 6/7 multiplied by 8/3.
Once we do that, we can start our multiplication.
Once we multiply, we get 48/21
We can both divide these by 3 to simplify it so once we divide we will get
16/7
This can be turned in a mix number and it would be 2 and 2/7
Can I get help on this also plz? I need a step by step explanation. Thank you so much!
Answer:
5) x=30
6) x=50
7) x=59
8) x=31
9) m<1=75 because they're corresponding and m<2=105 because it's supplementary with the 75 degrees angle
10) m<1= 120 because they're corresponding and m<2=60 because they're consecutive interior angles and add up to 180
in questions 5-7 you just set them equal to each other
in 8, you had to subtract 105 from 180 and then set 75 equal to 3x-18