The remaining zeros of Degree of f will be = -5 and 4i
According to the given question,
We can see that the given degree is = 3
∴ This means that there are 3 roots ( zeros )
We can conclude from the above statement that,
The number of roots = The degree that is given in the question.
For example, if the question gives the degree = x
Then the roots will also be = x
This question follows the complex conjugate root theorem,
This theorem states that the if there are complex roots with real coefficients then the root of its polynomial, will also be its complex conjugate.
The resultant conjugate of,
⇒ 5 = -5
⇒ -4i = +4i
Therefore, the remaining zeros of Degree of f will be = -5 and 4i
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Solve ABC using diagram and the given measurement A=64 a=7.4
The measurements in the given triangle ABC are A=64°, B=26°,
C=90°, a=7.4, b=3.61, c=8.23
What is meant by an angle?An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are located in the plane where the rays are located. The meeting of two planes can also create an angle. These are referred to as dihedral angles. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can likewise be used to establish an angle between two intersecting curves.
Given,
In ΔABC, A=64°, a=7.4
From the figure we know that C=90°, as the given figure is a right triangle.
As we already know that,
Angles sum in a triangle=180°
A+B+C=180°
64°+B+90°=180°
B=180°-154°
B=26°
By using sine rule,
a/SinA =b/SinB=c/Sinc
7.4/Sin 64°=b/Sin 26°=c/ Sin 90°
b=7.4Sin26°/Sin 64°
b=3.61
c=7.4 Sin 90°/Sin 64°
c=8.23
Therefore, the measurements in the given ΔABC are A=64°, B=26°,
C=90°, a=7.4, b=3.61, c=8.23
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Is 8y-5xy=9 linear or nonlinear
Answer: The equation 8y-5xy=9 is nonlinear because it contains the product of the variables x and y. In general, an equation is linear if it can be written in the form ax + by = c, where a and b are constants and x and y are variables. Equations that cannot be written in this form are nonlinear.
Question 3
Evaluate g(x)=-3x+1, when x=10
Give a numerical answer.
If Ethan bowled 9 games at Lucky Strike, how much would he pay total?
The amount that he would pay in total will be $28.80.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, the cost to bowl is $3.20. Ethan bowled 9 games at Lucky Strike, the amount that he would pay in total will be:
= $3.20 × 9
= $28.80
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Complete question
The cost to bowl is $3.20. Ethan bowled 9 games at Lucky Strike, how much would he pay total?
explain the difference between arithmetic growth and exponential (geometric growth). would you recognize them if they were described in writing and/or by picture?
When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.
When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. An illustration of arithmetic growth is the ongoing elongation of roots. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.
The amounts added grow by a fixed rate of growth, expressed in percentages. Due to the fact that these remain constant while the amounts added rise, growth is then typically measured in doubling times.
Due to the fact that all populations of organisms have the potential to experience exponential growth, the concept of exponential growth is particularly intriguing in the field of population biology.
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Outback Outfitters sells recreational equipment. One of the company’s products, a small camp stove, sells for $50 per unit. Variable expenses are $32 per stove, and fixed expenses associated with the stove total $108,000 per month. Required: 1. What is the break-even point in unit sales and in dollar sales? 2. If the variable expenses per stove increase as a percentage of the selling price, will it result in a higher or a lower break-even point? Why? (Assume that the fixed expenses remain unchanged.) 3. At present, the company is selling 8,000 stoves per month. The sales manager is convinced that a 10% reduction in the selling price would result in a 25% increase in monthly sales of stoves. Prepare two contribution format income statements, one under present operating conditions, and one as operations would appear after the proposed changes. Show both total and per unit data on your statements. 4. Refer to the data in (3) above. How many stoves would have to be sold at the new selling price to attain a target profit of $35,000 per month?
The break-even point in unit sales for Outback Outfitters is 4,200 units.
What is the break-even analysis?= Fixed Cost/Contribution margin per unit
= $176,400/$42
= 4,200 units.
The break-even point in sales dollars for Outback Outfitters is $588,000.
= $176,400/30%
= $588,000
If the variable expenses per stove increase as a percentage of the selling price, it will result in a higher break-even point.
Two Contribution format income statements:
Current Proposed
Sales units 16,000 20,000
Sales revenue $2,240,000 $2,100,000
Variable cost $1,568,000 $1,960,000 ($98 x 20,000)
Contribution margin $672,000 $140,000
Fixed expenses 176,400 $176,400
Net income (loss) $495,600 ($36,400)
Sales units per month = 16,000
Selling price per unit = $105 ($140 x 1 - 10%)
New sales units per month = 20,000 (16,000 x 1.25)
Variable expenses per unit = $98
Contribution margin per unit = $7 ($105 - $98)
Contribution margin ratio = 6.67%
The number of stoves to be sold at the new selling price to attain a target profit of $80,000 per month is 36,629 units.
= ($176,400 + $80,000)/$7
=36,629 units.
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1. A tire has the specification 225/60R14. What is the sidewall of the tire in inches (1 inch = 25.4 mm)?
a. 9.3in b. 60in
c. 8.9 in
d. 5.3in
2. If the diameter of a tire is 25 inches, approximate what distance does the tire cover in 8 rotations?
a. 628in
b. 392in
c. 60 in
d. 225in
The distance that tire covered in 8 rotations with diameter 25 inches is 628in using circle circumference's formula .
What is circumference of circle ?
The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.
The formula is :
2πr where r is the radius of the circle.
We know that diameter = 2*radius.
Given diameter = 25 inches
So, the radius = 25/2 inches.
So, the circumference = 2*(22/7)*(25/2)
Circumference of circle = distance covered by tire in one rotation.
So, the distance covered in 8 rotations = 8 * circumference
= 8* 2*(22/7)*(25/2)
= 628.5 inches
≈ 628 in
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Becca's dog-walking business started with 1 dog. By the end of the first month , she was walking 2 additional dogs per month . The graph represents the situation . How many dogs was Becca walking by the end of the third month?
The graph shows that Becca walks five dogs at the end of the third month.
How many dogs are there in the third month?
We know that we can be able to read off the graph of an function that has been shown such as the one that we have in the image that has been attached to this answer.
We can see that the graph of the function agrees that Becca's dog-walking business started with 1 dog. By the end of the first month , she was walking 2 additional dogs per month . We would now read off the graph to know the number of dogs that he walks after three months.
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what is the circumference
The circumference is 12.56
according to wine-searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. wine scores range from to , with a score of indicating a great wine, indicating an outstanding wine, indicating a very good wine, indicating a good wine, indicating a mediocre wine, and below indicating that the wine is not recommended. random ratings of a pinot noir recently produced by a newly established vineyard in follow: excel file: data07-11.xlsx 87 91 86 82 72 91 60 77 80 79 83 96 a. develop a point estimate of mean wine score for this pinot noir (to decimals). 82.00 b. develop a point estimate of the standard deviation for wine scores received by this pinot noir (to decimals). 9.6389
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389.
Below table showing calculation of Point Estimate of Mean and Standard Deviation:
Score X-X’ (X-X’)^2
87 5 25
91 9 81
86 4 16
82 0 0
72 -10 100
91 9 81
60 -22 484
77 -5 25
80 -2 4
79 -3 9
83 1 1
96 14 196
984 1022
Mean(X’) = Total Score/n
n = Total number = 12
X’ = 984/12 = 82
Standard Deviation (σ) = √∑(X-X’)^2/(n-1)
σ = √1022/(12-1)
σ = √1022/ 11
σ = 9.6389
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389
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ecall that one of the ten parts of the definition of a vector space says that if is a vector space, then there exists a vector in such that for all in hceggg
This means that for any vector v in the vector space V, there is a vector 0 in V such that v + 0 = v.
This is known as the identity property, and it states that adding 0 to any vector in V does not change the original vector. The identity property is an essential part of the definition of a vector space.
In general, a vector space is a set of objects called vectors that can be added together and multiplied ("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field.
A vector space is a set V together with two operations that satisfy the eight axioms listed below.
Closure under addition. For all vectors u and v in V, the vector u + v is also in V.Closure under scalar multiplication. For all vectors u in V and all scalars c, the vector cu is also in V.Associativity of addition. For all vectors u, v, and w in V, (u + v) + w = u + (v + w).Commutativity of addition. For all vectors u and v in V, u + v = v + u.Existence of an additive identity. There exists a vector 0 in V such that for all vectors u in V, 0 + u = u + 0 = u.Existence of additive inverses. For every vector u in V, there exists a vector -u in V such that u + (-u) = (-u) + u = 0.Compatibility of scalar multiplication with field multiplication. For all vectors u and v in V and all scalars c and d, (c + d)u = cu + du and c(dv) = (cd)v.Compatibility of scalar multiplication with field addition. For all vectors u and v in V and all scalars c and d, c(u + v) = cu + cv.To learn more about vectors, visit:
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Claude wants to a long-lasting perfume. On his first attempt, Claude combined 5 millimeters of a substance containing 2% sandalwood with another substance containing 6% sandalwood to get a substance containing 5% sandalwood. how many millimeters of the substance containing 6% sandalwood must he use?
In linear equation, 15 millimeters of the substance containing 6% sandalwood must he use.
What is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
x = amount of second substance
x + 5 = amount of first and second substances combined.
(0.02)5 ml + (0.06)x ml = (0.05)(x+ 5)ml
0.1 ml + (0.06)x ml = (0.05)x ml + (0.25) ml
(0.06)x ml - (0.05)x ml = (0.25) ml - (0.10) ml
(0.01)x ml = (0.15) ml
x ml = 15 ml
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A ball is dropped from a height of 80 ft. The elasticity of this ball is such that it rebounds three-fourths of the distance it has fallen. How high does the ball rebound on the fifth bounce? Find a formula for how high the ball rebounds on the nth bounce.
Formula for how high the ball rebounds on the nth bounce is 80 (3/4)ⁿ ft and the rebound on 5th bounce is 14.24 ft.
It is given that the ball is dropped from 80 ft and it rebounds (3/4)th of the height it has fallen.
Firstly , using logic ,
The height reached by the ball on its 1st rebound = 80(3/4) = 60 ft
Similarly , calculating on it's 2nd rebound = 60(3/4) = 45 ft
and on 3rd rebound = 45(3/4) ft.
This forms a sequence , known as GP (Geometric Progression).
A Geometric Progression in mathematics, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Hence , here the first term : a = 60 ft
and common ratio is : r = 3/4
the general term for rebound on nth bounce
= 60 * (3/4)ⁿ⁻¹ = 80 (3/4)ⁿ ft
Using the above expression , the rebound on 5th bounce = 60 * (3/4)⁵ = 14.24 ft.
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|x+9|=|-x-9|
How do I solve this equation and graph it?
The value of x is :
x≤ -9 or x > -9
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
|x+9|=|-x-9|
Both the sides have absolute symbols, consider as below:
x+9 = -x-9
=> 2x = -9 - 9 = -18
=> 2x = -18
=> x= -9
This means, x≤ -9 or x > -9
For graph:
consider as below:
y = |x+9|
y = |-x-9|
graph them without absolute symbols
consider upper v shaped graph. ignore downward v shaped graph
By taking some random values for x and finding the corresponding y values, we get the ordered pairs in the form of (x,y).
By plotting and joining those points, we get the graph as shown in the attachment.
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Haylee selects 10 small businesses at random from her state's directory. Let BBBB be the number of businesses she selects that have websites What type of variable is B? Binomial Geometric Neither
From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.
What is binomial variable ?The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probabilitq=1-pq=1-p).
This distribution is used in probability theory and statistics.
A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution.
The popular binomial test of statistical significance is based on the binomial distribution.
A sample of size n drawn with replacement from is widely used to model the number of successes using the binomial distribution.
Hence, From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answer:
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LMNO is a parallelogram. If NM\ =\ x+32\ and\ OL=2x+22,\NM = x+32 and OL=2x+22, find the value of x and then find NM and OL
Answer:
the value of x is 10
Step-by-step explanation:
Since LMNO is a parallelogram, the opposite sides are parallel and have the same length. This means that NO and LM have the same length, which we can call y. We can write the following equations to represent the given information:
NM = x + 32
OL = 2x + 22
NO = y
LM = y
Since NO and LM have the same length, we can set their lengths equal to each other to find the value of y:
x + 32 = y
2x + 22 = y
We can solve this system of equations by setting the two equations equal to each other and solving for x:
x + 32 = 2x + 22
-x = -10
x = 10
Substituting the value of x back into the equations for NM and OL, we find that:
NM = 10 + 32 = 42
OL = 2(10) + 22 = 32
Therefore, the value of x is 10, and the lengths of NM and OL are 42 and 32.
A study of the ability of individuals to walk in a straight line reported the accompanying data on cadence (strides per second) for a sample of n = 20 randomly selected healthy men.
0.92 0.85 0.92 0.95 0.93 0.85 1.00 0.92 0.85 0.81 0.76 0.93 0.93 1.05 0.93 1.06 1.08 0.96 0.81 0.95
A normal probability plot gives substantial support to the assumption that the population distribution of cadence is approximately normal. A descriptive summary of the data from Minitab follows.
Variable N Mean Median TrMean StDev SEMean
cadence 20 0.9230 0.9300 0.9233 0.0848 0.0190
Variable Min Max Q1 Q3
cadence 0.7600 1.0800 0.8500 0.9550
(a) Calculate and interpret a 95% confidence interval for population mean cadence. (Round your answers to four decimal places.)
( ,) strides per second
Interpret this interval. Choose one from (1) ~ (3)
(1)With 95% confidence, the value of the true mean cadence of all such men falls below the confidence interval. (2)With 95% confidence, the value of the true mean cadence of all such men falls above the confidence interval. (3)With 95% confidence, the value of the true mean cadence of all such men falls inside the confidence interval.
(b) Calculate and interpret a 95% prediction interval for the cadence of a single individual randomly selected from this population. (Round your answers to four decimal places.)
( , ) strides per second
Interpret this interval. Choose one from (1) ~ (4)
(1)If this bound is calculated once, there is a 5% chance that these bounds will capture a future individual value of cadence for a healthy man.
(2)If this bound is calculated sample after sample, in the long run, 95% of these bounds will capture a future individual value of cadence for a healthy man.
(3)If this bound is calculated once, there is a 95% chance that these bounds will capture a future individual value of cadence for a healthy man.
(4)If this bound is calculated sample after sample, in the long run, 95% of these bounds will fail to capture a future individual value of cadence for a healthy man.
(c) Calculate an interval that includes at least 99% of the cadences in the population distribution using a confidence level of 95%. (Round your answers to four decimal places.)
( , )strides per second
Interpret this interval. Choose one from (1) ~ (4)
(1)We can be 99% confident that the interval includes at least 95% of the cadence values in the population.
(2)We can be 95% confident that the interval includes at least 99% of the cadence values in the population.
(3)We can be 1% confident that the interval includes at least 95% of the cadence values in the population.
(4)We can be 5% confident that the interval includes at least 99% of the cadence values in the population.
a) The confidence interval for the population is (0.901,0.963)
b)The prediction interval for the population is (0.779,1.085)
c)The interval level at 99% is (0.626,1.238).
Given,
Sample size, n=20
Mean = 0.923
Standard deviation = 0.0848
a)
To determine the confidence interval at 95% use formula,
[tex]\mu\pm t*\frac{S}{\sqrt{n}}[/tex]
Where,
[tex]\mu[/tex] = mean and S = standard deviation
t-value can be calculated from the t-table
df = n-1=20-1=19
and significance level = 1-0.95=0.05
From table, t-value is 1.728
substituting the values in formula,
[tex]=0.932\pm 1.728*\frac{0.0848}{\sqrt{20}}\\\\=0.932\pm 1.728*0.018\\\\=0.932\pm0.031\\\\=0.901,\ 0.963[/tex]
We can conclude that the true mean cadence, 0.9233, is within the confidence interval.
b)
To determine the prediction level at 95% confidence level use formula,
[tex]\mu\pm t*S\sqrt{1+\frac{1}{n}}\\\\=0.932\pm0.0848*1.728\sqrt{1+\frac{1}{20}}\\\\=0.932\pm 0.153\\\\=0.779,\ 1.085[/tex]
We can conclude that if the bounds are calculated all at once, there is a 5% chance that they will capture a future individual cadence value for a healthy man.
c)
A tolerance interval with k = 99, confidence level 95%, and n = 20 is requested. The tolerance critical value is 3.615, according to the table of "tolerance critical values for normal population distributions" in your text.The interval is [tex]0.932 \pm 3.615(.0848)=(0.626,\ 1.238)[/tex]
Thus, we conclude that 99% confident that the interval will include at least 95% of the cadence values in the population.
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Ms. Brooks has 2 pieces of ribbon to make wreaths. One piece is 18 yards long and the other is 17 yards long. Each wreath requires 5 yards of uncut ribbon. How many wreaths can Ms. Brooks make?
The number wreaths that Ms. Brooks make will be 7 wreaths.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
It should be noted that an expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features. People make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects
Here, Ms. Brooks has 2 pieces of ribbon to make wreaths. One piece is 18 yards long and the other is 17 yards long.
Since each wreath requires 5 yards of uncut ribbon, the number of wreaths that Ms. Brooks make will be:
= (18 + 17) / 5
= 35 / 5
= 7 wreaths.
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Please help me with this question
To derive the formula that goes through these two points, we use the general equation for an exponential equation.
Y = a(b)^x
There we will substitute the two points into this equation to get two equations
45 = a(b)^2
5/9= a(b)^-1
By dividing the first equation by the second, we obtain:
27 = b^3
Therefore b= 3
We plug b=3 into the first equation using the second point:
45 = a(3)^2
We get a = 5
Therefore the equation is y = 5(9)^x
We can verify this equation by plugging in the two points given to see if it works.
5/9 = 5(9)^-1
5/9 = 5/9
And:
45 =5(9)^2
45 = 45
It does, so the equation is correct.
The answer is y =5(9)^x
What is exponential equation?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.Exponential equations are equations in which variables occur as exponents.For example, exponential equations are in the form a x = b y .To solve exponential equations with same base, use the property of equality of exponential functions .To learn more about exponential equation refer to:
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stockholder's equity of $350,000 and net income of 59,400. Payout ratio of 20% and return on assets of 9%. How much was paid in cash dividends and what were its average total assets?
If stockholder's equity of $350,000 and net income of 59,400. Payout ratio of 20% and return on assets of 9%. The amount that paid in cash dividends is $11,880 and its average total assets is $660,000.
How to find the cash dividend and the average assets?a. Cash dividend:
Cash dividend = Net Income ×Dividend Payout Ratio
Cash dividend = $59,400 × 20%
Cash dividend = $11,880
b. Average Assets:
Average Assets = Net Income × Return on Assets
Average Assets = $59,400 / 9%
Average Assets = $660,000
Therefore the amount that paid in cash dividends is $11,880 and its average total assets is $660,000.
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2. How do you know from the equation that a line is vertical or horizontal?
Vertical lines have the form x = a, where a stands for the common x-coordinate of all points, while horizontal lines have the form y = b, where b denotes the y-intercept. Horizontal lines run left to right.
Explain about the equation?The link between two expressions on either side of the sign is represented by a mathematical equation. One variable and an equal sign are typically present. For instance, 2x – 4 = 2.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Expressions that equal one another are the building blocks of an equation. The equation 4x2+3x = 22. A formula is an equation that has at least two variables and depicts the relationship between them.
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15. Suppose an economy's marginal propensity to consume (MPC) is 0.6. Then, the multiplier must be
a. 1.96.
b. 3.
c. 1.67.
d. 2.5.
The investment multiplier must be 2.5 i.e.Option (d).
What is an Investment multiplier?
The amount by which the growth in output or income exceeds the increase in investment is referred to as the investment multiplier. It is represented by the letter "k" and is calculated as the ratio of changes in investment and income.
Multiplier(k) = Change in income / change in investment = 1/ {1-MPC}
where MPC is the marginal propensity to consume
Given, MPC = 0.6
Then, the multiplier(k) = 1/( 1 - 0.6) = 1/ 0.4 = 10/4 = 2.5 times
Hence, the investment multiplier is 2.5 i.e.Option (d).
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Nadine's Nursery sells St. Augustine grass seeds for $10 per lbs. and Zoysia grass seeds for $15 per lbs. Nancy wants to buy 20 ;bs. of grass seeds and wants to pay an average of $12 per lbs. How much of each type should she get?
The quantity of each type that Nadine should get would be= 96 of St. Augustine grass seeds and 144 of Zoysia grass seeds.
What is an average cost ?An average cost is defined as the total cost of production divided by the total number of units produced.
The cost of St. Augustine grass seeds per lbs = $10
The cost of Zoysia grass seeds per Ibs = $15
The quantity of seed Nadine wants to buy = 20
The average amount the Nadine want to pay per Ibs = $12
That is the total money available for the grass seeds = 20 × 12 = 240
To find the number of each grass seed she can buy the following is carried out;
10 + 15 = 25 ( Total cost for both grass seed)
The number of St. Augustine grass seeds she can buy ;
= 10/25 × 240
= 2400/25
= 96
The number of Zoysia grass seeds she can buy;
= 15/25 × 240
= 3600/25
= 144.
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In △XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ.
AC = 7, AB = 5, and XY = 24. What is the perimeter of △XYZ?
Enter your answer in the box.
The perimeter of triangle XYZ is calculated as: 48 units.
What is the Perimeter of a Triangle?The perimeter of a triangle is found by summing all the lengths of the three sides of the triangle.
Given the following measures as shown in the image below as:
AC = 7
AB = 5
XY = 24
The perimeter of triangle XYZ = XY + YZ + XZ
Based on the triangle midsegment theorem, we have:
YZ = 2(AC) = 2(7)
YZ = 14
XZ = 2(AB) = 2(5)
XZ = 10
Therefore:
The perimeter of triangle XYZ = 24 + 14 + 10
The perimeter of triangle XYZ = 48 units.
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O MEASUREMENT AND DATA
Introduction to the probability of an event
A spinner with 12 equally sized slices has 5 red slices, 3 blue slices, and 4 yellow slices. The dial is spun and stops on a slice at random. What is the probabili
that the dial stops on a slice that is not red?
Write your answer as a fraction in simplest form.
Explanation
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The probability that the dial stops on a yellow or blue slice will be 0.6667.
What is probability?
Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
A spinner with 12 similarly measured cuts has 5 yellow cuts, 3 blue cuts, and 4 red cuts. The dial is turned and stops on a cut indiscriminately.
The total number of the event is given as,
Total events = 5 + 3 + 4
Total events = 12
The probability that the dial stops on a yellow or blue slice will be given as,
P = 3 / 12 + 5 / 12
P = 0.25 + 0.4167
P = 0.6667
The probability that the dial stops on a yellow or blue slice will be 0.6667.
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(2-2i)(3+3i)
56 points ]
Answer:
12
Step-by-step explanation:
Answer : 12
Step-by-step explanation:
The method that i used here was FOIL
(2 - 2i)(3 + 3i)
2x3=6
2x3i=6i
-2ix3=-6i
-2ix3i=-6i^2
6 + 6i - 6i - 6i^2
6-6i^2
i^2 is also known as (-1)
6 - 6(-1)
6 + 6
= 12
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 9200(1.018)²
Answer:
growth
1.8%
Step-by-step explanation:
If the number raised to the power x is between 0 and 1, it is decay since as the exponent increases, the value of the power expression decreases.
For example, think of 0.1, a number between 0 and 1.
0.1^x
x = 1, 0.1^1 = 0.1
x = 2, 0.1^2 = 0.01
x = 3, 0.1^3 = 0.001
As you see, as x increases, the value of the expression decreases from 0.1 to 0.01 to 0.001
Now look at a power in which the base is greater than 1.
If the number raised to the power x is greater than 1, it is growth since as the exponent increases, the value of the power expression increases.
For example, look at 1.5^x
1.5^x
x = 1, 1.5^1 = 1.5
x = 2, 1.5^2 = 2.25
x = 3, 1.5^3 = 3.375
As you see, as x increases, the value of the expression increases from 1.5 to 2.25 to 3.375.
Now our problem:
y = 9200(1.018)^x
What base is raised to x?
Answer: 1.018
Since 1.018 is greater than 1, as the exponent, x, increases, the value of 1.018^x increases. Therefore, this is exponential growth.
1.018 = 1 + 0.018 = 1 + 1.8%
The percentage is 1.8%
One way to measure the amount of energy that a moving object (such as a car) possesses is by finding its Kinetic Energy. The Kinetic Energy (Ex, measured in Joules) of an object depends on the object's mass (m, 2Ek measured in kg) and velocity (v, measured in meters per second), and can be written as v = . m What is the kinetic Energy of an object with a mass of 1,700 kilograms that is traveling at 50 meters per second? Ek Joules The volume of a cone of sand moved by harvester ants given it's radius can be found with the following 3V formular = A mound of gravel is in the shape of a cone with the height equal to twice the radius. 2л Calculate the volume of such a mound of gravel whose radius is 4.92 ft. Use = 3.14. V = (round to the nearest whole number)
The body has a kinetic energy of 2125000 joules, and the gravel mold has a volume of 11.9 cubic units.
Given that,
The Kinetic Energy of an object depends on the object's and velocity , and can be written as v = m
Kinetic Energy of an object with a mass = 1,700 kilograms
Traveling = 50 meters per second
Radius = 4.92 ft
Kinetic energy, which may be seen in the movement of an item or subatomic particle, is the energy of motion. Kinetic energy is present in every particle and moving object. Examples of kinetic energy in action include a person walking, a baseball soaring through the air, a piece of food falling from a table, and a charged particle in an electric field.
Kinetic Energy of a body is given by ,
1/2 mv²
Where m = mass = 1700 kg
v = velocity = 50m/s
Therefore ,
KE = 1/2 * 1700kg * 50m/s
KE = 2125000 J.
Now to calculate the volume
Let's assume that the solution to the problem will be found using your formula. If so, let's carry out the following operations when solving for v in the equation:
On multiplying the equation by 2, the outcome is
2[tex]r^{2}[/tex]
=3[tex]\sqrt{3V}[/tex]
To find volume
enter (v=(2[tex]r^{2}[/tex])/33)
rationalize the right side of the equation's numerator.
v=(2π[tex]r^{2}[/tex] )
A simplified version of 3/333 is
v=(2[tex]r^{2}[/tex])3/9.
Substitute
v=(23.143.1523)/9
v=11.9.
Therefore,
The body has a kinetic energy of 2125000 joules, and the gravel mold has a volume of 11.9 cubic units.
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Heights are generally normally distributed. Men have a mean of 69.5 inches and standard deviation 2.4 inches. Women have
a mean of 63.8 inches and standard deviation 2.6 inches. The US Air Force has a height requirement for their pilots to be
between 64 inches and 77 inches.
Make sure you are rounding z-scores properly to two places.
Part A: Find the two z-scores for women who meet this height requirement z =
and z=
I
(larger value)
For Blank 1
Part B: Using the z-scores from part A, find the proportion of women who meet the height requirement. Give this answer as a
decimal.
Z=
(smaller value)
Part C: Find the two z-scores for men who meet this height requirement z =
(larger value)
Part D: Using the z-scores from part C, find the proportion of men who meet the height requirement. Give this answer as a
decimal.
QUESTION 2
(smaller value) and
Part E: If the height requirement were changed to exclude only the shortest 1% of women and tallest 1% of men, what are the
new heights? The short value would be
in inches and the tall value would be
in inches. Please give these two values rounded properly to one decimal place.
Normal distribution curve is symmetric around the mean, it shows that values close to the mean happen more frequently than those distant from the mean.
What is meant by normal distribution curve?A bell-shaped (symmetric) curve, the normal probability distribution or the normal curve. The mean of it is represented by and the standard deviation by σ.
In this example, the mean and median are both equal and lie in the center of the distribution; they are 64, and the standard deviation is 7, with 68% of the values falling within the first standard deviation, 95% within the second standard deviation, and 99.7% within the third. Once more, variance is equal to the standard deviation squared.
According to the normal distribution curve:
"the percent of women whose heights are between 64 and 69.5 inches" represents the values within 2 standard deviation.
Area from a value (Use to compute p from Z)
Value from an area (Use to compute Z for confidence intervals)
Let the parameters be
Mean 64
Standard deviation 2.75
Above 1.96
Below 1.96
Between 64 and 69.5
Outside -1.96 and 1.96
Area (probability) 0.4772
And that value is 95 % of the whole data
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