The most appropriate choice for combination will be given by-
Models can wear 112 different types of outfit.
What is combination?
Combination determines the number of ways of selecting some number of particular items from a group of given item, here the order of selection do not matter.
If there are n objects and from there, r objects are chosen, number of ways will be given by
[tex]n \choose r[/tex] = [tex]\frac{n!}{(n - r)! \times r!}[/tex]
Here,
Number of tops = 7
Number of pants = 2
Number of jackets = 8
From 7 tops the designer can choose 1 top in [tex]7 \choose 1[/tex] ways
= [tex]\frac{7!}{(7-1)!\times 1 !}[/tex]
= [tex]\frac{7!}{6!}[/tex]
= [tex]7[/tex]
From 2 pants the designer can choose 1 pant in [tex]2 \choose 1[/tex] ways
= [tex]\frac{2!}{(2-1)!\times 1 !}[/tex]
= [tex]\frac{2!}{1!}[/tex]
= [tex]2[/tex]
From 8 jackets the designer can choose 1 jacket in [tex]8 \choose 1[/tex] ways
= [tex]\frac{8!}{(8-1)!\times 1 !}[/tex]
= [tex]\frac{8!}{7!}[/tex]
= [tex]8[/tex]
Total number of different outfits models can wear = [tex]7 \times 2 \times 8[/tex]
= 112
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If the product of the extremes is 8,then the geometric mean is..
A. 2
B. 4
C. 2/2
Answer: THE ANSWER TO THAT IS C
Step-by-step explanation:
what is the solution to the equation below? (round your answer to two decimal places.) 6•inx=9.1
ANSWER
B. x = 4.56
EXPLANATION
To solve this equation, first, we have to divide both sides by 6,
[tex]\begin{gathered} \frac{6\cdot\ln x}{6}=\frac{9.1}{6} \\ \\ \ln x=\frac{9.1}{6} \end{gathered}[/tex]Then apply the base exponent rule of logarithms,
[tex]a^{\log_ab}=b[/tex]So, in this case, we have to raise e to each side of the equation,
[tex]\begin{gathered} e^{\ln x}=e^{9.1/6} \\ \\ x\approx4.56 \end{gathered}[/tex]Hence, the solution is x = 4.56, rounded to two decimal places.
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How many squares will it take to fill up the large empty square?
A. 5
B. 10
C. 25
D. 50
Roland's farm land is assessed at 1.5 million dollars and the improvements for $500,000.
At a tax rate of 4 mills, how much are Rolan's monthly taxes?
At a tax rate of 4 mills, Rolan's monthly taxes are $667.00.
What is the mill rate?The amount of tax due per $1 of a property's assessed value is known as the mill rate. The word mill comes from the Latin millesimum, which means thousandth. In terms of property tax, 1 mill is the amount of property tax levied per $1,000 of the assessed value of a property. Divide the mill rate by 1,000 and multiply the assessed value of the property to determine the property tax.Given:
Assessed value = 1.5 million dollars
Amount for Improvements = $500,000
Tax rate = 4 mills
Total assessment of the property = Assessed value + Improvements
= 1,500,000 + 500,000
= $2,000,000
Multiply these 2 million by 4 mills then divide by 1000.
(2,000,000 × 4)/1000
= $8000 in annual taxes
To calculate the monthly tax amount divide by 12.
$8000/12 = $667.00
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Solve the following proportion for y.y/5 = 7/8Round your answer to the nearest tenth.
The given proportion is expressed as
y/5 = 7/8
If we crossmultiply, it becomes
y * 8 = 7 * 5
8y = 35
y = 35/8
y = 4.375
Rounding to the nearest tenth,
y = 4.4
Use the fact that
5x2 − y2 = c
is a one-parameter family of solutions of the differential equation
y
dy
dx
= 5x
to find an implicit solution of the initial-value problem
y
dy
dx
= 5x, y(3) = −8.
The required implicit solution to the initial-value problem would be 5x²- y² = 9.5 which is the equation of a hyperbola.
What is the hyperbola?Hyperbola is defined as a conic section, a two-branched open curve, produced by the intersection of a circular cone.
(x-h)²/b² - (y-k)²/a² = 1
We have been given that 5x²- y² = c is a one-parameter family of solutions of the differential equation.
To determine an implicit solution to the initial-value problem ydy/dx = 5x
⇒ y dy/dx = 5x
⇒ y dy = 5x dx
⇒ y²/2 = 5x²/2 + c
If y(3) = −8 which is the means that when substitute x = 3 then y = -8
⇒ (-8)²/2 = 5(3)²/2 + c
⇒ 64/2 = 5(9)/2 + c
⇒ 32 = 22.5 + c
⇒ c = 9.5
Substitute the value of c in the given function 5x²- y² = c
⇒ 5x²- y² = 9.5 which is the equation of a hyperbola.
Therefore, the implicit solution to the initial-value problem would be 5x²- y² = 9.5.
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A center pivot irrigation system provides water to a sector shaped field, find the area of the field if 0=140 degrees and r= 40 yd
The area of the sector is approximately 1954.77 square yards.
A circular sector, also known as a circle sector or a disc sector (symbol:), is a piece of a disc (a closed region bordered by a circle) encompassed by two radii and an arc. The smaller area is known as the minor sector, and the bigger is known as the major sector.
Any point on the circle outside of the sector can be connected to the arc's endpoints to produce half of the central angle.
We know that the area of a circle is πr² and the area of the sector of a circle with angle θ is given by θ/360 πr² .
Area of the sector
= 140°/360° × π × 40²
= 1954.7687... square yards.
≈ 1954.77 square yards.
Therefore the area of the sector is approximately 1452.113 square yards.
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Identify the independent and dependent variables
the amount of gasoline in a car's fuel tank and the amount of time spent driving
Answer:
The independent variable is the time spent drive and the dependent variable with the amount of gas in the tank
Step-by-step explanation:
Does the gas in the tank depend on the time driving or does the time driving depend on the amount of gas in the car.
The amount of gas is the tank is determined by how much time the car is driven.
What is 8 1/3 times 6 2/5
Answer:53.312
Step-by-step explanation: 8.33 x 6.40
-Describe the expression.Suvolino bolo2 * 5+7(3 + 13)+Which of the following describes(7 in the expression above?A. factor(B, sumC. quotientD. product
Answer
A. factor
Explanation
The given expression is 2 x 5 + 7(3 + 13)
In the expression given, '7' represents a factor because after adding 3 and 13, you would need to multiply it by 7.
Hence, the correct option is:
A. factor
John ordered a large three topping pizza for $7.50 and a large 8 topping pizza for $10. Write an equation in slope intercept form to describe the situation.
Explanation
Step 1
[tex]\begin{gathered} \text{large pizza(3 toppings)}\rightarrow7.5 \\ \text{large pizza( }8\text{ toppings)}\rightarrow10 \\ \text{then we have 2 points of the line} \\ (3,7.5) \\ (8,10) \end{gathered}[/tex]Step 2
find the slope
the slope is given by:
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1(3,7.5)
P2(8,10)
replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{10-7.5}{8-3}=\frac{2.5}{5}=0.5 \\ \text{slope}=0.5 \end{gathered}[/tex]Step 3
usin P1 (3,7.5) ans m= 0.5 find the equation
[tex]\begin{gathered} y-y_1=m(x-x_0) \\ \text{replace} \\ y-7.5=0.5(x-3) \\ y-7.5=0.5x-1.5 \\ y=0.5x-1.5+7.5 \\ y=0.5x+6 \end{gathered}[/tex]I hope this helps you
Classify each polynomial by degree and number of terms 1. X^3 + 5x 2. X^2 - 2x - 1 3. 5x^4 4. 6x^5 - 3x^2 + 7x + 9 5. -11x - 5 6. 4x^2 + 10THESE ARE THE OPTIONS Degree Name using degree 0 Constant1 Linear2 quadratic3 Cubic4 quartic5 quintic6 6th degree
1)
[tex]\begin{gathered} x^3\text{ + 5x} \\ \text{cubic , 2 terms} \end{gathered}[/tex]2) The term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree
[tex]\begin{gathered} x^2-2x-1 \\ \text{quadratic, 3 terms} \end{gathered}[/tex]3) of or relating to the fourth degree. a quartic polynomial or equation.
[tex]\begin{gathered} 5x^4 \\ \text{quartic, 1 term} \end{gathered}[/tex]4) quintic : a polynomial or a polynomial equation of the fifth degree.
[tex]\begin{gathered} 6x^5-3x^2\text{ + 7x + 9} \\ qu\text{intic , 4 terms} \end{gathered}[/tex]5)
[tex]\begin{gathered} =11x\text{ - 5} \\ L\text{inear , 2 terms} \end{gathered}[/tex]6)
[tex]\begin{gathered} 4x^2\text{ + 20} \\ \text{quadratic, 2 terms} \end{gathered}[/tex]The mean output of a certain type of amplifier is 129 watts with a variance of 100.
If 96 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 0.9 watts? Round your answer to four decimal places.
The probability is given by -0.001, that the mean of the sample would differ from the population mean by less than 0.9 watts.
What is normal probability distribution?
Normal distribution also known as the Gaussian probability, ia a probability distribution that is symmetric about the mean, showing that data bear the mean are more frequent in occurrence than data far from the mean.
In a set with mean μ and standard deviation (which is the square root of the variance) σ , the z score of a measure X is given by:
Z =X-μ/σ
we have given μ =129
σ = [tex]\sqrt{100}[/tex] n = 96
This is the pvalue of Z when X = 129+1.7 =130.7 subtracted by the pvalue of Z when X = 129 - 1.7 = 127.3
When X = 130.7
Z =X-μ/σ
Z = 130.7-129/10
Z = 0.17 pvalue = 0.1699
When X = 127.3
Z =X-μ/σ
Z = 127.3-129/10
=-0.17 pvalue
0.1699 - 0.1700 = -0.001
Hence the probability is -0.001
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3b(u - 8) - n(u – 8) =
Answer:
3bu - 24b -nu + 8n
Step-by-step explanation:
Expanded
write a quadratic equation that opens down and has vertex at (2,-8)
The quadratic equation that opens down and has vertex at (2,-8) is y = (-|a|)*(x - 2)² + (-8).
The graph of a quadratic function has the shape of a parabola. Although a parabola's "width" or "steepness" and direction of opening can differ, they all have the same basic "U" shape. If the leading coefficient is larger than zero, the parabola opens upward; if it is less than zero, it opens downward.
The quadratic equation's vertex form is y = a*(x - h)2 + k.
Given that (2,-8) or (h, k) is the vertex point (2,-8)
Since the graph starts out downward, a will have a negative value.
Since |a| is the magnitude of a, the quadratic equation will then be written as y = (-|a|)*(x - 2)2 + (-8).
Consequently, y = (-|a|)*(x - 2)2 + is a quadratic equation that opens downward and has a vertex at (2,-8). (-8).
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Find the unknown angle for the following right triangle:
Angle A Angle B Angle C
? 29 27°
The unknown angle for the given right triangle ABC which is angle A is: 63°
What is the angle in the right angle triangle?We are given the angles of a right angle triangle ABC as;
∠B = 90°
∠C = 27°
Now, it is pertinent to note that the sum of all angles in any given triangle is always 180°. This means that in our right angle triangle ABC, we can say that;
∠A + ∠B + ∠C = 180°
Thus;
∠A + 90 + 27 = 180
∠A + 117 = 180
∠A = 180 - 117
∠A = 63°
Thus, we conclude that the value of angle A is gotten as ∠A = 63°
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Complete question is;
Find the unknown angle for the following right triangle:
Angle A Angle B Angle C
? 90 27
Ms. U.S. Bonds invested a total of $4500, some at 9% per year and the rest at 6% per year. The return for the 9% investment exceeds that from the 6% investment by $180. How much did she Invest at each rate
Using simple interest, the amounts she invested are given as follows:
$3,000 at 9%.$1,500 at 6%.Simple InterestSimple interest is used when there is a single compounding per time period, usually measured in years.
The amount of money after t periods in is modeled by:
A(t) = P(1 + rt)
The interest accrued after t periods is modeled by:
I(t) = Prt
In which:
P is the initial amount.r is the interest rate, as a decimal.She had two investments, investing a total of $4500, hence:
[tex]P_1 + P_2 = 4500[/tex]
The return for the 9% investment exceeds that from the 6% investment by $180, hence:
[tex]I_2 = 0.06(4500 - P_1)[/tex][tex]I_1 = 0.09P_1[/tex][tex]I_2 = I_1 - 180[/tex]Then:
[tex]I_2 = 0.06(4500 - P_1)[/tex]
[tex]I_1 - 180 = 0.06(4500 - P_1)[/tex]
[tex]0.09P_1 - 180 = 0.06(4500 - P_1)[/tex]
[tex]0.15P_1 = 450[/tex]
[tex]P_1 = \frac{450}{0.15}[/tex]
[tex]P_1 = 3000[/tex]
Which is the amount invested at 9%, hence the amount invested at 6%, considering that a total of $4,500 was invested, is given by:
4500 - 3000 = $1,500.
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Factor completely the trinomial 10x^2 + 19x + 7
From the problem :
[tex]10x^2+19x+7[/tex]Factor completely :
We need to find the factors of 10 and 7
We have :
10 = 1 x 10
10 = 2 x 5
7 = 1 x 7
We will do trial and error, The sum of the product of the factors must be equal to the middle term which is 19
Let's say for 10 = 1 x 10 and 7 = 1 x 7
(1 x 7) + (1 x 10) = 17 not equal to 19
(7 x 10) + (1 x 1) = 71 not equal to 19
try the other factors of 10.
10 = 2 x 5 and 7 = 1 x 7
(2 x 7) + (5 x 1) = 19 Equal to 19
Now we have the factors, let's arrange in this way :
[tex](O+I)(I+O)[/tex]O will be the outer and I will be the inner.
O is the paired factors of 10 and 7
For O, we have 2 and 7
For I, we have 5 and 1
This will be :
[tex](2x+5)(x+7)[/tex]The answer is (2x + 5)(x + 7)
Help please this one is tricky
B; False
Here, we want to establish if there is a relationship between two variables
From the question, it was stated that at higher speeds, the ticket fee to be paid will be higher
So, what this mean is that the amount of ticket fee to be paid is a factor of the speed at which she was traveling
This directly makes the speed the independent variable while the ticket fee (value depends on the speed of travel) represents the dependent variable
Hence, we can establish that that the ticekt fee is a function of the speed and not the other way round
This makes the correct option FALSE
Plea helpppppp asap, Ik This is easy for you guys but yeah I’m just stupiad
Answer:
Figure 3
Step-by-step explanation:
That is a trapezoid, not a parallelogram.
Jan made a mixed vegetable soup using tomatoes and carrots. Forty percent of the
tomatoes. If she used a total of 50 tomatoes, how many carrots should she use?
Jan should use 75 carrots for mixed vegetable soup.
Let us assume the total number of tomatoes and carrots be x. So, as per the mentioned information, the equation will be -
40%×x = 50
Converting percentage to fraction
40/100×x = 50
x = 50×100/40
Cancelling zero and performing division
x = 5×25
Performing multiplication
x = 125
Total number of vegetables = number of tomatoes + number of carrots
125 = 50 + Number of carrots
Number of carrots = 125 - 50
Performing subtraction
Number of carrots = 75
Therefore, Jan should use 75 carrots.
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The complete question is -
Jan made a mixed vegetable soup using tomatoes and carrots. Forty percent of the mixed vegetables were tomatoes. If she used a total of 50 tomatoes, how many carrots should she use?
Answer:
Step-by-step explanation:
75 carrots should be used
A triangle has side lengths of (5k-3) centimeters, (k+1) centimeters, and (m-7) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
The expression for the perimeter of the triangle is 6k + m -9.
How to calculate perimeter of the triangle?
In mathematics, the perimeter of any closed shape means addition of all the sides. Therefore, triangle has three sides and their addition represents the perimeter. It can be measured in different units like meters, centimeters, etc.
According to the question, the given parameters for the triangle is as written below:
The side lengths are: (5k - 3); (k + 1) and (m - 7)
Now, the perimeter of a triangle is addition of all the sides. That means,
Perimeter of a triangle = 5k - 3 + k + 1 + m - 7 = 6k + m - 9
Hence, the expression for the perimeter of the triangle is 6k + m -9.
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A recipe for 2 dozen whole-wheat requires 600g of flour. How many muffins can be made with 900g of flour?
when we have a proportion it is defined as
[tex]\frac{a}{b}=k\cdot\frac{c}{d}[/tex]what this means is that we have a constant of proportionality which means that is the same term
[tex]\frac{8}{9}=\frac{16}{17}[/tex]there is not a proportion between both sides menaning that the expression is false.
A line has a slope of 8 and passes through the point (0,5). What is its equation inslope-intercept form?Write your answer using integers, proper fractions, and improper fractions in simplest form.
The form of the equation of the line in slope-intercept form
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept
The y-intercept is the value of the y-coordinate when the x-coordinate is equal to zero
Therefore in our case
m=8
b=5
We substitute the values
[tex]y=8x+5[/tex]ANSWER
y=8x+5
Decrease £50 by 60%
need help asap!! imma be posting a lot
When £50 is decreased by 60%, the remaining value is £20.
What is a percentage?A percentage refers to the ratio of a variable expressed as a fraction of 100.
Percentages show the proportional value contained in another.
We use the percent sign (%) to denote percentages, which may be increases or decreases.
Initial value = £50
Percentage decrease = 60%
Percentage change = 40% (1 - 60%)
In monetary terms, the final value after the percentage decrease = £20 (£50 x (1 - 60%).
Thus, when £50 is reduced by 60% the value left is only 40% of the former deal, which is £20.
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Add 7 3/10 simlify the answer and write it as a mixed number ?17/3011 7/2511 7/3011 17/30
To add mixed numbers first, we can add the whole numbers:
[tex]7+4=11[/tex]Now, we can add the fractions. For this, we can find the lowest common denominator (LCD) of both denominators. The LCD is the lowest number that is evenly divisible by both numbers. Since the denominators of the fractions are 10 and 15, the LCD is 30 because 30 is the smallest number that is divisible by 10 and 15. Then, we have:
[tex]\begin{gathered} \frac{3}{10}+\frac{4}{15}=\frac{3\cdot3}{10\cdot3}+\frac{4\cdot2}{15\cdot2} \\ \frac{3}{10}+\frac{4}{15}=\frac{9}{30}+\frac{8}{30} \\ \frac{3}{10}+\frac{4}{15}=\frac{9+8}{30} \\ \frac{3}{10}+\frac{4}{15}=\frac{17}{30} \end{gathered}[/tex]Therefore, the result of adding the given mixed numbers is:
[tex]$$\boldsymbol{7\frac{3}{10}+4\frac{4}{15}=11\frac{17}{30}}$$[/tex]A packet of carrot seeds has a germination rate of 92%. In other words, the probability of any
seed sprouting is 0.92. How many seedlings would you expect in a row of 50 seeds?
The number of constructive seedlings in a row of 50 seeds is 46.
What is probability of a given event and how can it be analyzed?
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability generally refers to the degree to which something is likely to occur. Utilize probability to ascertain how likely something is to occur. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty. Every event's probability in a sample space is one.
Given, the germination rate of the seeds to seedlings is = 92%
Therefore, the probability of any seed sprouting is 0.92.
Hence the required number of seedlings can be expected in a row of 50 seeds = 50*0.92 = 46 seeds
Thus, the number of constructive seedlings in a row of 50 seeds is 46.
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What is this number in standard form?
(5 × 1, 000) + (7 × 10) + (8 × 1) + (4 × ) + (1 × 1.000)
16,518
(or 1.6518 x 10⁴)
PLEASE PLEASE PLEASE!!!!!!!!!!HELP HELP HELP HELP HELP HELP!!!! IM CRYING IM STUCK
Answer:
[tex]y=\begin{cases}-\dfrac{7}{2}x-16&\text{for $-6\le x\le-4$}\\\\\dfrac{1}{5}x-\dfrac{6}{5}&\text{for $-4 < x < 1$}\\\\\dfrac{9}{4}x-\dfrac{13}{4}&\text{for $1\le x\le 5$}}\end{cases}[/tex]
Step-by-step explanation:
You want the piecewise function that describes the relation shown in the graph.
RelationThe relation shown consists of three line segments connecting the points ...
(-6, 5) and (-4, -2)
(-4, -2) and (1, -1)
(1, -1) and (5, 8)
LinesThe equations for the lines between the pairs of points can be written using the slope formula and the point-slope equation of a line.
The slope formula tells you the slope is ...
m = (y2 -y1)/(x2 -x1)
And the point-slope equation of a line is ...
y -y1 = m(x -x1)
If we add y1 to the equation of the line, and substitute the equation for m, we get ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . . . . . a 2-point formula for a line
ApplicationBetween x-values -6 and -4, the equation of the line will use the first pair of points:
y = (-2 -5)/(-4 -(-6))(x -(-6)) +5
y = -7/2(x +6) +5 = -7/2x -16
Between x-values -4 and 1, the equation of the line will use the second pair of points:
y = (-1-(-2))/(1 -(-4))(x -(-4)) +(-2)
y = 1/5(x +4) -2 = 1/5x -6/5
Between x-values 1 and 5, the equation of the line will use the last pair of points:
y = (8 -(-1))/(5 -1)(x -1) +(-1)
y = 9/4(x -1) -1 = 9/4x -13/4
Piecewise functionThe piecewise function uses the equation for the line that is applicable for the appropriate x-values. We have listed those sets of x-values above.
We need to make sure that the function has only one definition for any given value of x. When two segments have a point in common, we need to make sure only one segment includes it.
[tex]y=\begin{cases}-\dfrac{7}{2}x-16&\text{for $-6\le x\le-4$}\\\\\dfrac{1}{5}x-\dfrac{6}{5}&\text{for $-4 < x < 1$}\\\\\dfrac{9}{4}x-\dfrac{13}{4}&\text{for $1\le x\le 5$}}\end{cases}[/tex]
How to do because I dont know need help ASAP 20 points
Some arithmetic sequences could be easier to write as functions. As long as I know what value "n" has, I can find out any term in a particular Sequence whenever I need to. You might choose the implicit term over the prior term of a Sequence if it is known.
What is meant by Arithmetic Sequences?The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values.
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Some arithmetic sequences could be easier to write as functions. You are aware of the prior term.
Consider that we only have the numbers (...,4,...) from an arithmetic sequence with a common difference of 5.
The complete question is:
You are given the first four terms of an arithmetic sequence. Under what conditions might a recursive formula be preferred over the explicit formula? Under what conditions might an explicit formula be preferred over the recursive formula?
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