Casey is going to wear a gray sportscoat and is trying to decide what tie he should wear to work. In his​ closet, he has 29 ​ties, 15 of which he feels go well with the sport coat. If Casey selects one tie at​ random, determine the probability and the odds of the tie going well or not going well with the sport coat.

Answer:

{-3, √3, -√3, 13/3}

Step-by-step explanation:

Since the polynomial has rational coefficients, any irrational zeros must come in conjugate pairs. So, if √3 is a zero, then so is its conjugate, -√3.

We can write the polynomial with these zeros as:

p(x) = a(x + 3)(x - √3)(x + √3)(x - 13/3)

where a is some constant coefficient. Multiplying out the factors, we get:

p(x) = a(x + 3)(x^2 - 3)(x - 13/3)

To find the remaining zeros, we need to solve for x in the expression p(x) = 0. So we set up the equation:

a(x + 3)(x^2 - 3)(x - 13/3) = 0

This equation is true when any of the factors is equal to zero. We already know three of the zeros, so we need to solve for the fourth:

(x + 3)(x^2 - 3)(x - 13/3) = 0

Expanding the quadratic factor, we get:

(x + 3)(x - √3)(x + √3)(x - 13/3) = 0

Canceling out the (x - √3) and (x + √3) factors, we get:

(x + 3)(x - 13/3) = 0

Solving for x, we get:

x = -3 or x = 13/3

Therefore, the other zeros are -3 and 13/3.

The complete set of zeros is {-3, √3, -√3, 13/3}.

Hope it helps^^

the limit expression gives the value of the derivative of a function at a specific point. where f'(x_0) denotes the derivative of f(x) at x = x_0.

what is derivative  ?

The derivative of a function is a measure of how the function changes as its input variable changes. It gives the instantaneous rate of change or slope of the tangent line of the function at a specific point.

In the given question,

The expression you provided represents the limit definition of the derivative of a function f(x) at the point x = x_0. The limit evaluates the instantaneous rate of change or slope of the tangent line of the function f(x) at the point x = x_0.

To evaluate the limit, substitute x = x_0 + h in the expression of the function f(x) and simplify:

[tex]lim h - > 0 [f(x_{0} + h) - f(x_{0})] / h = f'(x_{0})[/tex]

where f'(x_0) denotes the derivative of f(x) at x = x_0.

Therefore, the limit expression gives the value of the derivative of a function at a specific point.

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The value of,

Given function f(x) = cx for 1 ≤ x ≤ 2

a) To find the value of constant x, we have to use the following p.d.f condition as shown below,

[tex]\int\limits^a_b {x} \, dx =1[/tex]

here, a is -∞ and b is ∞.

From the above condition to find the value of c,

[tex]\int\limits^2_1{cx^2} \, dx[/tex] = 1

c * [[tex]\frac{x^3}{3}[/tex]]²₁ = 1

c * [8/3 - 1/3] = 1

c * 7/3 = 1

c = 3/7.

b) To find the value of P(x>3/2) we have to substitute the value of 3/2 in the given expression of f(x) = 3/7 * x²

f(3/2) = 3/7 * (3/2)²

         = 3/7 * 9/4

         = 27/28.

From the above solution, we solved both problems.

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Answer: 14.5 kg

Step-by-step explanation:

Answer:

y=14

Concept Used:

Slope of a line:  [tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where (x1,y1) and (x2,y2) are passing points

Step-by-step explanation:

On substitution:

[tex]4 = \frac{y-(-10)}{2-(-4)}[/tex]

Solving for y:

y = 14

Answer: 8.25

Step-by-step explanation:

The information provided by each of the graphs is Sales from July to December and graph A best represents the data

From the question, we have the following parameters that can be used in our computation:

The graphs

On the graphs, we have the information to be

Sales from July to December

The graph that is the best representation of the data is the A

This is because the scale and origin of the graph are defined

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The correct answer is C: (-0.3,0) and (1.8,0) are zeros of the quadratic function because they are the points where the parabola intersects the x-axis.

The right response is C: (- 0.3,0) and (1.8,0) are zeros of as far as possible since they are the places where the parabola meets the x-turn.

plot the y-get at (0,1),

x = - b/2a

To find the x-heading of the vertex, which is x = 3/4. Substitute this worth into the capacity to find the y-course of the vertex, which is

f(3/4) = 1/8.

Plot the vertex at (3/4, 1/8).

Then, utilize this data to plot the remainder of the parabola. The zeros are the places where the parabola crosses the x-focus, which are close (- 0.3,0) and (1.8,0) obviously following changing in accordance with the closest 10th.

To track down the zeros of the quadratic capacity by illustrating, one ought to at first plot the y-get at (0,1) and a brief time frame later utilize the vertex condition to track down the headings of the vertex. Following plotting the vertex, the remainder of the parabola can be drawn. The zeros of the capacity are the x-gets, which can be found by finding the places where the parabola combines the x-turn. For this current situation, the zeros are close (- 0.3, 0) and (1.8, 0) resulting to adjusting to the closest 10th.

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Answer:

To solve for z in terms of x and y using the given equations:

x + y = z ........(1)

y - z = x ........(2)

From equation (2), we get:

y - x = z (by adding z on both sides)

Substituting this value of z in equation (1), we get:

x + y = y - x

2x = 0

x = 0

Substituting x = 0 in equation (2), we get:

y - z = 0

y = z

Therefore, the solution is:

z = y

We cannot determine a specific value of z without knowing the values of x and y.

Answer: 4.8 Inches

Step-by-step explanation:

6 is 60% of 10

Therefore  (60%*8 = 4.8)

*since they are similar, and therefore proportional

if a student scored a 69 on his first test, predict that his score on the second test will be approximately 64.57.

Students’ test scores on the first two tests in an introductory calculus class.

To make a prediction for the student's score on the second test based on their score of 69 on the first test, we need to find the regression equation for the data set.

The regression equation for these data is

y = 0.6443x + 19.943

Where y is the predicted score on the second test and x is the actual score on the first test.

Substituting x = 69 into this equation, we get

y = 0.6443(69) + 19.943 ≈ 64.57

Therefore, if a student scored a 69 on his first test, we predict that his score on the second test will be approximately 64.57.

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The probability that ten hats given to ten people will consist of more blue caps than red caps is given as follows:

a. 0.2.

Here, we have to calculate a probability:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes in which there are more blue than red caps are those in which the number of zeros is greater than the number of ones, hence the number of desired outcomes is of:

2. (simulation number 7 and simulation number 10).

Hence the probability is of:

p = 2/10

p = 0.2.

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Answer:

Step-by-step explanation:

The common difference between the number of jumping jacks is 50, as you correctly stated. This means that the number of jumping jacks increases by 50 for each additional minute.

The slope of the line that connects any two points on this table represents the rate of change of the number of jumping jacks with respect to time. Since the common difference is constant, the slope of the line that connects any two points on this table will be the same. In this case, the slope is 50.

The slope of the line that connects the first and fourth points is calculated as (200 - 50) / (4 - 1) = 150 / 3 = 50, not 150.

The common difference (aka slope aka rate of change) is constant because the number of jumping jacks increases by the same amount for each additional minute. This means that the relationship between time and the number of jumping jacks is linear.

The two roots of the quadratic equation x² - 5x + 3 = 0 are (5 + √13) / 2 and (5 - √13) / 2.

To find the roots of the quadratic equation x² - 5x + 3 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Substituting the values of a, b, and c from the given equation, we have:

x = (-(-5) ± √((-5)² - 4(1)(3))) / 2(1)

x = (5 ± √(25 - 12)) / 2

x = (5 ± √13) / 2

Therefore, the roots of the equation are (5 + √13) / 2 and (5 - √13) / 2.

To verify that these are indeed the roots of the equation, we can substitute each of these values for x in the original equation and check if the equation is satisfied. For example, if we substitute (5 + √13) / 2 for x, we get:

(5 + √13)² - 5(5 + √13) + 3 = 0

Simplifying this equation, we get:

13 - 5√13 + 8 + 13 - 5√13 + 3 = 0

This equation is true, which means that (5 + √13) / 2 is a root of the equation x² - 5x + 3 = 0. Similarly, we can verify that (5 - √13) / 2 is also a root of the equation.

These roots can be found using the quadratic formula, which is a useful tool for solving quadratic equations.

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The probability that the water will run out on a given day is  0.0038.

To find the probability that the demand for water on a given day exceeds the supply of 380 million gallons, we use the standard normal distribution to standardize the value of 380 million gallons as follows:

where;

x = of 380 million gallons,

µ is the mean daily demand of water = 300 million gallons,

σ is the standard deviation = 30 million gallons.

Substituting the given values:

z = (380 - 300) / 30

z = 2.67

Using a calculator, the probability that a standard normal random variable is greater than 2.67 is 0.0038.

Therefore, the probability that the water will run out on a given day is  0.0038.

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Answer:

All of them have a combined of 2,227 Stamps

Mean: 2014

After considering all the given data and running a series of calculation we reach the conclusion that the probability of receiving both orders as the same colors is 0.2184, under the condition that a company has the information that 32% of their customers order their product in Black and 26% in White and 22% in Grey.

Then the evaluated probability of both orders being the same color can be found by applying summation of the probability of both orders being black, both orders being white, and both orders being grey.

Now, the probability of both orders being black is 0.32 × 0.32
= 0.1024.

Similarly the probability of both orders being white is 0.26 × 0.26
= 0.0676.

Lastly, the probability of both orders being grey is 0.22 × 0.22
= 0.0484.

Hence, the evaluated probability of both orders being the same color is 0.1024 + 0.0676 + 0.0484 = 0.2184 (rounded to four decimal places).
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The probability that an eighth-grade girl will have long hair and be wearing a dress is 3/8 or 0.375, which is the same thing expressed as a decimal.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To solve the problem, we need to find the intersection of the events "having long hair" and "wearing a dress" and calculate the probability of that intersection.

Let L be the event "having long hair" and D be the event "wearing a dress". Then we know:

P(L) = 3/4, since three-fourths of the girls have long hair.

P(D) = 1/2, since half of the girls are wearing dresses.

To find P(L ∩ D), we need to multiply the probabilities of the two events:

P(L ∩ D) = P(L) × P(D) = (3/4) × (1/2) = 3/8

Therefore, the probability that an eighth grade girl will have long hair and be wearing a dress is 3/8 or 0.375, which is the same thing expressed as a decimal.

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Answer:

[tex]m = \dfrac{4}{\sqrt{3}} \text{ or, in rational form: } m = \dfrac{4\sqrt{3}}{3}[/tex]

[tex]n = \dfrac{2}{\sqrt{3}} \text{ or, in rational form: } n = \dfrac{2\sqrt{3}}{3}[/tex]

Not sure which form your teacher wants the answers, would suggest putting in both

Step-by-step explanation:

The missing angle of the triangle = 180 - (60 + 90) = 30°

We will use the law of sines to find m and n

The law of sines states that the ratio of each side to the sine of the opposite angle is the same for all sides and angles

Therefore since m is the side opposite 90° and 2 is the side opposite 60°,

[tex]\dfrac{m}{\sin 90} = \dfrac{2}{\sin 60}}\\\\[/tex]

sin 90 = 1

sin 60 = √3/2

So
[tex]\dfrac{m}{1} = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2 \cdot 2}{\sqrt{3}} \\\\m = \dfrac{4}{\sqrt{3}}\\\\[/tex]

We can rationalize the denominator by multiplying numerator and denominator by √3 to get
[tex]m = \dfrac{4\sqrt{3}}{3}[/tex]
(I am not sure what your teacher wants, you can put both expressions, they are the same)

To find n
Using the law of sines we get
[tex]\dfrac{n}{\sin 30} = \dfrac{m}{\sin 90}\\\\\dfrac{n}{\sin 30} = m\\\\\dfrac{n}{\sin 30} = \dfrac{4}{\sqrt{3}}\\\\[/tex]

sin 30 = 1/2 giving

[tex]\dfrac{n}{1/2} = \dfrac{4}{\sqrt{3}}\\\\n = \dfrac{1/2 \cdot 4}{\sqrt{3}} \\\\n = \dfrac{2}{\sqrt{3}}[/tex]

In rationalized form
[tex]n = \dfrac{2\sqrt{3}}{3}}[/tex]

Answer: 10w + 3 + 4.5w = 90

Step-by-step explanation:

a right angle is 90 degrees, so 10w + 3 and 4.5w have to add up to 90 degrees

The simplification of the function is r(x)=10x - 95.

We are given that;

s(x) = -85 and a(x) = 10(x - 1)

Now,

To create a function that combines them, you can substitute these expressions into the formula above:

r(x) = s(x) + a(x) r(x) = (-85) + 10(x - 1)

You can simplify this function by distributing the 10 and combining the constants:

r(x) = -85 + 10x - 10 r(x) = 10x - 95

Therefore, the function will be r(x)=10x - 95.

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Answer:

B. AB = CD = sqrt(13); DA = BC = sqrt(17)

This is because in a parallelogram, opposite sides are equal in length. In this statement, AB is equal to CD and DA is equal to BC, so opposite sides are equal. The values of AB, CD, DA, and BC are given as the square root of 13 and the square root of 17, which matches the condition of the statement.

In statement A, all sides are equal in length, which means the shape is a rhombus, not necessarily a parallelogram.

Answer:

Distance that car B travels =1.2× distance that car A travels

=1.2×221.5=265.8 km

Answer:

car B travels a distance of 265.8 km during the same time.

Step-by-step explanation:

Car A travels 221.5 km at a given time.

To find the distance traveled by car B, which is 1.2 times the distance traveled by car A, we can multiply the distance of car A by 1.2:

Distance of Car B = 1.2 * Distance of Car A

Distance of Car B = 1.2 * 221.5 km

Distance of Car B = 265.8 km

Therefore, car B travels a distance of 265.8 km during the same time.

Answer:  The value of the test statistic to 2 d.p is z= 1.65

Step-by-step explanation:

P cap= 0.72

n= 170

P= 0.66

q= 1- p

q= 1- 0.66

q= 0.34

Z=( p cap - p)/√(p*q)/n

Z= (0.72- 0.66)/√(0.66*0.34)/170

Z= 0.06/0.036332

Z= 1.65

Answer:

  117

Step-by-step explanation:

You want the cross product of vectors u = (12i -3j) and v = (-5i +11j).

The cross product of 2-dimensional vectors is a scalar that is effectively the determinant of the matrix of coefficients.

  u×v = (12)(11) -(-3)(-5) = 132 -15

  u×v = 117

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a. The radius of circle is 4 units.

b. The diameter of the circle is 2 x 4 = 8 units.

c. The area of the circle to be around 31 to 32 square units.

A circle is a geometrical shape consisting of all points that are at an equal distance from a central point.

The distance from the center to any point on the circle is called the radius of the circle.

a. To find the radius of the circle, we need to measure the distance from the center point N to any point on the circumference of the circle.

Using the grid, we can count the number of squares from N to the edge of the circle.

In this case, we can count 4 squares horizontally and 4 squares vertically.

b. The diameter of the circle is twice the radius. Therefore, the diameter of the circle is 2 x 4 = 8 units.

c. To estimate the area of circle using the grid, we can count the number of complete squares that are either fully inside the circle or partially covered by the circle.

In this case, we can count 31 complete squares. We can also see that there are some squares that are partially covered by the circle, so we can estimate that the total area of the circle is slightly more than 31 square units. Therefore, we can estimate the area of the circle to be around 31 to 32 square units.

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The probability of selecting all defective transistors is 1/560.

The probability of selecting all defective transistors can be calculated as:

P(all defective) = (number of ways to select 3 defective transistors) / (total number of ways to select 3 transistors)

The number of ways to select 3 defective transistors is simply the number of combinations of 3 defective transistors out of the total of 3, which is 1. The total number of ways to select 3 transistors out of 16 is:

total number of ways = number of combinations of 3 transistors out of 16

= (16 choose 3)

= 560

Therefore, the probability of selecting all defective transistors is:

P(all defective) = 1 / 560

To simplify the answer, we can write it as a fraction in lowest terms:

P(all defective) = 1 / 560 = 1/ (161514/321) = 1/560

Therefore, the probability of selecting all defective transistors is 1/560.

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The calculations of the down payments, monthly income or payments are as follows:

Part 1:

Annual income = $226,000

Federal Tax = $62,582

State Tax = $16,385

Local Tax = $5,537

Healthcare = $4,520

Yearly income = $136,976

Monthly income = $11,414.67.

Part 2:

Down payment = $150,000

The amount to borrow (Mortgage loan) = $600,000

Estimated interest = $810,000

Total installment payments = $1,410,000

Monthly payment = $3,916.67.

Part 3:

Down payment = $2,902.50

Mortgage loan = $16,447.50

Estimated interest = $3,700.69

Interest + Mortgage loan = $20,148.19

Monthly payment = $335.80.

Part 1:

Annual income = $226,000

Federal Tax:

25% of $89,350 = $22,337.50

28% of $97,000 = $27,160.00

33% of $39,650 = $13,084.50

Total federal tax = $62,582

State Tax = 7.25% of $226,000 = $16,385

Local Tax = 2.45% of $226,000 = $5,537

Healthcare = 2% of $226,000 = $4,520

f) Total of Federal, State, Local, and Healthcare = $89,024

Yearly income = $136,976 ($226,000 - $89,024)

Monthly income = $11,414.67 ($136,976 ÷ 12)

Part 2:

a) House price = $750,000

b) Down payment = 20%

= $150,000 ($750,000 x 20%)

c) Mortgage loan = $600,000 ($750,000 - $150,000)

d) Interest rate = 4.5%

Number of mortgage years = 30 years

Mortgage period in months = 360 months (30 x 12)

Estimated interest = $810,000 ($600,000 x 4.5% x 30)

Interest + Mortgage loan = $1,410,000 ($600,000 + $810,000)

Monthly payment = $3,916.67 ($1,410,000 ÷ 360)

Part 3:

Price of car = $19,350

Down payment = 15%

= $2,902.50 ($19,350 x 15%)

Mortgage loan = $16,447.50 ($19,350 - $2,902.50)

Number of years = 5 years

Mortgage period in months = 60 months (5 x 12)

Estimated interest = $3,700.69 ($16,447.50 x 4.5% x 5)

Interest + Mortgage loan = $20,148.19 ($16,447.50 + $3,700.69)

Monthly payment = $335.80 ($20,148.19 ÷ 60)

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The mixed fraction 1 and 1/4 is equal to 5/4 and the mixed fraction 1 and 1/2 is equal to 3/2.

Given first number = 1 and 1/4.

1 and 1/4 is a mixed fraction so, we can write it in the form as  [tex]1\frac{1}{4}[/tex] .

To find the value of  [tex]1\frac{1}{4}[/tex]  we have to multiply 4 with 1 and add the numerator part of the fraction which is 1 and then divide it by 4 which is the denominator. So,

 [tex]1\frac{1}{4}[/tex]  = ((4x1) + 1 )/4 = 5/4.

Similary, for 1 and 1/2,

[tex]1\frac{1}{2}[/tex] = ((2x1) + 1)/2 = 3/2.

From the above analysis, we can conclude that the value of 1 and 1/4 is 5/4 and the value of 1 and 1/2 is 3/2.

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