s
is inversely proportional to
t
.
When
s
=
0.3
,
t
=
8

Work out
t
when
s
=
24

Answer:

The bottom right.

Step-by-step explanation:

Hope its correct.

Answer:

D

Step-by-step explanation:

Answer:

What are the coordinates of the vertex of the function f(x) = x2 − 12x + 5?

Step-by-step explanation:

November 2021 EDGE

The finance charge that Mr. Jones paid is -0.85x + 24y, the correct option is C.

What is a simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression. like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

We are given that;

Mr. Jones paid=24y-0.85x

Now,

To determine the finance charge that Mr. Jones paid, you need to use the given expressions as follows:

The down payment is 0.15x

The number of monthly payments is 24

The total amount paid as monthly payments is 24y

The total amount paid for the refrigerator is 0.15x + 24y

The finance charge is the difference between the total amount paid and the original price of the refrigerator: (0.15x + 24y) - x

You can simplify this expression by combining like terms:

(0.15x + 24y) - x = -0.85x + 24y

Therefore, by simplification, the answer will be -0.85x + 24y.

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Answer:

The correct answer is B

Step-by-step explanation:

zzzz

1) The value of P(A∩B) = 0.

2) The value of P(A|B) = 0.

3) P(A|B) is not equal to P(A). A and B are independent events.

4) The statement "Mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent." is not accurate.

5) We can conclude that mutually exclusive events have a probability of intersection of zero and are not independent.

1) Since A and B are mutually exclusive, they cannot occur at the same time, so P(A∩B) = 0.

2) The conditional probability of A given B is defined as the probability of A occurring given that B has occurred. Since A and B are mutually exclusive, if B has occurred, then A cannot occur. Therefore, P(A|B) = 0.

3) No, P(A|B) is not equal to P(A). Since B has occurred, the sample space has been reduced to only those outcomes in which B has occurred. Therefore, the probability of A given that B has occurred can only be determined from the portion of the sample space in which both A and B occur.

However, since A and B are mutually exclusive, this probability is zero. Therefore, P(A|B) ≠ P(A).

4) The statement is not accurate. Mutually exclusive events and independent events are different concepts. Two events are mutually exclusive if they cannot occur at the same time, whereas two events are independent if the occurrence of one event does not affect the probability of the other event.

If two events are mutually exclusive, they are not independent because the occurrence of one event precludes the occurrence of the other event.

5) Mutually exclusive events have a relationship where if one event occurs, the other cannot. In contrast, independent events are events where the occurrence of one event does not affect the probability of the other event occurring.

Therefore, we can conclude that mutually exclusive events and independent events are not the same concept, and we must be careful not to confuse them.

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a. The value of c is 1/2.

b. The cumulative distribution function of x is \(F(x) = 0 for x < -1, F(x) = (1/2) + (1/2)x - (1/2)x^3 for -1 ≤ x ≤ 1, and F(x) = 1 for x > 1.\)

c. E(X) = 0. d. Var(X) = 1/3.

a. To find the value of c, we need to use the fact that the total area under the density function must be equal to 1:

Integral from -1 to 1 of f(x) dx = 1

Using the given formula for f(x), we get:

Integral from -1 to 1 of c\((1 - x^2)^-1\) dx = 1

Taking the integral of \((1 - x^2)^-1\) with respect to x, we get:

\(-ln|1 - x^2|\) from -1 to 1

Substituting the limits and equating to 1, we get:

-ln(1 - 1) + ln(1 - (-1)) = 1

ln(2) = 1

Therefore, c = 1/ln(2).

b. The cumulative distribution function (CDF) of x is given by:

F(x) = Integral from -∞ to x of f(t) dt

For x < -1, F(x) = 0 since the density function is 0 in this region.

For -1 ≤ x < 1, we have:

F(x) = Integral from -1 to x of \(c(1 - t^2)^-1 dt\)

Using substitution u = \(1 - t^2, du/dt = -2t\), we can rewrite this as:

F(x) = Integral from 0 to \(1-x^2 of c u^-1 (du/(-2t))\)

= (-1/2) c ln|u| from \(0 to 1-x^2\)

= (-1/2) c ln\((1/(1-x^2))\)

= (1/2) ln(1/\((1-x^2))\)

For x ≥ 1, F(x) = 1 since the density function is 0 in this region.

c. To find E(X), we need to take the expected value of X:

E(X) = Integral from -∞ to ∞ of x f(x) dx

For x < -1 or x > 1, f(x) is 0, so we can ignore those regions.

For -1 ≤ x ≤ 1, we have:

E(X) = Integral from -\(1 to 1 of x c(1 - x^2)^-1 dx\)

Using substitution u = 1 - x^2, du/dx = -2x, we can rewrite this as:

E(X) = Integral from 0 to 1 of \((1 - u) c u^-1 (-du/(2x))\)

= (-c/2) Integral from 0 to 1 of\((1 - u) u^-1 du\)

= (-c/2) ln(u) from 0 to 1

= (-c/2) ln(1/1)

= 0

Therefore, E(X) = 0.

d. To find Var(X), we first need to find \(E(X^2):\)

E(X^2) = Integral from -∞ to ∞ of\(x^2 f(x) dx\)

For x < -1 or x > 1, f(x) is 0, so we can ignore those regions.

For -1 ≤ x ≤ 1, we have:

E\((X^2)\)= Integral from -\(1 to 1 of x^2 c(1 - x^2)^-1 dx\)

Using substitution u = \(1 - x^2, du/dx = -2x\), we can rewrite this as:

E\((X^2)\) = Integral from 0 to \(1 of (1 - u) c u^-1 (-du/(2x))\)

= (-c/2) Integral

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Answer:

Step-by-step explanation:

I hope this helps

Using integer addition, the total profit from the Spanish Club's bake sale is $270.

Integer refers to whole numbers(non-fractional numbers) that can either be positive or negative, and zero.

Adding positive integers will result to a positive integer while adding negative integers will result to a negative integer. But, adding a negative integer to a positive integer is the same as subtracting its positive.

If the income from the Spanish Club's bake sale was $300 and the expenses for the sale is $30, the total profit will be:

income = +$300

expenses = -$30

Using integer addition,

profit = income + expenses

profit = +$300 + (-$30)

profit = $300 - $30

profit = $270

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Answer:

B

Step-by-step explanation:

The value of y for the given right angle triangle by the trigonometric function will be 12.43 ft thus option (B) is correct.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

The trigonometric functions found in the quadrants, as well as their graphs, domains, and differentiation and integration, will all be understood.

As per the given right angle triangle,

By cosine function,

cos43° = y/17

y = 17 cos43° = 12.43 feet

Hence "The trigonometric function will yield 12.43 feet as the value of y for the given right angle triangle".

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The hiker's distance and bearing from their starting point are approximately 7.155 miles and 28.07°, respectively.

Given that two hikers travel 8 mi southeast and then 6 mi east, we are to find the hikers distance and bearing from their starting point at this time.Long ExplanationThe bearing of the hiker refers to the angle between the hiker's direction and North. So, let us assume that the hiker has initially moved at a direction East, as shown below:We are given that the hiker has traveled 8 miles to the southeast.

Therefore, from the diagram, the distance traveled in the East direction is 8 sin(45) miles, and the distance traveled in the South direction is 8 cos(45) miles. East = 8 sin(45) = 8/√2 = 4√2 miles South = 8 cos(45) = 8/√2 = 4√2 miles We are then told that the hiker travels 6 miles east, from the last position.

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The length of each entertainment segment written as a decimal is 4.5 minutes

Total time of the TV program= 20 minutes

Number of commercials= 2

Time taken for each commercial= 13/4 minutes

Total time taken for 2 commercials= 2(13/4)

= 26/4

= 13/2 minutes

Number of minutes remaining after commercials= Total time of the TV program - Total time taken for 2 commercials

= 20 - 13/2

= (40-13) / 2

= 27/2 minutes

Number of entertainment segment = 3

Time spent on each entertainment segment= Number of minutes remaining after commercials / 3

= 27/2 ÷ 3

multiply by the reciprocal of 3

= 27/2 × 1/3

= 27/6 minutes

= 4.5 minutes

Therefore, each entertainment segment will take 4.5 minutes from the 20 minutes TV program.

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Answer: 1/2

Step-by-step explanation: 1/2 times 3 is the improper fraction 3/2

Answer:

The answer is 1/2

Step-by-step explanation:

1/3 x 3/2

To break it up you multiply the top numbers to get 3

The you'd multiply the bottom numbers to get 6

so your answer is 3/6 which is also equal to 1/2

Answer:

Um

Step-by-step explanation:

what are the statements?

The two points of tangency on the circle are (0, 5) and (-4, 1).

To find the coordinates of the point of tangency for the given circle with the tangent slope of -1, we need to use a few mathematical concepts and formulas.

Let's break it down:

The equation of the circle is given as \((x + 2)^2 + (y - 3)^2 = 8.\)

To determine the point of tangency, we need to find the tangent line that has a slope of -1.

First, we need to find the derivative of the circle equation.

Differentiating both sides of the equation with respect to x, we obtain:

2(x + 2) + 2(y - 3)(dy/dx) = 0.

Next, we substitute the given slope of -1 into the derived equation:

2(x + 2) + 2(y - 3)(-1) = 0.

Simplifying the equation, we have:

2x + 4 - 2y + 6 = 0,

2x - 2y + 10 = 0,

x - y + 5 = 0.

This equation represents the line that is tangent to the circle.

To find the point of tangency, we need to solve the system of equations formed by the circle equation and the tangent line equation:

\((x + 2)^2 + (y - 3)^2 = 8, (1)\)

x - y + 5 = 0. (2)

Solving equation (2) for x, we get:

x = y - 5.

Substituting this expression for x in equation (1), we have:

\((y - 5 + 2)^2 + (y - 3)^2 = 8,\)

\((y - 3)^2 + (y - 3)^2 = 8,\)

\(2(y - 3)^2 = 8,\)

\((y - 3)^2 = 4,\)

y - 3 = ±2.

Solving for y, we find two possible values:

y - 3 = 2, y - 3 = -2.

Solving each equation separately, we get:

y = 5, y = 1.

Substituting these values of y back into equation (2), we find the corresponding x-coordinates:

x = 5 - 5 = 0, x = 1 - 5 = -4.

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The class of biomolecules which pertains to the building blocks of proteins are b) amino acids.

Amino acids are the building blocks of proteins. Proteins are large, complex molecules made up of chains of amino acids linked together by peptide bonds. There are 20 different types of amino acids that can be found in proteins, each with its own unique side chain. These side chains give each amino acid its specific properties and functions.

When amino acids are linked together in a specific sequence, they form polypeptides, which then fold into complex three-dimensional structures to become functional proteins. The sequence of amino acids in a protein is determined by the genetic code, which is encoded in DNA.

In summary, amino acids are the building blocks of proteins. They are linked together in a specific sequence to form polypeptides, which then fold into functional proteins. The sequence of amino acids is determined by the genetic code. Hence, the correct answer is Option B.

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She ran a total distance of 28 miles in 5 hours.

We can solve this problem by using the formula: distance = rate × time

First, we need to calculate the distance traveled during the first 3 hours at 6 mph. Using the formula, we have:

distance = rate × time

distance = 6 mph × 3 hours

distance = 18 miles

Next, we need to calculate the distance traveled during the last 2 hours at 5 mph. Using the same formula, we have:

distance = rate × time

distance = 5 mph × 2 hours

distance = 10 miles

Finally, we can add the distances traveled during the first 3 hours and the last 2 hours to get the total distance:

total distance = 18 miles + 10 miles

total distance = 28 miles

Therefore, the runner ran a total distance of 28 miles in 5 hours.

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If your observed Z or t statistic falls in the "critical region," it means that the probability of obtaining a value as extreme or more extreme than the observed statistic is very low, assuming the null hypothesis is true.

The critical region is a range of values of a test statistic, such as Z or t, that indicate the rejection of the null hypothesis. In hypothesis testing, the null hypothesis is a statement that there is no significant difference between two groups or that there is no effect of an intervention. The alternative hypothesis is the opposite of the null hypothesis, and it suggests that there is a significant difference or an effect of the intervention.

The critical region is determined by the level of significance, which is a pre-specified threshold that is usually set at 0.05 or 0.01. If the observed test statistic falls within the critical region, it means that the probability of obtaining a value as extreme or more extreme than the observed statistic is very low, assuming the null hypothesis is true. This probability is called the p-value. Therefore, you would reject the null hypothesis and conclude that there is a significant difference or relationship between the variables being studied.

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Answer:

0.3636363636

Step-by-step explanation:

x = 6

Step 1: Simplify both sides of the equation.

5045x + 3000 = 5545x

Step 2: Subtract 5545x from both sides.

5045x + 3000 − 5545x = 5545x − 5545x

−500x + 3000 = 0

Step 3: Subtract 3000 from both sides.

−500x + 3000 − 3000 = 0 − 3000

−500x=−3000

Step 4: Divide both sides by -500.

−500x/−500 = −3000/−500

Answer: x=6

Answer:

13,440 per year.

Step-by-step explanation:

His pay check would be deducted over 93% which is 12,406 spent on bills, and about $90 left to spend on whatever he wants. (LoL)

The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.

Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:

x² + (LV/2)² = DV²/4

y² + (OE/2)² = LE²/4

Simplifying each equation and substituting the given values, we get:

x² + (LV/2)² = 81/4

y² + (OE/2)² = 225/4

We also know that the diagonals bisect each other, so we can set up another equation:

LV/2 + OE/2 = LO = VE

Substituting the given value for LE, we get:

LV/2 + OE/2 = 15

Solving this equation for one of the variables, we get:

LV = 30 - OE

Substituting this expression into the first equation above, we get:

x² + ((30 - OE)/2)² = 81/4

Simplifying and rearranging, we get:

OE² - 60OE + 675 = 0

Using the quadratic formula, we get:

OE = (60 ± √(3600 - 2700)) / 2

OE = 15 or 45

If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:

x² + 7.5² = 81/4

y² + 7.5² = 225/4

Solving these equations, we get:

x = 3√7

y = 9/√7

If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:

LV = OE = 15

x = 3√7

y = 9/√7

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Complete question:

LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.

In R^2, the triangle S has vertices (0,1), (-2,-1), and (2,-1).

To determine the homogeneous coordinates for these vertices, we need to add an extra coordinate, usually denoted by w, which is equal to 1.
Homogeneous coordinates allow us to work with points in projective space, making certain geometric transformations easier to handle.
So, the homogeneous coordinates for the vertices of triangle S are:
1. Vertex (0,1) becomes (0, 1, 1) in homogeneous coordinates.
2. Vertex (-2,-1) becomes (-2, -1, 1) in homogeneous coordinates.
3. Vertex (2,-1) becomes (2, -1, 1) in homogeneous coordinates.
These new coordinates, each with 3 entries, can be used in further calculations involving projective geometry or affine transformations.

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Based on the provided data and control limits, the process is not in a state of control.

To determine whether the process is in a state of control, we compare the sample proportion of defects to the control limits on the p-chart. The lower control limit (LCL) and upper control limit (UCL) for the p-chart have been given as 0.0024 and 0.37, respectively.

Looking at the data, we observe that in sample 2, the proportion of defects is 0.075, which is below the LCL. Similarly, in samples 5 and 6, the proportions of defects are 0.25 and 0.15, respectively, both of which are below the LCL. This indicates that the process is exhibiting points outside the control limits, which suggests that the process is out of control.Therefore, the correct answer is option b: No. The process is not in a state of control.

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Answer:

0.363636363636364

Step-by-step explanation:

100 goes into 257 0.363636363636364 times

Answer:

Fraction: 100/257

Decimal:  0.3891050583

Hope this Helps!

Answer:

ANGLES-

P=S

O=i

L=D

Y=E

SIDES-

PO=SI

OL=ID

LY=DE

YP=ES

Step-by-step explanation:

pretend the equal signs are congruency signs

Answer:

B

Step-by-step explanation:

the general slope intercept form is

y = ax + b

a is the slope, b is the y-intercept (the y value when x = 0).

a parallel line must have the same slope (1/2).

for b we simply put the x and y values of the given point into the equation

1 = 1/2 × -8 + b = -4 + b

b = 5

therefore,

y = 1/2 x + 5

is the correct solution.

Answer:

$130

Step-by-step explanation:

Answer:

$130

Step-by-step explanation:

1300×10%

$130

The slope of the line y = -2x + 7 is -2

So, any line paralell to this line, will have the same slope (-2)

Answer: -2