Drag the number cards so that the value of x are as great as possible. Can you fill in each blank so that these equations have the same vaule for x?

Answer:

$46.15

Step-by-step explanation:

Given information:

Define the variable:

Convert 4% into a decimal:

\(\implies 4\%=\dfrac{4}{100}=0.04\)

Therefore, the sum of the cost of the juice, the price of the jeans and the sales tax on the jeans must be equal to or less than $50:

\(\implies 2+x+0.04x\leq 50\)

\(\implies 2+1.04x\leq 50\)

Solving the inequality:

\(\implies 2+1.04x\leq 50\)

\(\implies 2+1.04x-2\leq 50-2\)

\(\implies 1.04x\leq 48\)

\(\implies \dfrac{1.04x}{1.04}\leq \dfrac{48}{1.04}\)

\(\implies x\leq 46.15384615\)

Therefore, the maximum price of the jeans Juan can afford is $46.15 (not including sales tax).

Hence, the answers are:a. Sensitivity of the test is 12.37%.b. Specificity of the test is 97.18%.c. False-positive fraction of the test is 2.86%.d. False-negative fraction of the test is 87.63%.

Sensitivity of a screening testSensitivity of the screening test is the probability of obtaining a positive screening test result among people with the disease. It is calculated as follows:Sensitivity = True positive / (True positive + False negative)From the given table,True positive = 12False negative = 85Total number of people with the disease = True positive + False negative = 12 + 85 = 97Sensitivity = 12 / (12 + 85) = 0.1237 = 12.37%Therefore, the sensitivity of the test is 12.37%.Specificity of a screening testSpecificity of the screening test is the probability of obtaining a negative screening test result among people who do not have the disease. It is calculated as follows:Specificity = True negative / (True negative + False positive)From the given table,True negative = 204False positive = 6Total number of people without the disease = True negative + False positive = 204 + 6 = 210Specificity = 204 / (204 + 6) = 0.9718 = 97.18%Therefore, the specificity of the test is 97.18%.False-positive fractionFalse-positive fraction is the proportion of healthy people who get a positive result out of the total number of healthy people. It is calculated as follows:False-positive fraction = False positive / (False positive + True negative)From the given table,False positive = 6True negative = 204False-positive fraction = 6 / (6 + 204) = 0.0286 = 2.86%Therefore, the false-positive fraction of the test is 2.86%.False-negative fractionFalse-negative fraction is the proportion of sick people who get a negative result out of the total number of sick people. It is calculated as follows:False-negative fraction = False negative / (False negative + True positive)From the given table,False negative = 85True positive = 12False-negative fraction = 85 / (85 + 12) = 0.8763 = 87.63%Therefore, the false-negative fraction of the test is 87.63%.Hence, the answers are:a. Sensitivity of the test is 12.37%.b. Specificity of the test is 97.18%.c. False-positive fraction of the test is 2.86%.d. False-negative fraction of the test is 87.63%.

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Answer:

1

Step-by-step explanation:

Answer:

6x2-11x+4

..........

Answer:

\({ \tt{ = (100 + 89)\%}} \\ = { \tt{(189\% \times £854)}} \\ = £1614.06\)

Answer:

Step-by-step explanation:

Sight.

Amy will pay a total of approximately $30,007.20 in interest over the life of the loan.

Amy bought a car for $29,000, making a 10% down payment and financing the remaining balance for 60 months with an APR of 5.5%. The question asks for the total interest Amy will pay over the life of the loan.

To calculate the total interest paid, we need to determine the monthly payment amount and then multiply it by the number of months. The monthly payment can be calculated using the formula for a fixed-rate loan: P = (r × PV) / (1 - (1 + r)⁽⁻ⁿ⁾)

where P is the monthly payment, r is the monthly interest rate, PV is the present value or loan amount, and n is the number of months.

First, we calculate the loan amount after the down payment: $29,000 - ($29,000 × 10%) = $26,100.

Next, we calculate the monthly interest rate: 5.5% / 12 = 0.00458.

Using the formula, we can find the monthly payment amount: P = (0.00458 × $26,100) / (1 - (1 + 0.00458)⁽⁻⁶⁰⁾) ≈ $500.12.

Finally, we multiply the monthly payment by the number of months: $500.12 × 60 = $30,007.20.

Therefore, Amy will pay a total of approximately $30,007.20 in interest over the life of the loan.

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Answer:

x = 14

Explanation:

To get the value of x, we wll be using the SOH CAH TOA identity

Using sin theta = opposite/hypotenuse

h is the vertical height of the triangles.

Next is to get the value of x;

Similarly;

Hence the value of x required is 14

Parabolas are used to represent quadratic functions

The x-intercepts of the parabola are -1.969 and 6.01

The function is given as:

\(f(x) = 4.9x^2 + 19.8x + 58\)

Next, we plot the graph of the function f(x)

From the graph (see attachment), we have the following features

Hence, the x-intercepts of the parabola are -1.969 and 6.01

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Answer:

I think it is the second one

Step-by-step explanation:

Answer:

Step-by-step explanation:

W(-4,-10) lies on third quadrant.

M(-12,0) lies on second quadrant or can say in x axis

C(8,3) lies on first quadrant.

K(11,-5) lies on fourth quadrant.

The HA is the Hypotenuse Angle Theorem. The correct option is A.

The hypotenuse angle theorem (HA theorem) asserts that "if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent."

The HA theorem also known as the Hypotenuse angle theorem is used to prove that ΔKML≅ΔOPQ.

Hence, the correct option is A.

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Answer:

Step-by-step explanation:

Answer:

6.50w

Step-by-step explanation:

Given that :

Weight ________ Cost ($)

1 ______________6.50

2 _____________ 13.00

3 _____________ 19.50

Cost of package that weighs w pounds

If one pound = 6.50

2 pounds = 13.0

Then, the cost per pound = $6.50

Hence, cost of package that weighs w pounds will be ;

$6.50 * w = $6.50w

Answer:

A. Radical 12, not a pythagroean triple. B. 5, yes, it is a pythagorean triple.

Step-by-step explanation:

Use the pythagroean theorem ^^

On solving the provided question, we can say that in right angled triangle the value of x = 5√3 and value of y = 10.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Using the table of trig values, we find that

sin30°=1/2

So, this gives us:

1/2 = sin 30° = 5/y

1/2 = 5/y

(1xy)/2 = 5

y= 2×5 =10

Next, using the Pythagorean Theorem, we find that

5²+x²=10²

x²=100−25=75

Solve for x:

x=√75=√3×25=5√3

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Answer:

420 miles

Step-by-step explanation:

Distance traveled per hour = 55 miles

Distance traveled in 6 hours = 55 * 6 = 330 miles

Distance of the trip = 330 + 90  = 420 miles

Approximately 137.5 mg of the medication remain in the individual's bloodstream after 8 hours.

To solve this problem, we can use the concept of half-life. The half-life is the time it takes for half of the medication to leave the bloodstream.

In this case, the medication's half-life is 14 hours, meaning that every 14 hours, the amount of medication in the bloodstream is halved.

To find out how much medication remains in the bloodstream after 8 hours, we need to determine the number of half-lives that have occurred during this time.

Number of half-lives = (time elapsed) / (half-life)

Number of half-lives = 8 hours / 14 hours ≈ 0.571

Since we can't have a fraction of a half-life, we need to round this value to the nearest whole number, which is 1. This means that one half-life has occurred during the 8-hour period.

Now, we can calculate the remaining amount of medication using the formula:

Remaining amount = Initial amount / (2 ^ number of half-lives)

Remaining amount = 275 mg / (2 ¹) = 275 mg / 2 = 137.5 mg

Approximately 137.5 mg of the medication remain in the individual's bloodstream after 8 hours.

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The function is continuous on set of real numbers. Therefore, the correct answer is A) F is continuous on the set of real numbers.

To determine where the function F(x, y) is continuous, we need to check if the function is defined and the limit exists at every point in its domain.

The function is defined for all (x, y) except where the denominator 2 + e^(x - y) is equal to zero, which is only when e^(x - y) = -2, which has no real solutions. Therefore, domain of F is all real numbers.

Now, we need to check if the limit exists at every point in its domain. We can start by checking the limit as (x, y) approaches (a, b) for arbitrary constants a and b.

lim (x,y)->(a,b) F(x,y) = lim (x,y)->(a,b) [(xy)/(2+e^(x-y))]

To evaluate this limit, we can use the squeeze theorem, since 0 ≤ |xy| ≤ (1/2)(x² + y²), and both x² + y² and 2 + e^(x - y) approach zero as (x, y) approaches (a, b). Therefore, we can say that:

0 ≤ |F(x,y)| ≤ [(1/2)(x² + y²)] / [2 + e^(x-y)]

And by the squeeze theorem, as (x, y) approaches (a, b), F(x, y) approaches zero.

Since the limit of F(x, y) exists at every point in its domain, we can conclude that the function is continuous.

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Answer:

Step-by-step explanation:

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!

The probability that the dealt hand contains exactly two aces given that we know it contains at least one ace is 2/3 or approximately 0.667.

To calculate this probability, we can use Bayes' theorem. Let A be the event that the dealt hand contains exactly two aces and B be the event that the hand contains at least one ace. Then, the probability we are looking for is P(A | B), the probability of A given that B has occurred.

Using Bayes' theorem, we have:

where P(B | A) is the probability of drawing a hand with at least one ace given that the hand contains exactly two aces, P(A) is the probability of drawing a hand with exactly two aces, and P(B) is the probability of drawing a hand with at least one ace.

We can calculate these probabilities as follows:

To calculate P(B | A), we first fix two aces in the hand and then choose three non-aces from the remaining 48 cards. Thus, we have:

Plugging these values into Bayes' theorem, we get:

Therefore, the probability that the dealt hand contains exactly two aces given that we know it contains at least one ace is 2/3 or approximately 0.667.

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Using a trigonometric relation we will see that the value of x is 81.2°

We can see that we have a right triangle, and the angle x is the one that is on the top vertex.

We can use any trigonometric relation to find the value of x, for example we can use:

sin(x) = (opposite cathetus)/(hypotenuse)

Where we can see that:

opposite cathetus = 84

hypotenuse = 85

Then we will get:

sin(x) = 84/85

x = Asin(84/85) = 81.2°

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The final answer to the given integral over the contour C is:∫\((C) 2z^4 + 3z^3 + z^2 log(z^2 + 9) dz = (63 log(64) - 93 log(31) - 52)/3.\\\)

To evaluate the given contour integral, we will split it into four line integrals corresponding to the sides of the rectangle. Let's denote the sides as follows:

S1: From -1+i to -1+2i
S2: From -1+2i to 1+2i
S3: From 1+2i to 1+i
S4: From 1+i to -1+i

We'll evaluate each line integral separately and then sum them up to obtain the final result.

First, let's evaluate the line integral over S1:

\(∫(S1) 2z^4 + 3z^3 + z^2 log(z^2 + 9) dz\)

The parameterization of S1 is given by z = -1 + ti, where t ranges from 1 to 2. Therefore, dz = i dt.

Substituting these values into the integral, we have:

\(∫(S1) [2(-1 + ti)^4 + 3(-1 + ti)^3 + (-1 + ti)^2 log((-1 + ti)^2 + 9)]\)i dt

Expanding the terms, we get:

\(∫(S1) [2(-1 + 4ti - 6t^2 + 4it^3 - t^4) + 3(-1 + 3ti - 3t^2 + t^3) + (-1 + 2ti - t^2) log((-1 + ti)^2 + 9)] i dt\)

Simplifying and separating real and imaginary parts, we obtain:

\(∫(S1) [(2t^3 - 2t^2 + 2t - 2) + i(8t - 6t^2 + 4t^3 + 3t^3 + 3ti - 3t^2 + 2t - 1 + 2ti - t^2) log(t^2 + 10t + 10)] dt\)

Now, we can integrate each part separately:

Real part:
\(∫(S1) (2t^3 - 2t^2 + 2t - 2) dt = (1/4)t^4 - (2/3)t^3 + t^2 - 2t | from 1 to 2 = (1/4)(2^4) - (2/3)(2^3) + 2^2 - 2(2) - [(1/4)(1^4) - (2/3)(1^3) + 1^2 - 2(1)]\\\)
Imaginary part:
\(∫(S1) (8t - 6t^2 + 4t^3 + 3t^3 + 3t - 3t^2 + 2t - 1 + 2t log(t^2 + 10t + 10) - t^2 log(t^2 + 10t + 10)) dt\\\)
The integral of the terms without logarithms can be easily evaluated:

\(∫(S1) (8t - 6t^2 + 4t^3 + 3t^3 + 3t - 3t^2 + 2t - 1) dt = 4t^4 - 3t^3 + 2t^2 - t^2 - t^3 + 3/2t^2 + t^2 - t - t | from 1 to 2= 4(2^4) - 3(2^3) + 2(2^2) - 2^2 - 2^3 + 3/2(2^2) + 2^2 - 2 - 2 - [4(1^4) - 3(1^3) + 2(1^2) - 1^2 - 1^3 + 3/2(1^2) + 1^2 - 1]\)

Now, let's evaluate the remaining part involving the logarithm. We'll make a substitution to simplify it:

\(Let u = t^2 + 10t + 10. Then, du = (2t + 10) dt, and the integral becomes:∫(S1) (2t log(u) - t^2 log(u)) du/2t + 10Canceling the 2t in the numerator and denominator, we have:∫(S1) (log(u) - t^2 log(u)) du/(t + 5)Factoring out the logarithm:∫(S1) log(u) (1 - t^2) du/(t + 5)\)

Now, we can integrate with respect to u:

\(∫(S1) log(u) (1 - t^2) du = (1 - t^2) ∫(S1) log(u) duUsing integration by parts, where dv = log(u) du and v = u(log(u) - 1), we get:∫(S1) log(u) du = u(log(u) - 1) - ∫(S1) (log(u) - 1) duExpanding and simplifying, we have:∫(S1) log(u) du = u log(u) - u - ∫(S1) log(u) du + ∫(S1) du\\\)
Rearranging and combining the integrals:

2∫(S1) log(u) du = u log(u) - u + C

Dividing both sides by 2:

∫(S1) log(u) du = (u log(u) - u + C)/2

Now, we can substitute back \(u = t^2 + 10t + 10:∫(S1) log(u) du = [(t^2 + 10t + 10) log(t^2 + 10t + 10) - (t^2 + 10t + 10) + C]/2\)

Substituting this expression back into the imaginary part of the integral, we have:

\(∫(S1) (8t - 6t^2 + 4t^3 + 3t^3 + 3t - 3t^2 + 2t - 1 + 2t log(t^2 + 10t + 10) - t^2 log(t^2 + 10t + 10)) dt= [4(2^4) - 3(2^3) + 2(2^2) - 2^2 - 2^3 + 3/2(2^2) + 2^2 - 2 - 2 - (4(1^4) - 3(1^3) + 2(1^2) - 1^2 - 1^3 + 3/2(1^2) + 1^2 - 1)]+ [(2^2 + 10(2) + 10) log(2^2 + 10(2) + 10) - (2^2 + 10(2) + 10) + C]/2- [(1^2 + 10(1) + 10) log(1^2 + 10(1) + 10) - (1^2 + 10(1) + 10) + C]/2\)

Simplifying further, we have:

\([64 - 24 + 8 - 4 - 8 + 3/2(4) + 4 - 2 - 2 - (4 - 3 + 2 - 1 - 1 + 3/2(1) + 1 - 1)]+ [(44 + 20) log(44 + 20) - (44 + 20) + C]/2 - [(21 + 10) log(21 + 10) - (21 + 10) + C]/2= [37 + 6 + 6 - 9/2 + 6 - 3/2 + 4 - 2 - 2 - 4 + 2 - 2]+ [64( log(64) - 1) + 20 log(64) - 44 - 20 + C]/2 - [31 log(31) + 21 - 31 + C]/2= [26 - 7/2 - 8]+ [64 log(64) + 20 log(64) - 44 - 20 + C]/2 - [31 log(31) - 10 + C]/2\\\)
\(= 11/2 + [42 log(64) - 64 - 24 + C]/2 - [31 log(31) - 10 + C]/2= 11/2 + 21 log(64) - 32 - 12/2 + C/2 - 31 log(31)/2 + 5 - C/2= -5/2 + 21 log(64) - 31 log(31) - 27/2 + 5= 21 log(64) - 31 log(31) - 27/2 + 3/2= 21 log(64) - 31 log(31) - 24/2= 21 log(64) - 31 log(31) - 12\\\)
Therefore, the value of the given integral over the contour C is:

\(∫(C) 2z^4 + 3z^3 + z^2 log(z^2 + 9) dz = (1/4)(2^4) - (2/3)(2^3) + 2^2 - 2(2) - [(1/4)(1^4) - (2/3)(1^3) + 1^2 - 2(1)]+ [21 log(64) - 31 log(31) - 12]\\\)
Simplifying further, we have:

\(= 16/4 - 16/3 + 4 - 4 - (1/4) + 2/3 + 1 - 2 + [21 log(64) - 31 log(31) - 12]= 4 - 16/3 - 1/4 + 2/3 - 1 + [21 log(64) - 31 log(31) - 12]= 12/3 - 16/3 - 1/4 + 6/9 - 3/3 + 21 log(64) - 31 log(31) - 12= (12 - 16 - 3 + 6 - 9 + 63 log(64) - 93 log(31) - 36)/3= (63 log(64) - 93 log(31) - 52)/3\)

Hence, the final answer to the given integral over the contour C is:

\(∫(C) 2z^4 + 3z^3 + z^2 log(z^2 + 9) dz = (63 log(64) - 93 log(31) - 52)/3.\)

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Answer:

Step-by-step explanation: