what is the specificity for the test based on these screening results (rounded to three decimal places)?

Answer:

Step-by-step explanation:

Perimeter

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Therefore, the total cost to the buyer, including VAT at 15%, is R73,60.

The term "VAT" usually refers to "Value Added Tax," which is a type of consumption tax that is levied on the value added to goods and services at each stage of production and distribution. It is commonly used by governments around the world as a way to generate revenue and to shift the tax burden from income and sales taxes onto consumption.

by the question.

To calculate the total cost to the buyer including VAT at 15%, you need to add the VAT amount to the original price. Here's how to do it:

Calculate the VAT amount:

VAT = 15% of R64,00

VAT = 0.15 x R64,00

VAT = R9,60

Add the VAT amount to the original price to get the total cost to the buyer:

Total cost = R64,00 + R9,60

Total cost = R73,60

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The approximate Z-score for this recruit is b. 0.18.

The mean of the head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. The head size of a recruit was found to be 23 inches.

The approximate Z-score for this recruit. The formula for Z-score is given by:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

where X is the head size of the recruit, μ is the mean head size of recruits, and σ is the standard deviation of head sizes of recruits. Substituting the given values in the above formula, we get,

Z=(23-22.8)(1.1)

Z=0.2/1.1

Z [tex]\approx[/tex] 0.18

Thus, the approximate Z-score for this recruit is b. 0.18.

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The magnitude of the projection of the two vectors is:

M =  8.73

If we have two vectors A and B, and we want the projection of A onto B, we need to solve:

projection = A·B/|B|

Here the vectors are <7, -6> and <5, -2>

First, the dot product between the two vectors gives:

7*5 - 6*-2 = 35 + 12 = 47

The dot product is 47.

And the module of the second vector is:

√(5² + (-2)²) = √(25 + 4) = √29

Then the magnitude of the projection is:

M = 47/√29 = 8.73

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Answer:

  (a) AC = 4√2 cm

  (b) AM = 2√2 cm

  (c) EM = √41 cm

  (d) EF = 3√5 cm

Step-by-step explanation:

You want to solve for various lengths in the right square pyramid shown with base edge 4 cm and lateral edge 7 cm.

Each right triangle can be solved for unknown lengths using the Pythagorean theorem: the square of the hypotenuse is the sum of the squares of the other two sides.

Right triangles of interest here are ...

  ADC . . . . for finding AC and AM (isosceles right triangle)

  CME . . . . for finding EM

  FME . . . . for finding EF

AC is the hypotenuse of ∆ADC, so ...

  AC² = AD² +DC²

  AC = √(4² +4²)

  AC = 4√2 . . . . cm

M is the midpoint of AC, so ...

  AM = AC/2 = (4√2)/2

  AM = 2√2 . . . . cm

FM is half the length of one side of the base, so is 2 cm. CM = AM = 2√2.

  CE² = CM² +EM²

  EM = √(CE² -CM²) = √(7² -(2√2)²)

  EM = √41 . . . . cm

EF is the hypotenuse of ∆EMF.

  EF² = EM² +FM²

  EF = √(EM² +FM²) = √(41 +2²) = √45

  EF = 3√5 . . . . cm

The selling price of laptop after VAT (15 percent) is Rs 4830.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Percent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.

A number that is expressed as a fraction of hundred is what it is.

it is mostly used to compare and determine ratios and is represented by the symbol %.

We are given that:-

so the amount after VAT = 4200+4200*15%

= 4200+4200+0.15

= 4200+630= 4830.

therefore, the selling price of laptop after VAT is Rs 4830.

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Step-by-step explanation:

1. sqrt(x + 6)/5 = 2

sqrt(x + 6) = 10

x + 6 = 100

x = 94

sqrt(94 + 6)/5 = 2

sqrt(100)/5 = 2

10/5 = 2

2 = 2

confirmed.

2.

sqrt(9x + 2) = sqrt(11x - 12)

9x + 2 = 11x - 12

14 = 2x

x = 7

sqrt(9×7 + 2) = sqrt(11×7 - 12)

sqrt(63 + 2) = sqrt(77 - 12)

sqrt(65) = sqrt(65)

confirmed.

3.

cubic root(6x + 3) + 10 = 13

cubic root(6x + 3) = 3

6x + 3 = 27

6x = 24

x = 4

cubic root(6×4 + 3) + 10 = 13

cubic root(24 + 3) + 10 = 13

cubic root(27) + 10 = 13

3 + 10 = 13

13 = 13

confirmed.

4.

2×sqrt(5x - 4) - 24 = -6

sqrt(5x - 4) - 12 = -3

sqrt(5x - 4) = 9

5x - 4 = 81

5x = 85

x = 17

2×sqrt(5×17 - 4) - 24 = -6

2×sqrt(85 - 4) - 24 = -6

2×sqrt(81) - 24 = -6

2×9 - 24 = -6

18 - 24 = -6

-6 = -6

confirmed.

The simplified expression is 2cos²(x) + sinx - 1 = 0

The expression we will be simplifying is

=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.

To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:

(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)

Simplifying this expression using the distributive property, we get:

(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)

Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:

1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1

Similarly, for the second fraction, we can use the same identity to obtain:

1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1

Substituting these values back into the original expression, we get:

1 + 1 = 2sinx/(sin⁴x - cos⁴x)

Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:

sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ

Substituting this back into the expression, we get:

2 = 2sinx/(sin²ˣ - cos²ˣ)

Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):

2 = -2sinx/cos(2x)

Multiplying both sides by -cos(2x), we get:

-2cos(2x) = 2sinx

Dividing both sides by 2, we get:

-cos(2x) = sinx

Using the double-angle formula for cosine, we get:

-2cos²(x) + 1 = sinx

Simplifying this expression, we get:

2cos²(x) + sinx - 1 = 0

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Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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Answer:

The perimeter of the shape is 53km.

Answer : 53km

Step-by-step explanation: To find the perimeter you need to add all the sides so 8+18+18+9=53 and dont forget the unit km! Have a great day! And good luck!

Answer:

9 words

Step-by-step explanation:

We know

He has 12 words to memorize, and he is 3/4 done.

How many words has Pablo memorized so far​?

We Take

12 x 3/4 = 9 words

So, Pable has memorized 9 words.

Answer:

P(A n B) = 1/4

Step-by-step explanation:

We know that:

P(A U B) = P(A) + P(B) - P(A n B)

Substituting the given values, we get:

3/8 = 1/2 + 3/4 - P(A n B)

Simplifying, we get:

P(A n B) = 1/4

Answer: P ( A n B ) = 7/8

Step-by-step explanation:  P ( A U B ) = P(A) + P(B) - P( A n B )

                                                         3/8   =   1/2  + 3/4 - P( A n B )

                                                         3/8   =   5/4 - P ( A n B )

                                               P ( A n B )  =  5/4 - 3/8

                                               P ( A n B )  =   7/8

a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.

b) The mean salary of the given model by using the probability density function is approximately $270.86.

a) The cumulative distribution function of the given random variable is provided as follows:

F(x) = {1−kx^−3 if x>44000, and 0 otherwise

The cumulative distribution function is given as

F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)

We need to check the value of the cumulative distribution function at 44000

We have, F(44000) = 0

0 = 1−k(44000)^−3

⇒ 1 = k(44000)^−3

⇒ k = 1/(44000)^−3

⇒ 5.427 x 10^−12

Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)

Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68

b) The probability density function is given as,

f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise

The mean or expected value of the random variable is given as

E(X) = ∫[−∞,∞]xf(x)dx

= ∫[44000,∞]x(3kx^−4)dx

= 3k∫[44000,∞]x^−3dx

= 3k[(−1/2)x^−2] [∞,44000]

= (3k/2)(44000)^−2

= 270.86 (approx.)

Therefore, the mean salary given by the model is $270.86 (approx.)

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Answer:

Sam's commission for last month can be calculated as follows:

Commission = 3% of sales

Commission = 3/100 * $46,400

Commission = $1,392

Therefore, Sam's total income for last month would be his salary plus commission:

Total income = Salary + Commission

Total income = $1,950 + $1,392

Total income = $3,342

So Sam earned $3,342 in total for last month.

Step-by-step explanation:

Step-by-step explanation:

the law of sine is

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides. A, B, C are the corresponding opposing angles.

you fill in what you know and then solve for what you don't know. these are just regular equations. you multiply or divide or add or subtract the same things on both sides and try to get the missing side isolated on one side of an equation.

Answer:

Step-by-step explanation:

C.) P = 3(a+2)-4

The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

Growth of apple tree= 2feet

Now,

Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:

3(h+2) - 4 = p

Simplifying, we get:

3h + 2 = p

Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.

Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:

P = 3a + 6

This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:

P = 2a + 10

This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:

P = 3a + 2

Therefore, by equation the answer will be P=3(a+2)-4.

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Answer:

D

Step-by-step explanation:

The square root of 50 is approximately equal to 7.07

-7.1111… can be rounded to -7.11

23/3 is equal to approximately 7.67

-7 1/5 is equal to -7.2

Answer:

Para calcular el precio original de los auriculares antes del descuento, podemos usar la fórmula:

Precio original = Precio después del descuento / (1 - Porcentaje de descuento)

Donde "Precio después del descuento" es el costo de los auriculares después del descuento, y "Porcentaje de descuento" es el porcentaje aplicado como descuento. En este caso, el porcentaje de descuento es del 20%, es decir, 0.2 en términos decimales.

Sustituyendo los valores conocidos, obtenemos:

Precio original = 260 / (1 - 0.2)

Precio original = 260 / 0.8

Precio original = 325

Por lo tanto, el costo original de los auriculares antes del descuento era de $325.:

Answer:

The answer is D. (1-0.2)h=260

Step-by-step explanation:

The following statements correctly describe how the graph of the geometric sequence: 640, 160, 40, 10, ... should appear:

The given sequence is 640, 160, 40, 10, ... which is a geometric sequence.

Here, the first term is 640 and the common ratio is ¼

The terms of a geometric sequence can be written as an = a₁(r)⁽ⁿ⁻¹⁾

Here, a₁ = 640, and r = ¼.

Hence, the nth term of the given sequence is given by the formula:

an = 640(1/4)⁽ⁿ⁻¹⁾

The graph of the given sequence will appear as shown below:

The given sequence is a decreasing sequence, which means the terms of the sequence keep decreasing as the value of n increases.

Therefore, the graph will show exponential decay.

The domain of the sequence will be the set of natural numbers, which is {1, 2, 3, ...}, since we cannot find any term before the first term.

Therefore, the first term is the initial term and we can count the other terms of the sequence in natural numbers.

Hence, the domain will be the set of natural numbers.

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Answer:

the graph will show exponential decay.

the domain will be the set of natural numbers.

Step-by-step explanation:

The answer above is correct.

We have that, the correct match of the description with its mathematical expression is provided with the mathematical expression "or".

Correct matching of the description to its mathematical expression is given as follows: The residual of an estimated regression equation is compared to the mathematical expression "or".

Explanation: A residual is the difference between the actual value of a variable and the predicted value of that variable. The residuals are denoted as "or". Therefore, the Residual of an estimated regression equation is compared to the mathematical expression "or".

Other options are incorrect as follows: Oba does not match any description given in the question. Therefore, it is a wrong option. Obo doesn't match any description given in the question. Therefore, it is a wrong option. Oy+ 61 does not match any description given in the question. Therefore, it is a wrong option.

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Answer:Given : number of hours spent studying for a history final exam and the score on that exam.

To Find : Which value is an outlier

(1.5, 65)

(3.5, 71)

(4.5, 98)

(6.5, 88)

Solution:

Number of hours spent studying =x            

Exam score   = y

x         y

1.5       65

2         68

3.5      71

4.5      98

6         82

1.5 -   2   difference = 0.5

2 - 3.5     difference = 1.5

3.5 - 4.5   difference = 1

4.5 - 6       difference = 1.5

No outlier

65  - 68   Difference  3

68 - 71      Difference  3

71 -  98      Difference  27

71 - 82     Difference  11

Hence 98 is outlier

(4.5    ,  98 )  is outlier

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Mrs. Juarez graded ten English papers and recorded the scores. 92 ...

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If the first quartile is 142 and the semi-interquartile range is 18, find ...

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Step-by-step explanation:

For the given functions, f(x)=x²+3x-7, g(x)=3x+5 and h(x)=2x²-4, f(g(x))= 9x² + 30x + 33, h(g(x))= 18x² + 60x + 46, (h-f)(x)= x² - 3x + 3, (f+g)(x)= x² + 6x - 2.

In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.

Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.

Functions can be represented in various ways, such as algebraic expressions, tables, graphs, or verbal descriptions. They can be linear or nonlinear, continuous or discontinuous, and may have various properties such as symmetry, periodicity, and asymptotic behavior.

To solve these problems, we substitute the function g(x) for x in f(x) and h(x) and simplify the resulting expressions.

f(g(x)):

f(g(x)) = f(3x+5) = (3x+5)² + 3(3x+5) - 7 (using the definition of f(x))

= 9x² + 30x + 33

h(g(x)):

h(g(x)) = h(3x+5) = 2(3x+5)² - 4 (using the definition of h(x))

= 18x² + 60x + 46

(h-f)(x):

(h-f)(x) = h(x) - f(x) = (2x² - 4) - (x² + 3x - 7) (using the definitions of h(x) and f(x))

= x² - 3x + 3

(f+g)(x):

(f+g)(x) = f(x) + g(x) = x² + 3x - 7 + 3x + 5 (using the definitions of f(x) and g(x))

= x² + 6x - 2

When multiplying out a squared term, such as (3x+5)², we can use the FOIL method, which stands for First, Outer, Inner, Last. We multiply the first terms, then the outer terms, then the inner terms, and finally the last terms, and then add up the results. For example:

(3x+5)² = (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)

= 9x² + 15x + 15x + 25

= 9x² + 30x + 25

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The zero product property states that if the product of two real numbers is 0, then one of the numbers must be 0.

The contrapositive of the above answer is "If neither of the numbers is 0, then the product is not 0."

In other words, if two non-zero numbers are multiplied, then the result is non-zero.

a)  We can use the zero-product property to factorize the expression as an example of[tex](x - 2) (x - 3) = 0[/tex], and obtain the two roots of the equation, [tex]x = 2[/tex]and [tex]x = 3[/tex]. Therefore, the zero-product property is a powerful tool that allows us to solve complex problems and equations involving algebraic expressions and real numbers.

b) A non-zero product can only be obtained by multiplying two non-zero numbers. So, if the product is zero, then at least one of the factors must be zero as well. This is the informal version of the contrapositive of the zero product property.

c)The zero product property is an essential concept in algebra that involves the understanding of real numbers and their product. It is widely used in algebra and calculus to solve equations and expressions that involve polynomial functions, quadratic equations, and exponential functions.

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Answer:

N

Q

Cost (dollars)

0

cost of the tickets in dollars.

32 Each ticket to ride a carousel costs $2 50. The table st

relationship between x, the number of tickets bought, -

Y

8 10

Number of Tickets

LA COORDINATE PLANE

Carousel Rides

Number of Tickets, x

1

5

2

3

Carousel Rides

which graph best represents the data shown in the table?

Carousel Rides

Carousel Rides

Cost (dollars)

DO

6

6

Cost (dollars)

12

0

Cost, y (dollars)

2.50

5.00

7.50

12.50

4

2

6

Number of Tickets

Carousel Rides

12

Step-by-step explanation:

Based on the data given in the table, the graph that best represents the relationship between the number of tickets bought and the cost of riding the carousel is the one that shows a linear relationship between the two variables.

The table shows that for each ticket bought, the cost of riding the carousel increases by $2.50. This means that the relationship between the number of tickets bought and the cost of riding the carousel is linear, with a slope of $2.50.

Therefore, the graph that best represents this relationship is the one that shows a straight line with a slope of $2.50 passing through the points (1, $2.50) and (5, $12.50). This graph is represented by the option labeled "Carousel Rides" with the x-axis showing the number of tickets bought and the y-axis showing the cost in dollars.

The possible probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice is 0.2.

Probability is a branch of math that studies the chance or likelihood of an event occurring.
A biased dice was rolled and the probability distribution of the outcomes are as follows then the outcomes are [tex] 1, 2, 3, 4, 5, 6[/tex]

Probability: [tex]0.2, 0.1, 0.3, 0.1, 0.2, 0.1[/tex]

To find the probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice.

Probability of getting [tex]3[/tex]:

Outcome = [tex]3[/tex]

Probability of getting = [tex]^3P(3) = 0.3[/tex]

So, the possible probability of getting [tex]3[/tex] is [tex]0.3[/tex].

Probability of getting [tex]5[/tex]

So, the outcome of [tex]5[/tex]

Probability of getting [tex]^5P(5) = 0.2[/tex]

So, the possible probability of getting 5 is 0.2.

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