Determine the values of A, B, and C when y - 7 = 3(x - 4) is written in standard form, Ax + By = C.

Answer:

According to the scale, 1 inch on the drawing represents 1.5 feet in real life. So, to find the actual length of the door, we need to multiply the length on the drawing by the scale factor:

4 inches x 1.5 feet/inch = 6 feet

Similarly, to find the actual width of the door, we need to multiply the width on the drawing by the scale factor:

7 inches x 1.5 feet/inch = 10.5 feet

Therefore, the actual measurements of the door are 6 feet by 10.5 feet.

Answer:

Step-by-step explanation:

its C

The equation which correctly relates the measure of diameter and radius of a circle is (c) r = d/2.

The Diameter (d) of a circle is defined as the distance across the circle through its center. The radius (r) of a circle is defined as the distance from the center of the circle to any point on the circle.

We know that the radius of the circle is half of diameter, because it extends from the center to the edge of the circle, while the diameter extends all the way across the circle.

So, we can express the relationship between d and r as:

⇒ d = 2r

To solve for r, we can divide both sides by 2:

We get,

⇒ r = d/2

Therefore, The correct equation is Option (c) r = d/2.

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The given question is incomplete, the complete question is

Which of the following correctly relates the measures of the diameter (d) and radius (r) of a circle?

(a) d = r/2

(b) r = 2d

(c) r = d/2

(d) d = 2/r

Answer: f(-1/2) = 16/3

Step-by-step explanation:

Substituting -1/2 for x in the given function:

f(-1/2) = (-2/3)(-1/2) + 5

f(-1/2) = 1/3 + 5

f(-1/2) = 16/3

Therefore, f(-1/2) = 16/3.

Answer:

x = 17

Step-by-step explanation:

Subtract 6x from both sides:

2x - 18 = 16

Add 18 on both sides to isolate the variable:

2x = 18 + 16

2x = 34

Divide by 2: x = 17

Answer:

Angle AIC is vertical.

Step-by-step explanation:

Defn of vertical angles

1. The total yards of each fabric that Karina will buy to make a quilt is as follows:

a) Green Fabric = 12 square yards

b) Burgundy Fabric = 19 square yards

2. The total yards of fabric she will buy is 31 square yards.

The total yards of fabric can be determined by unit conversion using division operation.

Given that 36 inches = 1 yard, the square inches of fabric are converted to square yards by dividing the total by 36.

The total number of green fabric Karina requires = 420 square inches

= 12 square yards (420/36)

The total number of burgundy fabric Karina requires = 688 square inches

= 19 square yards (688/36)

The total number of fabric (green and burgundy) = 1,108 square inches (420 + 688)

36 inches = 1 yard

1,108 inches = 30.78 square yards (1,108/36)

= 31 square yards or (12 + 19)

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Answer:

21 years old

Step-by-step explanation:

Set Alan's age as x, Bernice's age as y

2x=y

x-4+y-4=55

x+y=63

3y=63

x=21

y=42

If the slope of the graph is increasing from positive x-axis to negative x-axis, then the function is not that decreasing. Therefore, Jonathan's statement is incorrect.

The function is decreasing on intervals where the slope is negative. In this case, since the slope is increasing from positive x-axis to negative x-axis, the function is decreasing on the interval where x is negative.

To determine this interval more precisely, we would need to find the x-value(s) where the slope changes sign from positive to negative. These x-values correspond to critical points, such as local maximums or minimums. The function is decreasing before a local maximum and after a local minimum.

Therefore, Jonathan's statement is not correct, and the function represented by the graph is decreasing on the interval where x is negative.

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Answer:

the two numbers are 15 and 35, and their ratio is 3:7, and their difference is 20.

Step-by-step explanation:

Answer:

7,560 inches.

Step-by-step explanation:

Given: 7 in x 3 in x 6 in x 4 in x 15 in = ?

First, multiply 7 and 3:

21 in x 6 in x 4 in x 15 in

Then multiply 21 and 6:

126 in x 4 in x 15 in

Then multiply 4 and 15:

126 in x 60 in

Finally, multiply 126 and 60:

= 7,560 inches.

Answer:

Step-by-step explanation:

This is an example of a hypergeometric distribution problem, where we have a population of 10,000 clock radios with 500 defective ones, and we want to calculate the probability of getting at least one defective radio in a random sample of 10 without replacement.

The probability of getting no defective radios in the sample is:

(9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)

This is because, for the first radio, there are 9500 good radios out of 10,000, and for the second radio, there are 9499 good radios out of 9,999, and so on.

The probability of getting at least one defective radio in the sample is then:

1 - (9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)

which is approximately equal to 0.401.

Therefore, the probability that the entire batch will be rejected is 0.401.

The perimeter of the pond is 2.92 meters.

A right-angled triangle is a triangle in which one of the angles measures exactly 90 degrees, also known as a right angle.

The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.

The perimeter of a right-angled triangle is the sum of the lengths of its three sides.

Here we have

The Hypotenuse of the triangle is 1.46 m    

The angle between hypotenuse and perpendicular height = 73°

From triagonometric ratios,

=> cos A = Perpendicular height/ Hypotenuse.

=> cos (73) = Perpendicular height/1.46

=> Perpendicular height = 1.46 × 0.29 = 0.42 m

As we know from Pythagoras' theorem,

Hypotenuse² = side² + side²    

Side = √Hypotenuse² - side²  

= √[(1.46)²- (0.42)²]  = 1.04

Therefore, the sides of the pond are 1.46 m, 0.42 m, and 1.04

Hence, perimeter of the pond =  1.46 + 0.42 + 1.04 = 2.92 meters  

Therefore,

The perimeter of the pond is 2.92 meters.

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The complete Question is given below

Answer:

Area = 559.17 square feet

Perimeter = 94.26 ft

Step-by-step explanation:

Make sure all the units are the same and consistent.

r = radius of semi-circle

 = [tex]\frac{Diameter}{2}[/tex]

 = [tex]\frac{18}{2}[/tex] ft

 = 9 ft

Area of composite figure = Area of rectangle + Area of semi-circle:

                                          = [Length × Breadth] + [[tex]\frac{1}{2}[/tex] × (Area of circle)]
                                          = [24 ft × 18 ft] + [[tex]\frac{1}{2}[/tex] × ([tex]\pi r^{2}[/tex])]

                                          = 432 [tex]ft^{2}[/tex] + [[tex]\frac{1}{2}[/tex] × ([tex]\pi 9^{2}[/tex])] [tex]ft^{2}[/tex]

                                          = 432 + [[tex]\frac{1}{2}[/tex] × (3.14) ×(81)]

                                          = 559.17[tex]ft^{2}[/tex]

Perimeter of composite figure =

     Circumference of semi-circle + 3 outer sides of rectangle:

 = [[tex]\frac{1}{2}[/tex] × [tex]2\pi r[/tex]] + [24 + 18 + 24]

 = ( [tex]\pi r[/tex] + 66) ft

 = [(3.14)(9) + 66] ft

 = 94.26 ft

It ahs been proved by mathematical induction that the sum of the squares of 4 consecutive integers is an even integer.

To prove that the sum of the squares of 4 consecutive integers is an even integer.

Let x, (x + 1), (x + 2), (x + 3) be the four consecutive integers.

The sum of the squares of these integers are:

S = x² + (x + 1)² + (x + 2)² + (x + 3)²

Expanding this gives us:

S = 4x² + 12x + 14

Simplifying this gives:

S = 2(2x² + 6x + 7)

The number 2x² + 6x + 7 is either even number or odd number.

However, since it is multiplied by 2x² + 6x + 7, the sum will always be an even number.

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[tex]\begin{cases} x=\frac{2+i\sqrt{2}}{3}\implies 3x=2+i\sqrt{2}\implies 3x-2-i\sqrt{2}=0\\\\ x=\frac{2-i\sqrt{2}}{3}\implies 3x=2-i\sqrt{2}\implies 3x-2+i\sqrt{2}=0 \end{cases} \\\\\\ \stackrel{ \textit{original polynomial} }{a(3x-2-i\sqrt{2})(3x-2+i\sqrt{2})=\stackrel{ 0 }{y}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ \textit{difference of squares} }{[(3x-2)-(i\sqrt{2})][(3x-2)+(i\sqrt{2})]}\implies (3x-2)^2-(i\sqrt{2})^2 \\\\\\ (9x^2-12x+4)-(2i^2)\implies 9x^2-12x+4-(2(-1)) \\\\\\ 9x^2-12x+4+2\implies 9x^2-12x+6 \\\\[-0.35em] ~\dotfill\\\\ a(9x^2-12x+6)=y\hspace{5em}\stackrel{\textit{now let's make}}{a=-\frac{1}{9}} \\\\\\ -\cfrac{1}{9}(9x^2-12x+6)=y\implies \boxed{-x^2+\cfrac{4}{3}x-\cfrac{2}{3}=y}[/tex]

In the word problem,

a)Gallons per minute change is -2/3 gallons per minute

b) 7.5 minutes to drain the other 5 gallons

c)The tank was full 4 1/2 minutes before Jada arrived.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

a) Gallons per minute change is -2/3 gallons per minute  since it decreases by 2 gallons in 3 minutes.

b)  we have 5 gallons and lose 2/3 gallons per minute

=> (2/3 gal/minute)(x minutes) = 5 gallons

=> x = 5(3/2) = 15/2 = 7.5 minutes to drain the other 5 gallons

c)  There was 10 gallons when the tank is full . That is 3 gallons more than the 7 gals there when Jada arrived.

=>  (2/3)(x) = 3

=> x = 3(3/2) = 9/2 = 4 1/2 minutes

The tank was full 4 1/2 minutes before Jada arrived.

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Answer:

Se depositan $ 8.000 en un banco que reconoce una tasa de interés del 36% anual, capitalizable mensualmente. ¿Cuál será el monto acumulado en cuatro años?

Step-by-step explanation:

Para resolver este problema, podemos utilizar la fórmula del interés compuesto:

A = P*(1 + r/n)^(n*t)

Donde:

A: el monto acumulado después de t años

P: el capital inicial

r: la tasa de interés anual

n: el número de veces que se capitaliza el interés por año

t: el tiempo en años

En este caso, tenemos:

P = $8.000

r = 36% = 0.36

n = 12 (ya que la tasa de interés se capitaliza mensualmente)

t = 4 años

Sustituyendo estos valores en la fórmula, obtenemos:

A = $8.000*(1 + 0.36/12)^(124)

A = $8.000(1 + 0.03)^48

A = $8.000*(1.03)^48

A = $16.751,83

Por lo tanto, el monto acumulado en cuatro años será de $16.751,83.

The correct answer is C. A normal distribution is a symmetric probability distribution that is bell-shaped when graphed. When plotted on a horizontal scale, the curve starts on the horizontal axis, rises to a central peak, and then falls back to the horizontal axis.

The curve is symmetric, meaning that the left and right halves of the curve are mirror images of each other. The curve approaches the horizontal axis but never touches it, which indicates that there is a non-zero probability of observing values at any distance from the mean, although the probability decreases as the distance from the mean increases.

Normal distribution is a type of probability distribution that is commonly found in natural and social phenomena, where the majority of the observations tend to cluster around the mean, with fewer observations further away from the mean.

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The code segment that assigns bonus correctly for all possible integer values of score is D, which uses nested if statements to implement the game's rules for assigning a value to bonus based on the value of score.

The code segment that assigns bonus correctly for all possible integer values of score is D:

IF(score < 50)

{

   bonus ← Ø

}

ELSE

{

   IF (score > 100)

   {

       bonus ← score (10)

   }

   ELSE

   {

       bonus ← score

   }

}

This code segment correctly implements the rules for assigning a value to bonus based on the value of score. It first checks if score is less than 50, and if so, it assigns 0 to bonus. If score is greater than or equal to 50, it checks if score is greater than 100, and if so, it assigns 10 times score to bonus. Otherwise, it assigns score to bonus. This covers all possible integer values of score and ensures that bonus is assigned correctly according to the game's rules.

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Complete question is in the image attached below

The given statement "Star clusters with lots of bright, blue stars of spectral type O and B are generally younger than clusters that don't have any such stars." is True. The reason for this is that O and B stars are short-lived and burn through their fuel quickly.

The reason for this is that O and B stars burn through their fuel quickly, causing them to exhaust their nuclear fuel and end their lives in a relatively short period, typically within a few tens of millions of years.

On the other hand, stars of lower mass and cooler temperatures, like G and K type stars like our sun, have longer lifetimes and take billions of years to exhaust their nuclear fuel.

Therefore, clusters without any bright, blue stars are likely to have evolved for longer periods, allowing these short-lived stars to have already expired.

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In order to see the school of fish, the scuba diver descended to a depth of 14 feet below sea level.

Hοw far sοmething stretches is described by the cοncept οf depth. The pοοl has a six-fοοt depth. Unknοwn is the well's depth. We can use the fοllοwing equatiοn tο determine the scuba diver's initial depth:

Initial depth = Final depth + Depth Change The scuba diver's change in depth is positive because he rose f feet (positive because he went up) and ended up 16 feet below the surface. Therefοre:

initial depth = 16 + f - 30 initial depth.

Simplifying the phrase:

Original depth = -14 + f

The scuba diver reached his initial depth there after descended another 14 feet below sea level to observe the school of fish.

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Questions-

A scuba diver was 30 feet below sea level when he ascended f feet to a depth of 16 feet below sea level to see a school of fish. what is her new elevation now?

Step 1: Arrange the arrays so that A and B are in the same order: A = [ 1 2 4 0 5 6 ], B = [ 7 3 2 5 1 9]

Step 2: To find C = A+B, add each element of A and B together.

C = [1+7, 2+3, 4+2, 0+5, 5+1, 6+9]

C = [8, 5, 6, 5, 6, 15]

Step 3: To find D = A-B, subtract each element of B from A.

D = [1-7, 2-3, 4-2, 0-5, 5-1, 6-9]

D = [-6, -1, 2, -5, 4, -3]

Answer:

2

Step-by-step explanation:

since d=7 and the equation is d-5 in the place of d we'll put 7 therefore 7-5=2

Uri paid a total of $85.47 for the landscaping service including tax and tip.

Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.

Given that company charged $74 for the service plus 5% tax.

The tax is 5%, that is:

Tax = 5% of $74 = 0.05 x $74 = $3.70

Cost after tax = $74 + $3.70 = $77.70

Now, tip is 10%:

Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77

Total cost = $77.70 + $7.77 = $85.47

Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.

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i) Find the mean, median, and mode of the frequency table as follows:

ii) The average that justifies the teacher's statement congratulating the class that 'over three quarters were above average' is the average mark of 10, which is 5.

The mean refers to the average or the quotient of the total values divided by the number of items.

The median is the middle value in the data, which occurs with marks 8 for the 13th and 14th students.

The mode is the value that occurs most frequently, which is 3 which occurs 6 times.

Frequency Table:

Mark   Frequency  Cumulative Frequency

3              6                            18 (0 + 3 x 6)

4              3                            30 (18 + 4 x 3)

5              1                            35 (30 + 5 x 1)

6              2                           47 (35 + 6 x 2)

7              0                           47 (47 + 7 x 0)

8              5                           87 (47 + 8 x 5)

9              5                         132 (87 + 9 x 5)

10            4                         172 (132 + 10 x 4)

Mean = 6.6 (172/26)

Median = 8

Mode = 3

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a) D. No. A person can be both male and bet on professional sports at the same time

b) If the events A and B are independent, P(A&B) = P(A) x P(B)

P(male and also bets on professional sports) = 0.484x0.13 = 0.0629

c) P(male or bets in professional sports) = P(male) + P(bets in professional sports) - P(male and also bets on professional sports)

= 0.484 + 0.13 - 0.0629

= 0.5511

d) A. The assumption was incorrect and the events are not independent

(if the were independent, the percentage would have been 6.29)

e) A. P(male or bets on professional sports = 0.484 + 0.13 - 0.081

= 0.5330

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Answer:

Step-by-step explanation:

In the boys triangle:

  [tex]tanx=\frac{56}{48}[/tex]

        [tex]x=tan^{-1}(\frac{56}{48} )=49.4\textdegree[/tex]

Because triangles are similar:

   [tex]tan 49.8=\frac{h}{32}[/tex]

[tex]h=32tan49.8 = 37.3[/tex]

The probability that, out of 18 independent samples received from one river, just two were contaminated is 0.8438.

In the following 18 samples to be evaluated,

Let X = the number of samples that now the pollutant is present in.

Thus, with p = 0.10 and n = 18, X is a binomial random variable.

Using the binomial theorem:

[tex](^{n} _{r} ) p^{x} q^{n-x}[/tex]

p = 0.10

q = 1 - 0.10 = 0.9

n = 18

The likelihood that only two samples out of 18 obtained in different ways from the same river were polluted

P(x = 2) = [tex](^{18} _{2} ) (0.1)^{2} (0.9)^{18-2}[/tex]

=  [tex](^{18} _{2} ) (0.1)^{2} (0.9)^{16}[/tex]

= 153 x 0.01 x 0.1853

= 0.8438

Thus, the probability that, out of 18 separate samples received from one river, just two were contaminated is 0.8438.

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