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Answer:

d² - 24d + c = (d - 12)² - 144 + c

The measure of angle D is 45°

Similar triangles have the same corresponding angle measures and proportional side lengths. When two triangles are similar, the corresponding angles are equal.

And also the ratio of corresponding sides of similar triangles are equal.

To know the corresponding angles

side AC is corresponding to side EF, therefore angle D is congruent to angle A

angle D = 45°

OR , we can use the sum of angles In a triangle , which is 180°

angle D = 180 -( 72+63)

= 180 - 135

= 45°

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Answer:

20 miles / 5 days / 2 trips = 2 miles each way

Step-by-step explanation:

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

12%

Explanation:

The $18 don't matter in this problem.

120/1000 is not a lot so it would be predicted to be 12% due to the amount.

Answer: \(8\) and \(8\)

Step-by-step explanation:

Let the numbers be \(x\) and \(y\).

\(x+y=16 \implies y=16-x\\\\xy=64 \longrightarrow x(16-x)=64\\\\16x-x^2 =64\\\\x^2 -16x+64=0\\\\(x-8)^2=0\\\\x=8 \implies y=8\)

it's the top left corner

Answer:

top left!

Step-by-step explanation:

add it all together and get that! :D

The list that gives the sample space for pulling two slips of paper out of the bucket with replacement is List 4.

Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.

The sample space for pulling two slips of paper out of the bucket with replacement means that after drawing the first slip of paper, it is returned to the bucket before drawing the second slip. This means that each draw is independent of the previous draw, and the possible outcomes of each draw remain the same for all subsequent draws.

The possible outcomes for each draw are {Red, Blue, Yellow}, and there are three possible outcomes for each draw.

Since we are drawing with replacement, each draw has the same possible outcomes and the same number of outcomes. So, the total number of possible outcomes for two draws is simply the number of outcomes for a single draw raised to the power of 2:

\(3^2 = 9\)

Therefore, the list that gives the sample space for pulling two slips of paper out of the bucket with replacement is List 4.

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16 is the number which is one-fifth of a number when one-fourth of that same number is 20.

As per the given data:

One-fourth of the number is resulted to 20.

Here we have to determine the result of one-fifth of the same number from the given options.

An expression for a portion of a whole is a fraction.

For any real numbers, the fractional component of x is defined.

Let the number be X.

One-fourth of a number is 20 which means:

Multiply the one-fourth fraction with an unknown number which results in the number 20.

\($\frac{1}{4}\)  (X) = 20

X = 20 × 4

X = 80

Now we have to determine that one-fifth of the same number.

Multiply the one-fifth fraction by 80.

We get:

= \($\frac{1}{5}\) (80)

= \($\frac{1}{5}\)   × 5 × 16

= 16

One-fifth of the number 80 is 16

Therefore Option (D) - 16 is the correct answer.

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The commutative property of multiplication says that:

a x b = b x a

It means that no matter the order of the factors, the product is the same.

So, the statement that uses the commutative property of multiplication is:

8 x 4 = 4 x 8

Answer: 8 x 4 = 4 x 8

Answer:

4.5

Step-by-step explanation:

y : 2

y = 9 so, we have:

9 :2 =4.5

Explanation

In the question, we can find the missing angles which can be seen below.

Via this, the triangles are similar based on Angle-Angle-Angle similarity

Answer:

Where's the picture?

The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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Answer:

net salary = 8047.5

Step-by-step explanation:

his basic salary is 8700

7.5% of that is (8700)(0.075) = 652.5

He gives this away, so his net salary will become

8700 - 652.5 = 8047.5 = net salary

The mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

To find the mean number of movies the students saw, you need to calculate the average of the given data. Here are the reported numbers of movies seen by the 6 students: 14, 11, 15, 19, 12, 10.

To calculate the mean, you sum up all the reported numbers and divide by the total number of students. In this case, the total number of students is 6.

So, let's calculate the mean:

(14 + 11 + 15 + 19 + 12 + 10) / 6 = 81 / 6 = 13.5

Therefore, the mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

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68% of states have an infant mortality rate between 5.36 and 8.60 percent.

In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.

In this problem, we have that:

Assuming that the distribution is normal, what percentage of states have an infant mortality rate between 5.36 and 8.60 percent (per 1,000 live births)?

\(\sf 5.36 = 6.98 - 1\times1.62\)

So, 5.36 is one standard deviation below the mean.

\(\sf 8.60 = 6.98 + 1\times1.62\)

So 8.60 is one standard deviation above the mean.

Therefore, by the Empirical Rule, 68% of states have an infant mortality rate between 5.36 and 8.60 percent.

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Regine's father is currently receiving a salary of 29037.50.

A percentage increase in mathematics is the proportion by which a quantity or value has grown in comparison to its initial value. It is computed by subtracting the original value from the new value, multiplying the result by 100, and then subtracting the difference between the two values. The percentage increase formula is:

(new value - original value) / 100% of the original value is the percentage increase.

The yearly increase is 15%, thus:

salary increase = 25250 x 0.15 = 3787.50

The current salary is:

current salary = salary from two years ago + salary increase

current salary = 25250 + 3787.50

current salary = 29037.50

Hence, Regine's father is currently receiving a salary of 29037.50.

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Mr. X reduces his weight in a ratio of 4:17. This means that for every 4 units of weight he loses, his initial weight was divided into 17 equal parts.

To determine the ratio by which Mr. X reduces his weight, we need to compare his initial weight of 85 kg with his target weight of 65 kg.

The reduction in weight is calculated as the difference between the initial weight and the target weight, which in this case is 85 kg - 65 kg = 20 kg.

The ratio can be expressed as a fraction, where the numerator represents the reduction in weight and the denominator represents the initial weight:

Reduction in weight / Initial weight

Substituting the values, we have:

20 kg / 85 kg

Simplifying the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 5 in this case:

(20 kg / 5) / (85 kg / 5) = 4/17

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Unit analysis is a tool that we can use to convert units. It involves multiplying the original number by a fraction to cancel out units.

We're given:

\(\dfrac{3240\hspace{4}feet}{hour}\)

We also know that:

\(\dfrac{hour}{60\hspace{4}minutes}\)

Multiply the two to cancel out the hour:

\(\dfrac{3240\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{3240\hspace{4}feet}{60 minutes}\)

Simplify:

\(=\dfrac{54\hspace{4}feet}{minute}\)

\(\dfrac{54\hspace{4}feet}{minute}\)

The derivative, d/dx (eˣ) of the function eˣ is eˣ

To prove that d/dx (eˣ) = eˣ

The definition for the derivative of the function eˣ is:

\(\frac{d}{dx}[e^{x} ] =\lim_{\Delta x \to 0} \frac{e^{x+\Delta x} -e^{x} }{\Delta x}\)

         \(=\lim_{\Delta x \to 0} \frac{e^{x}.e^{\Delta x} -e^{x} }{\Delta x}\)

Factor out eˣ since it is not affected by the limit:

        \(=e^{x}\lim_{\Delta x \to 0} \frac{e^{\Delta x} -1 }{\Delta x}\)

Let n = e^(Δx)  - 1

n + 1 =  e^(Δx)

ln(n+1) = Δx

Δx → 0 ⇒ n → 0

Thus, substitute n into the expression above, this gives:

       \(=e^{x}\lim_{n \to 0} \frac{n}{\ln(n+1)}\)

Multiply through by 1/n:

       \(=e^{x}\lim_{n \to 0} \frac{1}{\frac{1}{n} \ln(n+1)}\)

      \(=e^{x}\lim_{n \to 0} \frac{1}{ \ln(n+1)^{\frac{1}{n} } }\)

Note: a ln(b) = ln(bᵃ)

The definition of e is:

\(e =\lim_{n \to 0} {(n+1)^{\frac{1}{n} } }\)

Substitute the value of e into the initial expression:

      = eˣ . 1/ln(e)              (ln e = 1)

     = eˣ . 1/1

     = eˣ

Therefore,  d/dx (eˣ) = eˣ

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Answer:

Step-by-step explanation:

Given the AP

We can see that

The sum of the first n terms formula is

     \(S_n=\cfrac{n}{2} [2a+(n-1)d]\)

Substitute the values and considering n = 19, find the sum  

    \(S_{19}=\cfrac{19}{2} [2*3+(19-1)*5]=\cfrac{19}{2} [6+90]=912\)

Answer:

912

Step-by-step explanation:

Sum of the first n terms of an arithmetic series:

\(S_n=\dfrac12n[2a+(n-1)d]\)

where:

Given arithmetic series:  3 + 8 + 13 + 18 + ...

Therefore:

To find the sum of the first 19 terms, substitute the given values together with n = 19 into the Sum formula:

\(\implies S_{19}=\dfrac{1}{2}(19)\left[\:2(3)+5(19-1)\:\right]\)

\(\implies S_{19}=\dfrac{19}{2}\left[\:6+90\:\right]\)

\(\implies S_{19}=\dfrac{19}{2}\left[\:96\:\right]\)

\(\implies S_{19}=912\)

Answer:

0

Step-by-step explanation:

Since the line is horizontal and it isn't moving up or down and is in a still motion, the slope would be 0.

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Answer:

149 sq. ft

Step-by-step explanation:

For the triangle:

Base = 16-9 = 7 ft

Area of Triangle = 1/2 of  b.h

= 1/2 of 7 * 6

= 21 sq. ft

Area of Rectangle = l.b

= 5 * 16

= 128 sq. ft

Total Area = 149 sq. ft

Answer: 5+6i

Step-by-step explanation: 36 is a perfect square. So you’d simplify it and get 6i. Then it’s 5+6i

Answer:

5+6i

Step-by-step explanation:

Square root of -36 is 6i. 5+6i

Answer:

12,924

Step-by-step explanation:

76x168= 12,768

and...

69+87= 156

now we add them together...

12,768+156= 12,924

Hope this helped you- have a good day bro cya)

Answer:

{(-5, -5),(-9,0),(-8,5), (-6,5)}

Step-by-step explanation:

A function cannot have a domain that is assigned to multiple values (range).

The first set has 6 assigned to both 7 and -6.

The second set has -7 assigned to both 7 and -7.

The third set has -9 assigned to both 2 and -8.

Answer:

18

Step-by-step explanation: