50 POINTS ASAP Triangle 1 and triangle 2 are similar right triangles formed from a ladder leaning against a building.


Triangle 1 Triangle 2
The distance, along the ground, from the bottom of the ladder to the building is 12 feet. The distance from the bottom of the building to the point where the ladder is touching the building is 18 feet. The distance, along the ground, from the bottom of the ladder to the building is 8 feet. The distance from the bottom of the building to the point where the ladder is touching the building is unknown.


Determine the distance from the bottom of the building to the point where the ladder is touching the building for triangle 2.
27 feet
18 feet
12 feet
5 feet

If the cost per person for a bus rental varies inversely to the number of people, it will cost approximately $21.29 per person if 60 people go on the trip. The closest option is D) $21.29.

In an inverse variation, as the number of people increases, the cost per person decreases. Let's set up a proportion using the given information.

If 44 people go on the trip and the cost per person is $30, we have the equation 44 * 30 = 60 * x, where x represents the cost per person when 60 people go on the trip.

Solving this equation gives us 1320 = 60x. Dividing both sides by 60, we find x ≈ 22. Therefore, the cost per person when 60 people go on the trip is approximately $22.

However, none of the answer choices match this approximation. The closest option is D) $21.29, which is the rounded value of the answer. Therefore, the correct answer is D) $21.29, rounded to the nearest cent.



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Answer:

Step-by-step explanation:

Well let Krutica’s age = x

K = x,    G = x+5,    D = x-6

K+G+D = 86  

x + x+5 + x-6 = 86

3x = 87

x = 29

Gordon is the eldest of the few:

29 or x+5=

34 years old

Answer: Gordon is 34 years old

Answer:

9.006

Step-by-step explanation:

Answer:

The probability that neither land on orange is (1/2)* (7/8) = 7/16. Hence, the probability that at least one lands on orange is 1 - 7/16 = 9/16.

Step-by-step explanation:

me big brain

15 cookies ------------------------- 1/4 cup of sugar

90 cookies ------------------------ x

(90 x 1/4) / 15

x = 22.5 /15

x = 1.5 cups

In the first step she did a multiplication but it's a division.

Using arithmetic operations it is obtained that the patient inhales approximately 29,520 times in a 24-hour day.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

We can start by converting the patient's breathing rate from seconds to minutes, since we have the heart rate in minutes.

Use the arithmetic operation of multiplication and division -

The patient inhales once every 3 seconds, which is equivalent to -

(1 inhale / 3 seconds) x (60 seconds / 1 minute) = 20 inhales per minute

Next, we can use the patient's heart rate to find the number of breaths per heartbeat, and then multiply by the heart rate to get the total number of breaths per minute -

Breaths per heartbeat = 1 inhale / 4 heartbeats (since each heartbeat corresponds to 4 phases of the cardiac cycle, during which the patient inhales and exhales once)

Breaths per minute = (Breaths per heartbeat) x (Heart rate)

= (1/4) x 82

= 20.5

So the patient takes approximately 20.5 breaths per minute.

Multiplying this by the number of minutes in a day (24 hours x 60 minutes per hour = 1440 minutes) gives -

Breaths per day = (Breaths per minute) x (Minutes per day)

= 20.5 x 1440

= 29,520

Therefore, the number of inhales is 29,520.

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We are given the following two expressions

Let us simply both expressions.

For the 1st expression, recall the product rule of exponents given by

Applying the above rule to the 1st expression

For the 2nd expression, recall the quotient rule of exponents given by

Applying the above rule to the 2nd expression

As you can see, both expressions are not equivalent.

Therefore, the correct answer is option C

490

472 <490<500

it fits the criteria

Answer:

3,409.6 steps

Step-by-step explanation:

Given parameters:

Duration of the walk  = 9.00am to 3.00pm

Number of steps walked  = 20458 steps

Unknown:

Number of steps per hour =?

To solve this;

            Number of steps per hour  = \(\frac{Number of steps}{Duration}\)

  Duration  = 9 am to 3pm  = 6hrs

  Now input the parameters:

         Number of steps per hour = \(\frac{20458}{6}\)   = 3,409.6 steps

Total number of steps per hour is 3,409.6 steps/hour.

D=5

to make the $75 for the $125

Answer:

What equation will you use to solve this word problem?

✔ 50 + 15d = 125

What equivalent equation can you write after combining like terms?

✔ 15d = 75

How many days will Maisie have to walk the dogs?

✔ 5 days

Step-by-step explanation:

I got it right so hope this helped you and other people out :)

Answer: The correct answer is C

-1/4r+6p

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

Answer:

£191.36

Step-by-step explanation:

Sum the parts of the ratio, 1 + 4 = 5 parts

Divide 320 by 5 to find the value of one part of the ratio.

320 ÷ 5 = 64 ← value of 1 part of the ratio , thus

4 parts = 4 × 64 = 256

Thus he bought 64 first class and 256 second class.

Cost = (64 × £0.67) + (256 × £0.58)

        = £42.88 + 148.48

        = £191.36

Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

To find the order of matrix:

To prove:

Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

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To construct a square inscribed in circle E using the diameter and its perpendicular bisector, draw the diameter, construct the perpendicular bisector, connect the points of intersection on the circle to the diameter, and erase any unnecessary lines.

To construct a square inscribed in circle E using the diameter and its perpendicular bisector, you can follow these steps:

Draw the diameter of the circle. This will serve as the base of the square.

Construct the perpendicular bisector of the diameter. To do this, draw a line perpendicular to the diameter at its midpoint. This will intersect the diameter and divide it into two equal parts.

From the point of intersection between the diameter and the perpendicular bisector, draw a line segment perpendicular to the diameter, extending towards the circle. This line will intersect the circle at two points.

Draw two more line segments, each connecting one of the points of intersection on the circle to the endpoints of the diameter. These line segments will form the remaining sides of the square.

Finally, erase any unnecessary construction lines, and you will have constructed a square inscribed in circle E, with each side of the square touching the circle at a point.

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Answer:

commutative

meaning the order of the numbers doesn't matter (for multiplication and addition)

Answer:

142

Step-by-step explanation:

Ok explanation

we know the sides 9, 11, 38, and 13.

there are 2 missing sides we need to find

so the first one whic is the longer one is we know that the 38 is already 1 part of it but not the whole thing. We know the 9 is part of the 38 since it connects. So that gives us that side of 47.

Now for the shrter side, we know 1 part of it is 13 And the other part is 11. So we Add them up and get 24

Now the sides are 9, 11, 38, 13, 47, and 24

We add them up and get 142

Answer:

142 mi

Step-by-step explanation:

Top = 9 +38 = 47

Right Side = 13

Bottom Right = 38

11 + 9 = 20

Left Side = 24

47 + 13 +38 + 20 + 24 = 142

Step-by-step explanation:

\(3x + 3x + 1 + 3x + 2 = 39 \\ 9x + 3 = 39 \\ 9x = 39 - 3 \\ 9x = 36 \\ x = \frac{36}{9} \\ x = 4\)

Answer:

x = 4

Step-by-step explanation:

combine all of the 3x first to get:

9x + 1 + 2 = 39

9x + 3 = 39

subtract 3 from both sides:

9x = 36

divide by 9

x = 4

Answer:

isosceles and obtuse

Step-by-step explanation:

isosceles, because it has 2 sides which equal to each other

obtuse, because the angle is more than 90 degree

Answer:

89.835

Step-by-step explanation:

Since the question asks to round to four, the number right to four is five so you round up 89.83450 to 89.835.

Answer:

Area = base x height

Step-by-step explanation:

Therefore, the range of g(x) is [0,∞], or [0,∞] in interval notation. The graph of the function (x) = 4x is compressed by a square root function with a value of 4.

Elements and their variations, algorithms and supporting structures, shapes and their locales, and locations where they can be obtained are all included in the study of mathematics. The relationship between a group of inputs, each of which comes with a corresponding output, is referred to as a "function." A function is a relationship between the inputs and the results where each input makes a singular, unique result. Every function has a domain and a codomain, also known as a scope. F is typically used to indicate functions (x). An x is the input. Based on the following criteria, there are four primary types of functions that are available: on capabilities, one-to-one features, many-to-one functions, inside capabilities, and on functions.

given

A square root function with a value of 4 compresses the graph of the function (x) = 4x vertically by a factor of 4.

We must take 3 out of the formula in order to move the graph down by three units:

g(x) = 4√x - 3

The set of all x-values for which the expression 4x - 3 is defined and yields a real integer is the domain of g(x). Due to the fact that the square root of a negative integer is not a real number, the expression is defined for all non-negative values of x.

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Answer:

Step-by-step explanation:

In an isosceles trapezoid, two pairs of adjacent angles are supplementary. It means that the sum of the adjacent angles is 180°

Looking at the diagram, angle X and angle W are adjacent angles. It means that

X + W = 180

Since X = 105, then

105 + W = 180

W = 180 - 105 = 75°

Since W = b + 25°, then

b + 25° = 75

b = 75 - 25 = 50°

Answer: In an isosceles trapezoid, two pairs of adjacent angles are supplementary. It means that the sum of the adjacent angles is 180°Looking at the diagram, angle X and angle W are adjacent angles. It means that X + W = 180Since X = 105, then105 + W = 180W = 180 - 105 = 75°Since W = b + 25°, thenb + 25° = 75b = 75 - 25 = 50°

Step-by-step explanation:

Answer:

first one

Step-by-step explanation:

Answer:

Positive is the answer.

Answer:

D

Step-by-step explanation:

Just did it

Point estimate of the population mean number of sit-ups is \(18.933$\).

The margin of error is 5.615.

The 95 percent confidence interval of the population mean number of sit-ups is \([13.318,24.548]\end{aligned}$$\)

As per the given question 15 individuals were selected and the number of sit-ups that each could complete was recorded.

The results are {27, 12, 18, 5, 16, 25, 30, 13, 35, 10, 1, 13, 33, 24, 22}

(a):

The sample mean is,

\($\overline{\mathrm{X}}=\frac{\sum \mathrm{x}}{\mathrm{n}}\\\\\)

\(=\frac{27+12+18+5+16+25+30+13+35+10+1+13+33+24+22}{15} \\\\\)

\(=18.9333$\)

The point estimate of the population mean number of sit-ups is,

Point estimate \($=\overline{\mathrm{X}}=18.933$\)

(b):

The sample standard deviation is,

\($\mathrm{s}=\sqrt{\frac{\sum X^2-\frac{\left(\sum X\right)^2}{n}}{n-1}}\)

\($\mathrm{s}=\sqrt{\frac{18.9333^2-\frac{\left(18.333\right)^2}{15}}{15-1}}=10.1381$\)

The confidence level is, c=0.95

The significance level is \($\alpha=1-c=1-0.95=0.05$\)

The degrees of freedom is given by,

\($$=\mathrm{n}-1\\=15-1\\=14$$\)

The critical value is, \($t_{\frac{\alpha}{2} , d f}=t_{\frac{0.05}{2,14}}=2.145$\)

The Excel function is, TINV(0.05,14)

The margin of error is,

\($$\begin{aligned}\mathrm{E} & =\mathrm{t}_{\frac{\alpha}{2}, \mathrm{df}} \times \frac{\mathrm{s}}{\sqrt{\mathrm{n}}} \\& =2.145 \times \frac{10.1381}{\sqrt{15}} \\& =5.615\end{aligned}$$\)

(c):

The 95% confidence interval of the population mean number of sit-ups is,

\(\begin{aligned}95 \% \text { C. I. } & =\overline{\mathrm{X}} \pm \mathbf{E} \\& =18.933 \pm 5.615 \\& =[13.318,24.548]\end{aligned}$$\)

Therefore, \($\overline{\mathrm{X}}=18.9333\), \($$\begin{aligned}\mathrm{E} & =5.615\end{aligned}$$\) and 95% confidence interval of the population mean number of sit-ups is \([13.318,24.548]\end{aligned}$$\).

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Sum of the series [infinity] ln n² / (8 + 7n²)² is π² / 6.

Series [infinity] 1/n² convergent to π² / 6.

We can use the limit comparison test.

First, note that both ln n² and (8 + 7n²)² are positive for all n ≥ 1.

Let a_n = ln n² / (8 + 7n²)².

Then, consider the series b_n = 1/n².

We know that b_n is a convergent p-series with p = 2.

Next, we take the limit of the ratio of a_n and b_n as n approaches infinity:

lim (n→∞) a_n / b_n = lim (n→∞) (ln n² / (8 + 7n²)²) / (1/n²)

Using L'Hôpital's rule twice, we can simplify this limit as follows:

= lim (n→∞) [(2/n) / (-28n / (8 + 7n²))]

= lim (n→∞) -14n / (8 + 7n²)

Since the numerator and denominator both approach infinity as n approaches infinity, we can apply L'Hôpital's rule again:

= lim (n→∞) -14 / (14n)

= 0

Since the limit is finite and positive, we can conclude that the series [infinity] ln n² / (8 + 7n²)² converges by the limit comparison test.

To find its sum, we can use a known result that the series [infinity] 1/n² converges to π² / 6.

Therefore, the sum of the series [infinity] ln n² / (8 + 7n²)² is π² / 6.

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