Solve the word problem using a proportion. Danny, who was 6 ft tall, cast a 15 ft shadow. The building he was standing next to cast a 35 ft shadow. How tall was the building? 30 ft, 70 ft, or 14 ft? ​

The constant of proportionality here would be 1 that is k = 1

The ratio that establishes a proportionate link between any two given values is referred to as the constant of proportionality. The constant of proportionality may also be referred to by the labels constant ratio, constant rate, unit rate, constant of variation, or even rate of change.

The constant of proportionality here would be 1 because :

weight of apples ∝ cost of apples

removing the proportionality sign and we get a constant

weight of apples = k ( cost of apples )

here k = 1

as the units in x axis increase simultaneously the y axis units are also increasing

this indicates that there is a direct proportional relation between the cost of apples and the weight of apples.

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Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).

Probability is a measure of the likelihood or chance that a particular event or outcome will occur. It is expressed as a value between 0 and 1, where 0 represents an event that is impossible to occur, and 1 represents an event that is certain to occur.

To solve this problem, we can use the formula for the standard deviation of the sample mean:

Standard deviation of sample mean = standard deviation / √(sample size)

Plugging in the given values:

Standard deviation of sample mean = 7 / √(31)

Next, we can calculate the z-score, which is the number of standard deviations the sample mean is below the population mean:

z-score = (sample mean - population mean) / standard deviation of sample mean

Plugging in the given values:

z-score = (141.5 - 145) / (7 / √(31))

Using a calculator, we find that the z-score is approximately -2.22.

Finally, we can use a standard normal distribution table or a calculator to find the probability that a z-score is less than -2.22.

Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).

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Answer:

x=2, y=5. (2, 5).

Step-by-step explanation:

x=7-y

x=-2y+12

----------------

7-y=-2y+12

7-y-(-2y)=12

7-y+2y=12

7+y=12

y=12-7

y=5

x=7-5=2

To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

Answer:

x = 16.5

Step-by-step explanation:

340 = 7 + 20x + 3 , that is

340 = 10 + 20x ( subtract 10 from both sides )

330 = 20x ( divide both sides by 20 )

16.5 = x

The probability of selecting an 8 is \(\frac{4}{52}\) since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to \(\frac{1}{13}\). The probability of selecting a face card is \(\frac{12}{52}\) since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to \(\frac{3}{13}\).  1 - \(\frac{3}{13}\) = \(\frac{13}{13}\) - \(\frac{3}{13}\) =\(\frac{10}{13}\).

There are four suits (hearts, spades, diamonds, and clubs), each with 13 cards from Ace to King, in a conventional 52-card deck of playing cards. As a result, there are four of each potential card.

(A) The probability of selecting an 8 is  \(\frac{4}{52}\) since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to \(\frac{1}{13}\).

(B) The probability of selecting a face card is \(\frac{12}{52}\) since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to \(\frac{3}{13}\).

(C) The probability of NOT selecting a face card is \(\frac{40}{52}\) since there are 4 of each card from Ace through 10 that are not face cards. This simplifies to 10/13. The solution to part B's question can be used as another way to approach this issue. If the probability of selecting a face card is 3/13, then the probability of NOT selecting a face card has to be 1 - \(\frac{3}{13}\) = \(\frac{13}{13}\) - \(\frac{3}{13}\) =\(\frac{10}{13}\). Recall that you must deduct from 1 since the probability of all conceivable outcomes must add up to 1, or 100%.

Therefore, the probability of selecting an 8 is \(\frac{4}{52}\) since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to \(\frac{1}{13}\). The probability of selecting a face card is \(\frac{12}{52}\) since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to \(\frac{3}{13}\). the probability of NOT selecting a face card has to be 1 - \(\frac{3}{13}\) = \(\frac{13}{13}\) - \(\frac{3}{13}\) =\(\frac{10}{13}\).

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Answer:

37.7 feet

Step-by-step explanation:

The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.

For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).

When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).

In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.

Answer:

0

Step-by-step explanation:

1. First, we should know the slope-intercept form of any equation: y = mx + b.

2. In the equation y = -2/3(x), it appears that the variables we can see are y, m, and x. However, the y-intercept, b, is still there with the value of 0.

Therefore, the y-intercept is 0.

Answer:

-5, 0, 1 , 5

Step-by-step explanation:

What you want to do is find all of the points on the graph:

(-5,-1), (-5,3),(0,3),(1,0),(5,2)

The domain would be -5,-5,0,1,5 because it is in the x-axis.

          Look at it as this (-5,-1) (-5,3) (0,3) (1, 0) (5,2)

   The numbers in bold  are the X-axis which is another word for domain

For example (-5, -1), -5 would be in the X-axis and -1 would be in the Y-axis, It goes "x,y" all the time.

Since there are two -5's on the domain, you just ignore one of the -5's.

Hope this helps!!

the answer is 153.86 ft squared

= the formula for the area of a circle is A=πr2

= area = pi x radius squared

= the radius is 7 feet, square that to get 49

= multiply 49 by pi to get the area: 153.86 square feet

153.86 ft squared

Answer:

153.86 ft squared

Step-by-step explanation:

As per given question we have provided that :

We need to find :

Here's the required formula :

\({\dashrightarrow\sf{A = \pi {r}^{2}}}\)

Substituting all the given values in the formula to find the area of circular pool :

\({\dashrightarrow{\sf{Area = \pi {r}^{2}}}}\)

\({\dashrightarrow{\sf{Area = 3.14{(7)}^{2}}}}\)

\({\dashrightarrow{\sf{Area = 3.14{(7 \times 7)}}}}\)

\({\dashrightarrow{\sf{Area = 3.14{(49)}}}}\)

\({\dashrightarrow{\sf{Area = 3.14 \times 49}}}\)

\({\dashrightarrow{\sf{Area = 153.86}}}\)

\(\star{\underline{\boxed{\sf{\red{Area = 153.86 \: {ft}^{2}}}}}}\)

Hence, the area of circular pool is 153.86 ft².

\(\rule{300}{1.5}\)

Answer: one senior ticket is $8 and one student ticket is $14

Hope this helps a little

Answer:Change values to whole numbers.

Convert any mixed numbers to fractions.

Convert 3 1/8

3 1/8 = 25/8

We now have:

5 : 3 1/8 = 5 : 25/8

Convert the whole number 5 to a fraction with 1 in the denominator.

We then have:

5 : 3 1/8 = 5/1 : 25/8

Convert fractions to integers by eliminating the denominators.

Our two fractions have unlike denominators so we find the Least Common Denominator and rewrite our fractions as necessary with the common denominator

LCD(5/1, 25/8) = 8

We now have:

5 : 3 1/8 = 40/8 : 25/8

Our two fractions now have like denominators so we can multiply both by 8 to eliminate the denominators.

We then have:

5 : 3 1/8 = 40 : 25

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 40 and 25 is 5

Divide both terms by the GCF, 5:

40 ÷ 5 = 8

25 ÷ 5 = 5

The ratio 40 : 25 can be reduced to lowest terms by dividing both terms by the GCF = 5 :

40 : 25 = 8 : 5

Therefore:

5 : 3 1/8 = 8 : 5

Step-by-step explanation:

The equation of the line in slope-point form is:

y - 7 = -4/5(x + 6)

The equation of a line in slope-point form is given by:

y - y₁ = m(x - x₁)

where:

(x₁, y₁) represents the coordinates of a point on the line.

m represents the slope of the line.

m = (y₂ - y₁)/(x₂ - x₁)

(x₁, y₁) represents the coordinates of the 1st point on the line

where (x₂, y₂) represents the coordinates of the 2nd point on the line

We have

(x₁, y₁) = (-6, 7)

(x₂, y₂) = (4, -1)

m = (y₂ - y₁)/(x₂ - x₁)

m = (-1 - 7) / (4 - (-6))

m = -8/10

m = -4/5

Using y - y₁ = m(x - x₁):

y - 7 = -4/5(x - (-6))

y - 7 = -4/5(x + 6)

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A fraction is a way to describe a part of a whole. The decimal form of 2 2/5 is 2.4.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The decimal form of 2 2/5 can be written as,

2 2/5 = 2 + 2/5 = 2 + 0.4 = 2.4

Hence, the decimal form of 2 2/5 is 2.4.

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Answer:

how to help. what is the question.

Answer:

a. P ( X > 12 ) = 0.5254

b. P ( X < 15 ) = 0.7172

c. P ( 9 < X < 13 ) =  0.3179

d. Not unusual

Step-by-step explanation:

Solution:-

- We will define our random variable X as follows:

       X: The weights of the male babies less than 2 month old in USA ( lb )

- The distribution given for the random variable ( X ) is defined to follow normal distribution.

- The normal distribution is identified by two parameters mean ( u ) and standard deviation ( σ ). The distribution is mathematically stated or expressed as:

                               X ~ Norm ( u , σ^2 )

- The parameters for the normal distribution followed by the random variable ( X ) are given. Hence,

                              X ~Norm ( 12.3 , 4.7^2 )

- We will use standard normal tables to determine the following probabilities:

a) What proportion of babies weigh more than 12 pounds?

- To use the standard normal tables we need to standardized our limiting value of the required probability by finding the corresponding Z-score value.

- The formula used to compute the Z-score value is given below:

                                \(Z-score = \frac{x - u}{sigma}\)

- We are requested to compute the probability p ( X > 12 ). the limiting value is 12 pounds. We will use the conversion formula and compute the Z-score:

                               \(Z-score = \frac{12 - 12.3}{4.7} \\\\Z-score = -0.06382\)

- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:

                            P ( X > 12 ) = P ( Z > -0.06382 ) = ...

                            P ( Z > -0.06382 ) = 1 - P ( Z < -0.06382 )  

Use standard normal look-up table:

                            P ( X > 12 ) =  1 - 0.4746

                            P ( X > 12 ) = 0.5254  ... Answer

Answer: The proportion of babies that weigh more than 12 pounds is the probability of finding babies weighing more than 12 pounds among the total normally distributed population. The proportion is 0.5254

b) What proportion of babies weigh less than 15 pounds?

- We are requested to compute the probability p ( X < 15 ). the limiting value is 12 pounds. We will use the conversion formula and compute the Z-score:

                             \(Z-score = \frac{15-12.3}{4.7} \\\\Z-score = 0.57446\)

- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:

                            P ( X < 15 ) = P ( Z < 0.57446 )

                            P ( X < 15 ) = 0.7172

Answer: The proportion of babies that weigh less than 15 pounds is the probability of finding babies weighing less than 15 pounds among the total normally distributed population. The proportion is 0.7172

c) What proportion of babies weigh between 9 and 13 pounds?

- We are requested to compute the probability p ( 9 < X < 13 ). the limiting value are 9 and 13 pounds. We will use the conversion formula and compute the Z-score:

                           \(Z_1 = \frac{9-12.3}{4.7} = -0.70212\\\\Z_2 = \frac{13-12.3}{4.7} = 0.14893\\\)

- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:

                          P ( 9 < X < 13 ) = P ( -0.70212 < X < 0.14893 )

        P ( -0.70212 < X < 0.14893 ) = P ( X < 0.14893 ) - P ( X < -0.70212 )  

Use standard normal look-up table:

                            P ( 9 < X < 13 ) =  0.5592 - 0.2413

                            P ( 9 < X < 13 ) =  0.3179  ... Answer

Answer: The proportion of babies that weigh less than 13 pounds but greater than 9 pounds is the probability of finding babies weighing less than 13 pounds and more than 9 pounds among the total normally distributed population. The proportion is 0.3179

d)

Is it unusual for a baby to weigh more than 18.1 pounds?

- We are requested to compute the probability p (  X > 18.1 ). the limiting value is 18.1 pounds. We will use the conversion formula and compute the Z-score:

                             \(Z-score = \frac{18.1-12.3}{4.7} \\\\Z-score = 1.23404\)

The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:

                            P ( X > 18.1 ) = P ( Z > 1.23404 )

                            P ( X > 18.1 ) =  0.1086

Answer: The proportion of babies that weight more than 18.1 pounds are 0.1086 of the total babies population. We can say that the proportion of babies that weigh more than 18.1 pounds are significant because the proportion lies is significant. Not enough statistical evidence to be classified as "unusual".

The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.

Speed is simply referred to as distance traveled per unit time.

It is expressed as;

Speed = Distance ÷ time.

Given that the car is traveling at a rate of 30 meters per second.

First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.

1 kilometer = 1000 meters

1 hour = 3600 seconds

Hence;

Speed = 30m/s = ( 30 × 3600/1000 )kmh

Speed = 108 kmh

Next, the distance covered in 5 hours will be:

Speed = Distance / time

Distance = speed × time

Distance = 108 kmh × 5 h

Distance = 540 km

Therefore, the disatnce covered is 540 kilometers.

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Answer:

Factor using the perfect square rule.

(x−8)^2

Step-by-step explanation:

hope this helps

Answer:

\((x-8)^{2}\)

Step-by-step explanation:

Quadratic expression:
\(x^{2} - 16x + 64\)

Where

a = 1

b = -16

c = 64

Quadratic expression can be factorized using the Double Bubble Method

Double Bubble Method:

Step 1:

        Multiply a and c

a×c = 1 × 64
       = 64

Step 2:

      Write a complete list of pairs of factors of ac and choose the most appropriate and suitable pair of factors that would add or subtract to equal to the value of b = \(-16\). Accordingly assign the signs to the two factors

Pair of factors: \(-8\) and \(-8\)

Step 3:

   Use the two factors to rewrite the bx term:

\(x^{2} - 8x -8x + 64\)

Step 4:

 Factorize by Grouping:

\(x(x-8) -8(x - 8)\)

Step 5:

Extract the common factor expression \((x - 8)\) to obtain double-bubble expressions:

\((x - 8)(x-8)\)

Step 6:

Apply the Law of indices:

\(a^{n}\) × \(a^{m}\) = \(a^{n + m}\)

∴\((x-8)^{1}\) × \((x-8)^{1}\) = \((x-8)^{1+1}\)

                              = \((x-8)^{2}\)

The proportion of 1040r tax forms completed in less than 77 minutes = 0.06301

How to find the proportion of the tax forms?

The time required to complete a 1040r tax form = normally distributed

Mean = \(\mu\) = 100 minutes

Standard deviation  = \(\sigma\) = 15 minutes

The proportion of 1040r tax forms completed in less than 77 minutes is given by ,

P( X< 77 ) = P ( Z < \(\frac{77-100}{15}\)  )

                = P( Z < - 1.53 )

                =0.06301

Cumulative probability in the normal distribution =0.06301 or 6.301%

What is normal distribution?

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Answer:

The required forms of 314, 207

1. 3 lakh fourteen thousand two hundred seven. (word form)

2. 300000 + 10000 + 4000 + 200 + 7 (expanded form)

Answer:

The line crosses the x-axis at 0.3, so the x-intercept is 0.3

The line crosses the y-axis at 0.4, so the y-intercept is 0.4

The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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Answer:

from the graph I think it's 16

Step-by-step explanation:

I m pretty sure that the correct answer is 24

16/2=8

16+8=24

x=24

I hope it helps

can I be brainliest

have a nice day

Account Compounding Interest after 6 years

1 quarterly

A1 = -$1798.42

2 monthly $

A2 = -$1798.01

3 daily $

A3 =  -$1797.96

1) An account with quarterly compounding: After 6 years, the formula to calculate the interest is:

Interest = Principal \(\times\)(1 + (rate / \(n))^{(n * t)}\) - Principal

Substituting the given values:

Principal = $2200

Rate = 3% = 0.03

n = 4 (quarterly compounding)

t = 6 years

Interest = $2200 \(\times\) (1 + (0.03 / \(4))^{(4 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0075)^{(24)}\) - $2200

Interest ≈ $401.58 - $2200

Interest ≈ -$1798.42 (rounded to two decimal places).

2) An account with monthly compounding: After 6 years, the formula remains the same, but the compounding frequency changes:

   Principal = $2200

   Rate = 3% = 0.03

   n = 12 (monthly compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(12))^{(12 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0025)^{(72)}\) - $2200

Interest ≈ $401.99 - $2200

Interest ≈ -$1798.01 (rounded to two decimal places)

3) An account with daily compounding: Using the same formula with the compounding frequency:

   Principal = $2200

   Rate = 3% = 0.03

   n = 365 (daily compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(365))^{(365 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.000082)^{(2190)}\) - $2200

Interest ≈ $402.04 - $2200

Interest ≈ -$1797.96 (rounded to two decimal places)

In all three cases, the interest earned is negative, indicating that the accounts would have lost money rather than gained interest.

This suggests that there might be an error in the calculations or the provided interest rates. It's important to verify the given information to ensure accurate calculations and resolve any discrepancies.

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Answer:

x = 1/4c + 1/4k **i may be wrong**

Answer:

4

Step-by-step explanation:

Let the number be x.

3 + 4x = 19

4x = 19 - 3

    = 16

x = 16 ÷ 4

x = 4

The number is 4.

Answer/Step-by-step explanation:

Based on the inscribed angle theorem, any inscribed angle = ½ of its intercepted arc

Thus:

✔️Inscribed angle = 57°

Intercepted arc would be: 2*57 = 114°

✔️Intercepted arc would be: 123°

Inscribed angle = ½(123) = 61.5°

✔️Intercepted arc would be: 46°

Inscribed angle = ½(46) = 23°

✔️Inscribed angle = 69°

Intercepted arc would be: 2*69 = 138°

✔️Intercepted arc would be: 155°

Inscribed angle = ½(155) = 77.5°

Answer:

605*2/5=121*2=242 miles so B would be the answer

Step-by-step explanation: