A 5 foot girl is standing in the Grand Canyon, and she wants to estimate the height (depth) of the canyon. The sun casts her shadow 9 inches along the ground. To measure the shadow cast by the top of the canyon, she walks the length of the shadow. She takes 280 steps and estimates that each step is roughly 3 feet. Approximately how deep is the Grand Canyon?​

The length of BC rounded to 3 significant figures is approximately 3.62 units.

We can use trigonometric function to find the length of BC. First, we can use the fact that ∠CAB = 90° to determine that ∠ACB = 25° (since the angles in a triangle sum to 180°).

Next, we can use the law of sines to relate the lengths of the sides and angles of the triangle:

sin(∠ABC) / AB = sin(∠ACB) / BC

Substituting in the values we know:

sin(65°) / 8.6 = sin(25°) / BC

Solving for BC:

BC = sin(25°) × 8.6 / sin(65°) ≈ 3.62

Rounding to 3 significant figures, we get BC ≈ 3.62 units

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Answer:

8x + 8·7

8(x + 7)

15y - 1

Step-by-step explanation:

8x + 8·7

8x + 56

8(x + 7)

8(x) + 8(7)

8x + 56

9 + 16y - 8 - y  Combine like terms

15y - 1

Helping in the name of Jesus.

Answer:

x=0.8

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

x=0.8

Answer:

x = 1.2

Step-by-step explanation:

see image. If the problem is two big, ugly fractions equal to each other, then you can cross-multiply. There are lots of different ways to solve it. This is just one way. I think the problem is to help you practice dealing with decimals and mixed numbers, multiplying and/or dividing with fractions, and distributive property. See image.

Answer: The answer would be about 38.88 meters

Step-by-step explanation:

First you transfer Kilometers per hour into Meters per second.

35 KM/H = 9.72 M/S

The formula for distance is D = Speed x Time

9.72 x 4 seconds = 38.88 Meters that he will travel in 4 seconds

Answer: 27.5 centimeters

Step-by-step explanation:

angle A measures 20 degrees and we know it's a write tringle so 180-(90+20)=70 degrees

so, angle B measures 70 degrees.

using the law of cosines:

[tex]\frac{sin70}{b} =\frac{sin20}{10}[/tex]

[tex]b=\frac{10sin(70)}{sin(20)}[/tex]

so, side b =[tex]\frac{10sin(70)}{sin(20)}[/tex]

Using the Pythagorean theorem to find the hypotenuse:

hypotenuse[tex]=\sqrt{(\frac{10 sin70}{sin20})^{2} + 10^{2} }[/tex]

approximately = 27.5  centimeters

The margin of error for a sample mean at a 95% confidence level can be calculated using the formula

E = (1.96 * (sample standard deviation/√sample size).

Therefore, the margin of error is E = (1.96 * (sample standard deviation/√sample size)) = (1.96 * (s/√n)).

Round the answer to two decimal places, and the margin of error is [tex]E = (1.96 * (s/√n)) = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n).[/tex]
Therefore, the margin of error at a 95% confidence level is E = 1.96 * (s/√n).

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Approximately 21 pH values would have to be included in each sample to estimate the difference between the mean acidity for rainfalls at the two different locations to the nearest 0.2 pH, with probability near 0.90.

What is the standard error?

Standard error is a measure of the variability or uncertainty of a statistic. It is the standard deviation of the sampling distribution of a statistic, and it estimates how much the sample statistic may vary from the true population parameter due to random sampling error.

To estimate the difference between the mean acidity for rainfalls at two different locations, we can use the formula for the standard error of the difference between means:

[tex]SE = \sqrt{[(s1^2 / n1) + (s2^2 / n2)]}[/tex]

where s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and SE is the standard error of the difference between means.

We want our estimate to be correct to the nearest 0.2 pH, with probability near 0.90. This means we want to find the sample size n that will give us a margin of error of 0.2 pH with a confidence level of 90%.

We can use the following formula to find the sample size:

[tex]n = [(z*\sigma / E)^2][/tex]

where z is the z-score for the desired confidence level (0.90), σ is the population standard deviation (0.35), and E is the margin of error (0.2).

First, we need to find the z-score for a 90% confidence level. This can be found using a standard normal distribution table or calculator. For a 90% confidence level, the z-score is approximately 1.645.

Substituting these values into the formula, we get:

n = [(1.645*0.35 / 0.2)^2]

= 20.95

Rounding up to the nearest whole number, we get a sample size of n = 21 for each sample.

Therefore, approximately 21 pH values would have to be included in each sample to estimate the difference between the mean acidity for rainfalls at the two different locations to the nearest 0.2 pH, with probability near 0.90.

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630 .18 feet tall is the gateway arch by the trigonometric ratio

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.

As given

The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St. Louis, Missouri is 39 degrees.

Now by using the trigonometric property

[tex]tan\theta=\frac{P}{B}[/tex]

As the diagram is given below.

AB=CB tan39

AB = 778 tan 39

AB= 630.18 feet

Hence the gateway arch is 630.18 feet tall.

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-4x + y = 7 is the line parallel tο the line graphed. Optiοn D is cοrrect.

Parallelism is a writing style that uses similar grammatical structures, phrases, οr wοrds tο make a pοint. It is used tο emphasize a pοint and make the writing mοre interesting and easier tο understand. Parallelism is used in different types οf writing such as persuasive writing, pοetry, stοries, and legal dοcuments.

Parallelism can alsο be used in speech, allοwing the speaker tο emphasize their pοint. It creates balance and structure in the writing, making it mοre οrganized and easier tο read. Parallelism can alsο be used tο create rhythm in the writing. By creating rhythm, the writing becοmes mοre memοrable and easier tο understand.

The line parallel will have a same slοpe

Lets find the slοpe

Any two pοints form the graph are, (1, 1) and (0, -3)

Slope m = [tex]$ \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Slope m = [tex]$ \frac{-3 -1}{0 - 1}[/tex]

m = 4

Nοw, frοm the given οptiοns,

a. y=x+3 is nοt parallel as it have a οppοsite slοpe.

b. 4x + 3y = 6, write in y-intercept fοrm

   y =  (-4x + 6)/y. Nοt parallel

c. y =- 3x+2 is nοt parallel as it have a οppοsite slοpe.

d. -4x + y = 7, write in y-intercept fοrm

   y = 4x + 7, That is parallel as the slοpe is same.

Therefοre, -4x + y = 7 is the line parallel tο the line graphed.

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Complete question:

Answer

43.96

14 x 3.14 = 43.96

hope this helped!

After answering the presented question, we can conclude that expressions Therefore, the answer is: y = -2w + 2x + 2z

In mathematics, you can double, divide, add, or subtract something. The following is an expression: Expression, numerical value, and math operator A mathematical expression is made up of numbers, parameters, and functions. Opposing sentences and expressions are possible. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and a mathematical action between them. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical sign +.

To solve for y

[tex]w = x - y/2 - z\\2w = 2x - y - 2z\\2w - 2x - 2z = -y\\y = -2w + 2x + 2z[/tex]

Therefore, the answer is:

y = -2w + 2x + 2z

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The angles (x + 7)° and (3x - 21)° are vertical angles and the value of x is equal to 14.

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

so we shall solve for x and y as follows:

3x - 21 = x + 7

3x - x = 21 + 7 {collect like terms}

2x = 28

2x/2 = 28/2 {divide through by 2}

x = 14

Therefore, the value of x is equal to 14 for the vertical angles (x + 7)° and (3x - 21)°.

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Therefore , the solution of the given problem of unitary comes out to be the response is option b 455.

By combining what was learned and implementing this variable technique, which also includes all supplemental information from two people who used a particular tactic, the task can be finished. In other words, if the desired result occurs, either the entity specified in the expression will also be identified, or both crucial procedures will actually skip the colour. A refundable fee of Rupees ($1.01) may be needed for forty pens.

Here,

The following combination formula determines how many ways a company can choose three candidates from a shortlist of fifteen:

=> C(15,3) = 15! / (3! (15-3)!)

=>  (15 x 14 x 13) / (3 x 2 x 1)

=> 455

Consequently, the response is (b) 455.

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Answer: X>4

Step-by-step explanation:

First divide both sides by 4 and then

4 divided by 4 is 1 so what remains is x>16/4 and that is x>4

The simplified expression, given the rule for exponentiation of powers, is 1, 024 x ³⁰.

To simplify the expression ((2x³) ⁵ ) ², we need to apply the rule for exponentiation of powers which states " When an expression is raised to a power, and that result is raised to another power, we can simplify by multiplying the exponents."

Using this rule, we can simplify the expression as follows:

( ( 2 x ³ ) ⁵ ) ² = (2 ⁵ x (3 x 5) ) ^ 2

= ( 32 x ¹⁵ ) ²

= 1, 024 x ³⁰

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If  she can make 7 bags in one day, the percent increase in the number of bags Hannah can make is 75%.

To calculate the percent increase in the number of bags Hannah can make, we need to find the difference between the number of bags she can make now and the number she could make before, and then express this difference as a percentage of the original number of bags she could make.

The difference between the number of bags she can make now and the number she could make before is:

7 bags - 4 bags = 3 bags

To express this difference as a percentage of the original number of bags she could make, we can use the following formula:

percent increase = (difference ÷ original value) x 100%

In this case, the original value is 4 bags, so we have:

percent increase = (3 bags ÷ 4 bags) x 100% = 75%

This means that she can now make 75% more bags per day than she could before she got her new sewing machine.

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Answer:

Step-by-step explanation:

To find the volume of a sphere, we use the formula:

V = (4/3) * π * r^3

where r is the radius of the sphere.

We are given that the radius of the sphere is 7 cm and we can use 3 as an approximation for π. Substituting these values in the formula, we get:

V = (4/3) * 3 * 7^3

V = (4/3) * 3 * 343

V = 4 * 343

V = 1372

Therefore, the volume of the sphere is 1372 cubic centimeters.

Fraction value [tex]16\frac{17}{27}[/tex] as a percentage is [tex]1662\frac{26}{27} %[/tex] %

Fraction value [tex]16\frac{17}{27}[/tex] as a decimal is 16.629629

Percentage, decimal, and fraction are all ways of representing numbers that are related to each other. Here's a brief explanation of each:

Percentage: A percentage is a number expressed as a fraction of 100, with the symbol % (percent) added. For example, 50% is the same as 50/100 or 0.5.

Decimal: A decimal is a way of representing fractions using the base-10 numbering system. It is written with a decimal point between the whole number and the fractional part. For example, 0.5 is the same as 5/10 or 50/100 or 50%.

Fraction: A fraction is a way of representing a part of a whole or a ratio of two numbers. It is expressed as a ratio of two integers, with the numerator (top number) representing the number of parts being considered, and the denominator (bottom number) representing the total number of equal parts. For example, 1/2 is the same as 0.5 or 50%.

Fraction value [tex]16\frac{17}{27}[/tex] as a percentage is [tex]1662\frac{26}{27} %[/tex] %

Fraction value [tex]16\frac{17}{27}[/tex] as a decimal is 16.629629

For other values see the below figure.

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Answer: 28.3 inches long

Step-by-step explanation:

Since the triangle is isosceles, the two legs have the same length. Let's call the length of each leg "x". We can use the Pythagorean theorem to solve for x:

x^2 + x^2 = 40^2

2x^2 = 1600

x^2 = 800

x ≈ 28.3

Therefore, each leg of the triangle is approximately 28.3 inches long.

Bod is 22 years old, Brian is 24 years old, and Mark is therefore 15 years old.

A variable in mathematics is a symbol or letter that denotes a possible number or quantity. It frequently serves as a placeholder for an unknowable number that needs to be calculated or solved for in mathematical expressions or equations. For instance, the factors x and y are used in the equation y = 3x + 5. The value of x, which can be any integer, determines the value of y. If we know the number of x, we can find a solution for y.

given

Let's indicate their ages with variables:

Mark's age: M

Body Age: B Equals M + 7

Br = B + 2 = (M + 7) + 2 = M + 9 is Brian's age.

Their total age is 61, so we can create the following equation:

M + (M + 7) + (M + 9) = 61

M is simplified to 3M Plus 16 and the answer is 61.

3M = 45

M = 15

Bod is 22 years old (15 + 7), Mark is 15 years old (15 + 7), and Brian is 24 years old (22 + 2).

Bod is 22 years old, Brian is 24 years old, and Mark is therefore 15 years old.

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The pressure exerted by the block on the ground is 225 N/m² and 600 N/m² respectively.

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

The equation for pressure is:

Pressure = Force / Area

A block exerts a force of 9 N on the ground

a) If the area of its base is 0.04 m², hence:

Pressure = Force / Area = 9 N / 0.04 m² = 225 N/m²

a) If the area of its base is 0.015 m², hence:

Pressure = Force / Area = 9 N / 0.015 m² = 600 N/m²

The pressure exerted on the ground is 225 N/m² and 600 N/m² respectively.

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Answer:

y = 2/3x - 2

Step-by-step explanation:

The inequality and the shaded region are added as attachment

The given parameter from the question is represented as

0.4r ≤ 120 and r ≥ 4(360/5)

Evaluate the expression by products and quotients

So, the expression becomes

r ≤ 300 and r ≥ 288

When these inequalities are combined, we have the following compound expression of inequality

288 ≤ r ≤ 300

Next, we plot the graph of the inequality

The inequality is added as an attachment

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2 decimal point of 25% of 401.16 is 100.29

In the question, we are ask to calculate the percentage of 25 multiplied by 401.16 and then round the answer to 2 decimal point

The first step is to work of 25%. This can be done by dividing 25 by 100

= 25/100

= 0.25

The next step is to multiply this value (0.25) by 401.16

= 0.25 × 401.16

= 100.29

The answer rounded to 2 decimal point is 100.29

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The 8 students at the pizza party ate 2 and 2/3 pizzas if each student ate 1/3 of a pizza.

If each of the 8 students ate 1/3 of a pizza, we can find the total number of pizzas by multiplying the number of students by the fraction of a pizza each student ate:

8 students × 1/3 pizza per student = 8/3 pizzas

However, it's more common to express the result as a mixed number or decimal. To convert the improper fraction 8/3 to a mixed number, we can divide the numerator by the denominator:

8 ÷ 3 = 2 with a remainder of 2

Therefore, the students ate 2 and 2/3 pizzas altogether. Alternatively, we can convert the improper fraction to a decimal by dividing the numerator by the denominator:

8/3 = 2.67

Therefore, the students ate approximately 2.67 pizzas altogether.

To recap, if each of the 8 students at the pizza party ate 1/3 of a pizza, they ate 8/3 pizzas altogether, which is equal to 2 and 2/3 pizzas or approximately 2.67 pizzas.

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The ordered pair for point H would be (-9,8).

Graph is a mathematical structure used to model pairwise relations between objects. It consists of a set of nodes, which represent the objects, and a set of edges, which represent the relations between pairs of objects. Graphs can be used to represent networks, flows, and even data structures such as trees or linked lists. They are also used in various optimisation problems, such as route finding and scheduling.

The correct answer is B) (-9,8). To find the location of point H, Jessica needs to move 5 units to the left on the x-axis, which would put it at -9. She then needs to move 5 units up on the y-axis, which would put it at 8. Therefore, the ordered pair for point H would be (-9,8).

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The ordered pair for point H would be (-9,8).

Graph is a mathematical structure used to model pairwise relations between objects. It consists of a set of nodes, which represent the objects, and a set of edges, which represent the relations between pairs of objects.

The correct answer is B) (-9,8). To find the ordered pair for point H, you need to add 5 units to the x-coordinate of point G, and 5 units to the y-coordinate of point G. Since the x-coordinate of point G is -4 and the y-coordinate of point G is 3, the x-coordinate of point H would be -4 + 5 = -9 and the y-coordinate of point H would be 3 + 5 = 8. Therefore, the ordered pair for point H would be (-9,8).

The correct answer is B) (-9,8). To find the location of point H, Jessica needs to move 5 units to the left on the x-axis, which would put it at -9.

She then needs to move 5 units up on the y-axis, which would put it at 8. Therefore, the ordered pair for point H would be (-9,8).

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Answer:

To solve this expression, we can use the order of operations, which tells us to perform the operations inside the parentheses first, and then multiply by -2.

So, we have:

(12 + 13) (-2)

= (25) (-2) // simplify the parentheses by adding 12 and 13

= -50 // multiply 25 by -2

Therefore, (12+13)(-2) equals -50.

The probability that at least one trip will travel before Isabella was born is 0.9999, or 99.99% (rounded to the nearest hundredth).

We can use the complement rule to find the probability that at least one trip will travel before Isabella was born. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is at least one trip traveling before Isabella was born.

The probability of none of the 555 trips traveling before Isabella was born is (1-0.25) raised to the power of 555, since the probability of each trip not traveling before Isabella was born is 1 - 0.25 = 0.75.

So, the probability of at least one trip traveling before Isabella was born is:

P(at least one before she's born) = 1 - (1-0.25)^{555}

P(at least one before she's born) = 1 - 0.75^{555}

P(at least one before she's born) = 0.9999 (rounded to the nearest hundredth)

Therefore, the probability that at least one trip will travel before Isabella was born is 0.9999, or 99.99% (rounded to the nearest hundredth).

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Answer: The given quadratic expression is:

9x² - 14x + 16

To factorize it, we can use the quadratic formula:

x = [-(-14) ± √((-14)² - 4(9)(16))] / 2(9)

Simplifying under the square root:

x = [-(-14) ± √(4)] / 18

x = [14 ± 2] / 18

x = (16/18) or x = (12/18)

Simplifying:

x = (8/9) or x = (2/3)

So the roots of the quadratic are x = 8/9 and x = 2/3. Therefore, we can factorize the quadratic expression as:

9x² - 14x + 16 = 9(x - 8/9)(x - 2/3)

Step-by-step explanation: