A tree casts a shadow 15 m long. At the same time, the shadow cast by a 30-cm tall statue is 53 cm
long. Find the height of the tree. Round results to the nearest unit.
A) 26 m
B) 8 m
C) 7 m
D) 27m

Answer:

The walking distance that is saved by cutting across the lot is approximately 18 feet.

Answer:

5.6

Step-by-step explanation:

The expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

The amounts of packets of crisps purchased are given as follows:

The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.

Hence the expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

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Answer:

shown below

Step-by-step explanation:

4 x 2 = 8

1 x 2 = 2

a⁸b²

(a⁵b²)(a²b⁶)

a⁷a⁵b⁶b²a²b⁸

a¹⁴b¹⁶

8 - 14 = -6

2 - 16 = -14

a^-6 b^-14

next one

25^3x-21

/

25^2x+14

1^x-35

Answer:

-1, √4/5, -6/5, √3, 2, -3√9, 2√125

Step-by-step explanation:

The statement refers to the way that symbols are represented in sequences, a common practice in formal language theory, by employing a notation that makes symbols a part of the sequence.

In formal language theory, a language is often defined as a set of strings over an alphabet. By representing any alphabetic sequence of symbols as a single string using the notation outlined in the statement, we are able to recognise the language that comprises that sequence as a collection of strings. A subset of the language having all possible strings over the alphabet (a, b, and c) is the set of strings abc, which may be used to represent the language including the sequence (a, b, and c). So, this notation offers an easy approach to discuss languages and the sequences that make up such languages.

Hence, the statement relates the symbols and sequences.

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In conclusion  the value that correctly fills in the blank in the table is 0.69.

Why it is?

To find the relative frequency of boys, we need to use the information given in the frequency table. We know that the total number of boys is 120 - 37 = 83, since the total number of students is 120 and the number of girls is 37.

We can then calculate the relative frequency for boys by dividing the number of boys who prefer math or social studies (40 + 43 = 83) by the total number of students (120):

Relative frequency for boys = (40 + 43) / 120 ≈ 0.69

Rounding to the nearest hundredth, we get:

Relative frequency for boys ≈ 0.69

Therefore, the value that correctly fills in the blank in the table is 0.69.

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Answer:

Check pdf

Step-by-step explanation:

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second,  64.23 feet/second long it will take for the object to hit the ground below. This can be solved using the concept of law of conservation of energy.

Three fundamental quantities all maintain their original values. Energy, momentum, and angular momentum are these. Energy is a conserved quantity, which could surprise you if you've read instances in previous pages, such the kinetic energy of charging elephants. The first law of thermodynamics, generally known as the law of conservation of energy, stipulates that the energy of a closed system must remain constant and cannot rise or fall on its own without external intervention.

Given that,

Height of the cliff, h= 55 Foot

Initial speed of the projectile, u = 85 m/s

Let, the projectile hit the ground with velocity "v"

Applying the law of conservation of energy,

mgh + 1/2 mu² = 1/2 mv²

or, m (gh + 1/2 u²) = 1/2 mv²

or, (gh + 1/2 u²) = 1/2 v²

or, 10 × 55 + (1/2 × (55)²) = 1/2 v²

or, 550 + 1512.5 = 1/2 v²

or, 2062.5 = 1/2 v²

or, 4125 = v²

or, v = 64.23 feet/second

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Answer:

First, the image with 5blue boxes and 3 pink boxes is correct.

Next, 40 people like Hypesters

Step-by-step explanation:

Just compare LIKE things and be careful about the order, always keep the same order.

Hypesters:Skirmish

5 (Hypesters) : 3 Skirmish

5:3

□□□□□: ■■■

? : 24

We'll use ratios that look like fractions to solve this math question.

5/3 = ?/24 Let's put an x for the number we don't know.

5/3 = x/24 crossmultiply

5(24) = 3x

120 = 3x divide by 3

120/3 = x

40 = x

If 24 people like Skirmish, then 40 people like Hypesters.

The computation of the factors shows that the greatest number of bags that Lucia can make will be 16.

From the information given, Lucia has 48 markers and 64 stickers that she wants to give as favors for a party.

The computation of the factors shows that the greatest number of bags that Lucia can make will be calculated through then factors. This goes thus:

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48

Factors of 64 = 1, 2, 4, 8, 16, 32, and 64.

Therefore, the highest common factor is 16.

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Answer:

16

Step-by-step explanation:

Answer:

Area=144m²

Step-by-step explanation:

I hope you don't have any difficulty in understanding this answer

The roster method of the set A' = {14, 15, 20}

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

A typical example of the roster method is to write the set of numbers from 1 to 5 as {1, 2, 3, 4, 5}.

Therefore,

U = universal sets = {14, 15, 16, 17, 18, 19, 20}

A = {16, 17, 18, 19}

Therefore, let's find A' as follows:

A' is the value not in A. Hence, in roster method.

A' = {14, 15, 20}

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We have:

$15 a day

17 cents per mile = $0.17

Total charge = $50.02

Then, let x miles was it driven.

We have the following equation:

Next, solve for x

Answer: they drove 206 miles

Vertex: (1, -36); intercepts: x = 7, -5 (option D)

Given:

To find:

the vertex and the x-intercepts

i) Vertex is given as (h, k). To determine the vertex, we will apply the formula:

Vertex (h, k): (1, -36)

ii) x-intercept is the value of x when y = 0. To determine x-intercept, we will substitute y with 0. Then solve for x

A multiplication equation to show an equivalent fraction of 15 using fifteenths would gives 10/75

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

We have to write an equivalent fraction of 15 using fifteenths.

2/15

So let multiply by 5 .

2 / 15 x  5/ 5 = 10/75

Thus, 10/75 is equivalent expression.

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Answer:

a

The 95% confidence interval is   \(0.5753<  p <0.62474\)  

b

 This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval

c

 The margin of error is   \(E =    0.02474 \)  

d

 The confidence interval becomes wider

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 1506

    The sample proportion is  \(\^ p = 0.60\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

     \(E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } \)

=>   \(E =    1.96 * \sqrt{\frac{0.60 (1- 0.60)}{1506} } \)    

=>   \(E =    0.02474 \)  

Generally 95% confidence interval is mathematically represented as  

      \(\^ p -E <  p <  \^ p +E\)

=>   \(0.60 - 0.02474 <  p <0.60 + 0.02474\)  

=>   \(0.5753<  p <0.62474\)  

This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval

Generally the level of confidence varies directly with the critical value of \(\frac{\alpha }{2}\) and this in turn varies directly with the margin of error which when sample proportion is constant it determines the width of the confidence interval so when the level of confidence increases the confidence interval becomes wider  

Answer:

the answer is 1/2 because of the multiple of 3

The elephant grass will grow 105/4 inches in 7 days

The elephant grass grows 3 3/4 inches in a day

The number of inches it can grow in 7 hours can be calculated as follows

15/4= 1

x= 7

cross multiply both sides

x= 15/4 × 7

x= 105/4

Hence the elephant grass will grow 105/4 inches in 7 days

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Answer:

0.3

Step-by-step explanation:

Answer:

3 tenths or 30%

Step-by-step explanation:

The perimeter of the triangle is

To ascertain the perimeter of a triangle whose verticies reside at points P(-3, -2),Q(0, 2), and R(1, -2),calculate the distances between these points and then add them.

Using the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance for PQ =√((0 - (-3))^2 + (2 - (-2))^2)

Distance for PQ =√(3^2 + 4^2)

Distance for PQ = √(9 + 16)

Distance for PQ = √25

Distance for PQ = 5

Distance for PR = (1 - (-3))

Distance for PR = 4

Distance for QR =√((1 - 0)^2 + ((-2) - 2)^2)

Distance for QR =√(1^2 + 4^2)

Distance for QR =√17

Perimeter

Perimeter = Distance PQ  +  Distance PR  +  Distance QR

Perimeter =  5  +   4   +   √17

Perimeter = 9 +√17 units    

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The perimeter of the triangle is

To ascertain the perimeter of a triangle whose verticies reside at points P(-3, -2),Q(0, 2), and R(1, -2),calculate the distances between these points and then add them.

Using the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance for PQ =√((0 - (-3))^2 + (2 - (-2))^2)

Distance for PQ =√(3^2 + 4^2)

Distance for PQ = √(9 + 16)

Distance for PQ = √25

Distance for PQ = 5

Distance for PR = (1 - (-3))

Distance for PR = 4

Distance for QR =√((1 - 0)^2 + ((-2) - 2)^2)

Distance for QR =√(1^2 + 4^2)

Distance for QR =√17

Perimeter

Perimeter = Distance PQ  +  Distance PR  +  Distance QR

Perimeter =  5  +   4   +   √17

Perimeter = 9 +√17 units    

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The calculated measure of m∠PNM is 87 degrees

from the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

PM = 360 - 64 - 122

Evaluate

PM = 174

Next, we have

m∠PNM = 1/2 * 174

So, we have

m∠PNM = 87

Hence, the measure of m∠PNM is 87 degrees

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The equvalent fractions of 5/7 using 35 as a common denominator is 25/35.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, it should be noted that the fraction given is 5/7.

The equivalent fraction will be:

= 5/7 × 5/5

= 25/35

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Complete question

Write the equvalent fraction of 2/5 using 35 as a common denominater

\(\dfrac{2 \tfrac 12 }{\tfrac 52}\\\\\\\\= \dfrac{\left(\tfrac 5 2\right)}{\left(\tfrac 52 \right) }\\\\\\\\=1\)