Tyler rides his bike from his house to his cousin's house. He bikes a total of 1.8 kilometers to get there and back. What is the distance, in meters, between Tyler's house and his cousin's house?

Answer:

perimeter of ΔDEF  ≈ 32

Step-by-step explanation:

To find the perimeter of the triangle, we will follow the steps below:

First, we will find the length of the side of the triangle DE and FF

To find the length DE, we will use the sine rule

angle E  = 49 degrees

e= DF = 10

angle F = 42 degrees

f= DE =?

we can now insert the values into the formula

=  

cross-multiply

f sin 49° = 10 sin 42°

Divide both-side by sin 49°

f = 10 sin 42° / sin 49°

f≈8.866

which implies DE ≈8.866

We will now proceed to find side EF

To do that we need to find angle D

angle D + angle E + angle F = 180°  (sum of interior angle)

angle D + 49° + 42° = 180°

angle D + 91° = 180°

angle D= 180° - 91°

angle D = 89°

Using the sine rule to find the side EF

angle E = 49 degrees

e= DF = 10

ange D = 89 degrees

d= EF = ?

we can now proceed to insert the values into the formula

=  

cross-multiply

d sin 49° = 10 sin 89°

divide both-side of the equation by sin 49°

d= 10 sin 89°/sin 49°

d≈13.248

This implies that length EF = 13.248

perimeter of ΔDEF = length DE + length EF + length DF

                                  =13.248   +  8.866  + 10

                                   =32.144

                                    ≈ 32 to the nearest whole number

perimeter of ΔDEF  ≈ 32

Answer:

\(\dfrac{c}{2}\)

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)

Applying this logic to the given expression:

\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)

↓ simplify multiplication of fractions

\(\dfrac{a \cdot bc}{2b \cdot a}\)

↓ rewrite to align like variables

\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)

↓ separate out variables that are divided by each other

\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)

↓ represent them as 1

\(1 \cdot 1 \cdot \dfrac{c}{2}\)

↓ rewrite without unnecessary 1's

\(\dfrac{c}{2}\)

Answer:

120

Step-by-step explanation:

A higher percentage of people who did not wear wrist guards (41.67%) experienced wrist injuries compared to those who did wear wrist guards (11.32%).

Based on the information provided, we can analyze the data on injuries to in-line skaters. Let's break down the given numbers:

Total number of people interviewed: 161

Number of people wearing wrist guards: 53

Number of people wearing wrist guards with wrist injuries: 6

Number of people not wearing wrist guards: 108

Number of people not wearing wrist guards with wrist injuries: 45

From this information, we can calculate the following:

Percentage of people wearing wrist guards with wrist injuries:

(Number of people wearing wrist guards with wrist injuries / Number of people wearing wrist guards) × 100

= (6 / 53)× 100 ≈ 11.32%

Percentage of people not wearing wrist guards with wrist injuries:

(Number of people not wearing wrist guards with wrist injuries / Number of people not wearing wrist guards)×100

= (45 / 108) ×100 ≈ 41.67%

These calculations provide insights into the likelihood of wrist injuries in relation to wearing wrist guards while inline skating. The data suggests that the percentage of wrist injuries among those wearing wrist guards is lower (11.32%) compared to those not wearing wrist guards (41.67%). This indicates that wearing wrist guards may offer some protection against wrist injuries while inline skating.

Learn more about percentage here:

https://brainly.com/question/843074

#SPJ11

Answer:

The distance traveled between 10 minutes and 15 minutes is increasing.

Step-by-step explanation:

Jacob is going on a road trip across the country. He covers 10 miles in 15 minutes.Therefore, between the 10 minutes and 15 minutes, Jacob was in motion and if he covers 10 miles in 15 minutes with a constant speed, then Jacob will cover \frac{10}{15} \times (15 - 10) =  3.33 miles in that period.So, the distance traveled between 10 minutes and 15 minutes is increasing.

Answer:

D on edmentum

Step-by-step explanation:

The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.

Given that the population mean, \(\mu\) = 90 wpm

The standard deviation of the population ,\(\sigma\) = 10

Sample size, n = 12

Sample mean, \(\bar x\) = 95

The reading rate of students follows the normal distribution.

Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)

        = \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)

        = 1.732

Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)

                                                                                       = P(z>1.732)

                                                                                       = 1- P(z<1.732)

                                                                                       = 0.4582

[The value 0.4582 found from the area under the normal curve using tables].

Learn more about Normal Distribution at https://brainly.com/question/27701525

#SPJ4

Answer: Answer

1.0/5

1

angelinagalindo127

Ambitious

40 answers

2.2K people helped

Answer:

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.Step-by-step

Step-by-step explanation: |\   /|

\|_|/

/. .\

=\_Y_/=

{>o<}

Any counting number can be written as the sum of distinct powers of 2.(proved).

What is counting number?

Counting numbers are nothing but  the natural numbers that can be used for counting. The numbers start from 1 and the series continues as 1, 2, 3, 4, 5, 6,-- and so on. Zero can not be included in counting numbers because we cannot count 0.

To prove this statement we have to consider two cases.

Let, n be any counting number or natural number. Then the power of 2 can be written as 2ⁿ.

n can be even or odd.

n=1:

If n=1 then it can be written as 2⁰

Let us assume that for n≤ k that n can be written as the sum of distinct powers of 2.

Now let us take, n= k+1.

Here one case is n is odd.

Then n≤ k+1

   so, n-1≤ k

By the induction hypothesis n-1 can be written as distinct power of 2.

n is the sum of these distinct powers of 2 as well 2⁰, which is not among them. as n-1 is even.

Now if n is even,

so n=2m (say) for m≤ k

Thus, by the induction hypothesis m can be written as distinct power of 2.

If for each power of 2 in this sum , increment the exponent by 1 then the resulting sum of distinct powers of 2 equals n= 2m

Hence, the statement is true.

To know more about counting numbers

https://brainly.com/question/2228445

#SPJ4

If you provide the desired standard error value, I can help you calculate the corresponding population standard deviation.

The standard error is a measure of the variability or uncertainty of a sample mean. It is calculated by dividing the population standard deviation by the square root of the sample size. Therefore, if we want the standard error to be smaller, the population standard deviation should be larger.

To determine how large the population standard deviation needs to be, we need to specify a desired standard error value. Without that information, it is not possible to provide a specific answer. The relationship between the population standard deviation and the standard error is inversely proportional, so as the population standard deviation increases, the standard error decreases.

Know more about standard deviation here:

https://brainly.com/question/23907081

#SPJ11

Answer:207.24 and 483.56

Step-by-step explanation:

The formula for the surface area of a cylinder is:

A=2πrh+2πr2

Meaning that we only have to plug the values in.

2π(3)(8)+2π(3)²

=48π+18π

=66π

=66(3.14)

=207.24

Second Cylinder:

2π(7)(4)+2π(7)²

=56π+98π

=154π

=154(3.14)

=483.56

Answer:answer is D

Step-by-step explanation:

Answer:

Cannot be determined

Step-by-step explanation:

The scores are not independent

Answer:

Step-by-step explanation:

A B D

Answer:

Its A,B,D

i got them right on the quiz :)))

Answer: miss bailey bought 8 for 3 dollars each  

Step-by-step explanation:

so if a binder cost 12 subtract that form the $36 and you are left with $24. divided it by 8 and are left with 3

The simplified expression of cos^2x sin^4x is cos^2x - 2cos^4x + cos^6x.

The expression cos^2x sin^4x can be simplified by using the trigonometric identity that states sin^2x + cos^2x = 1.

We can rewrite cos^2x sin^4x as cos^2x (sin^2x)^2. Then, using the trigonometric identity sin^2x + cos^2x = 1, we can substitute (1 - cos^2x) for sin^2x.

This gives us cos^2x (1 - cos^2x)^2, which can be expanded using the binomial theorem to give cos^2x (1 - 2cos^2x + cos^4x).

Finally, we can simplify this expression further by distributing the cos^2x term and collecting like terms to get cos^2x - 2cos^4x + cos^6x.

Therefore, the simplified expression of cos^2x sin^4x is cos^2x - 2cos^4x + cos^6x.

Learn more about expression here

https://brainly.com/question/1859113

#SPJ11

Answer:

21 (Thats a joke incase this is serious, if it is 19)

Step-by-step explanation:

The x-intercepts can be found by setting y = 0 and solving for x. In this case, the x-intercepts are -6 and 5/2 and the parabola opens upward, and the domain is all real numbers while the range is y ≥ y-coordinate of the vertex.

To find the vertex, we can use the formula x = -b/2a, where a and b are the coefficients of the quadratic function. In this case, the vertex occurs at x = -6/2 = -3.

The direction of the opening can be determined by the coefficient of x^2. If the coefficient is positive, the parabola opens upward, and if it's negative, the parabola opens downward. In this case, since the coefficient is positive, the parabola opens upward.

The domain is the set of all real numbers, as there are no restrictions on x. The range depends on the direction of the opening. Since the parabola opens upward, the range is y ≥ the y-coordinate of the vertex. In this case, the range is y ≥ the y-coordinate of the vertex at x = -3.

In summary, the x-intercepts are -6 and 5/2, the vertex is (-3, y), the parabola opens upward, and the domain is all real numbers while the range is y ≥ y-coordinate of the vertex.

To learn more about “parabola” refer to the https://brainly.com/question/4061870

#SPJ11

Answer:

f(x) = -2x – 7 ; if x < -5

-(x + 2)² + 6 ; if -5 ≤ x < 0

√(x) – 1 ; if x ≥ 0

Answer:

30 minutes

Step-by-step explanation:

The percentage rises up by 40% every 20 minutes and if we divide that in half he paints 20% in 10 minutes. Wilson needs to paint 60% more of the bookcase. 40% plus 20% is 60%. So we just add 20 with 10 to get 30 minutes.

Answer:

x = 4

Step-by-step explanation:

This is an equation but solving inequalities is very similar to solving equations.

\( - 2x + 3 = - 5\)

Subtract 3 from both sides.

\( - 2x = - 8\)

Divide by - 2 from both sides.

\(x = 4\)

(I originally typed the equation as - 2x + 3 = 5, my bad.)

Answer:

x=4

Step-by-step explanation:

m

a

t

h

w

a

y

Answer:

The answer is 1. This table is an example of the principle of independence.

Step-by-step explanation:

This means any Trade activity is performed without reliance on another party.

He got the perfect answer to his question and he can get his answer without any other information.

Answer:

159 feet of fabric

Step-by-step explanation

We are told that 1 curtain is 36inches long

Since 1 foot = 12inches

x foot = 36inches

Cross multiply;

12 * x = 36

12x = 36

x = 36/12

x = 3

Hence 36inches is same as 3 feet

If Charlotte's curtain company wants to make 53 curtains, the length of 53 curtain is expressed as;

1 curtain = 3feet

53 curtain = y

y = 53 *3

y = 159 feet

Hence she will need 159 feet of fabric

Noote that the measure of angle R is 27°. Here is how we got that.

Since the largest triangle is right triangle, the vertical segment is the perpendicular bisector of right angle with vertex at the center of circle.

Then we have

m∠R + 18° = 90°/2

m∠R + 18° = 45°

m∠R = 45° - 18°

m∠R = 27°

Note that the angle on the top of the triangle is right angle, 90 deg. Its altitude is the vertical segment, which is also angle bisector. It bisects the right angle and each formed angle measures 90/2 = 45°

Learn more about angle  at:

https://brainly.com/question/2845107

#SPJ1

Full Question:

Although part of your question is missing, you might be referring to this full question:

See the attached iamge.

Answer: 6 and 7

Step-by-step explanation:

Take the square root of 36 and 49 as example. The square root of 36 is 6, and the square root of 49 is 7. So the square root of 40 is in between 6 and 7

Answer:

Step-by-step explanation:

b). Since relation between the number of spring rolls and number of people is,

Number of spring rolls ∝ Number of people

Therefore, Number of spring rolls (R) = k × Number of people (P)

With the help of this proportional relation,

If the number of spring rolls (R) are 6 and the number of people (P) are 3.

6 = 3k

k = 2

So the equation that defines the relation will be,

R = 2P

a). For R = 1,

1 = 2P ⇒ P = 0.5

For R = 10,

10 = 2P ⇒ P = 5

For R = 16,

16 = 2P ⇒ P = 8

For R = 25,

25 = 2P ⇒ P = 12.5

For R = n,

n = 2P ⇒ P = \(\frac{n}{2}\)

He will travel around 75 miles if he drives for one hour at the same rate.

The unitary approach is a methodology for solving problems that involves first determining the value of a single unit and then multiplying that value by the required value. The term unitary refers to a single or unique entity. As a result, the goal of this approach is to determine values in reference to a single unit. For example, if a car travels 44 kilometers on two litres of gasoline, we may use the unitary technique to calculate how far it will go on one litre of gasoline. The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value.

Here,

If he drove 15 miles in 12 minutes,

In 60 minutes, he will drive,

=60*15/12

=75 miles

He will go about 75 miles when he drove one hour in total at the same rate.

To know more about unitary method,

https://brainly.com/question/28276953

#SPJ1

The value of x + y in the given expression is determined as -21.

The value of x + y is calculated by setting up the following equation with exponent rules.

From the first function, we will have the following equation;

\(2^{3x} = 8^{y +3}\)

Simplify the equation as follows;

\(2^{3x} = 2^3^{(y +3)}\\\\\)

3x = 3(y + 3)

x = y + 3

From the second expression, we will have the following;

\(4^{x + 1} = \frac{16^{(y + 1)}}{8^{(y + 3)}}\)

Simplify as follows;

\(2^{2}^{(x + 1)} = \frac{2^4^{(y + 1)}}{2^3^{(y + 3)}}\)

\(2(x + 1) = \frac{4(y + 1)}{3(y + 3)}\)

2(x + 1) = 4(y + 1) - 3(y + 3)

2x + 1 = 4y + 4 - 3y - 9

2x = y - 6

Substitute the value of x;

2( y + 3) = y - 6

2y + 6 = y - 6

y = -6 - 6

y = -12

x = y + 3

x = -12 + 3

x = -9

The value of x + y = -9 - 12 = -21

Learn more about summation here: https://brainly.com/question/24495014

#SPJ1

Answer:

121

Step-by-step explanation:

Given

f(x) = - (x + 8)(x - 14) ← expand factors using FOIL

     = - (x² - 6x - 112) ← distribute by - 1

     = - x² + 6x + 112

Given a quadratic in standard form. y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

f(x) = - x² + 6x + 112 ← is in standard form

with a = - 1 and b = 6, thus

\(x_{vertex}\) = - \(\frac{6}{-2}\) = 3

Substitute x = 3 into f(x) for corresponding value of y

f(3) = - (3)² + 6(3) + 112 = - 9 + 18 + 112 = 121

vertex = (3, 121 ) ← with y = 121

Answer:

D. 121

Step-by-step explanation: