Jerry flew a total of 4,320 miles over 3 months.
• He flew 6 flights each month.
• He flew the same distance each flight.

How many miles was each of Jerry’s flights?

Answer:

1.5 hours

Step-by-step explanation:

Number of miles = 25 miles

Average speed = 7.4 miles per hour

Break after 13.9 miles

How many more hours does he run

Speed = distance / time

Total time for 25 miles :

Time = distance / speed

Time = 25 / 7.4

Time = 3.378 hours

Total time to cover 13.9 miles :

Time = 13.9 / 7.4

Time = 3.378 hours

Time = 1.878 hours

Difference = (3.378 - 1.878) hours = 1.5 hours

Hence, he to ran for 1.5 hours after taking a break

The total time required for the 25 miles run is 3.378 hours and he will run for 1.5 hours after the break.

Given information:

Roberto runs 25 miles.

The average speed is 7.4 miles per hour.

He takes a break after 13.9 miles.

Now, speed is defined as the ratio of distance and time.

So, the time taken by him to run first 13.9 miles will be,

\(s=\dfrac{d}{t}\\7.4=\dfrac{13.9}{t_1}\\t_1=1.878\)

So, he ran for 1.878 hours to cover 13.9 miles.

Now, the total time of the 25 miles run will be,

\(T=\dfrac{25}{7.4}\\T=3.378\)

So, the total time of the run is 3.378 hours.

After the break, he will run for 3.378-1.878 hours = 1.5 hours.

Therefore, the total time required for the 25 miles run is 3.378 hours and he will run for 1.5 hours after the break.

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Answer:

right triangle

Step-by-step explanation:

Hey there!

A triangle has to have three vertices that add up to 180 degrees

The angle measurments 50 and 40 are already given and added up, they equal 90 degrees

Now out of 180 degrees, 90 degrees is already shown

What you need to do now is try to find how much more degrees you need to get 180 degrees

As you know 180-90=90

So this means that the missing angle is 90 degrees

Now that we know this, we can find out what type of triangle this is

Since the triangle has an angle that is equal to 90 degrees, or it has a right angle, the triangle can be called a right triangle

A right triangle is a triangle that has an angle that is equal to 90 degrees

So this triangle is a right triangle

The simplification of the equation above in words is = Twelve minus thirteen X.

In mathematics, coefficients are those numbers that multiplies a variable. For example in 13x, the coefficient is 13 which multiplies a variable known as X.

The equation given is,

10 - 13x + 2

Arrange the digits without a coefficient together.

That is ,

10+2 -13x

12 - 13x

Therefore the simplification of the given equation in words is Twelve minus thirteen X.

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Answer:

I am assuming any number in between these two, so let's just say 6,550.

Step-by-step explanation:

If you count up from 6,534, you will eventually get to 6,550. If you continue to count up, you will eventually reach 6,565 which is bigger than 6,550.

The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.

a) We are given the equation 8 tan θ = 3 cos θ.

Dividing both sides of the equation by cos θ, we have:

8 tan θ / cos θ = 3

Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:

8 (sin θ / cos θ) / cos θ = 3

Simplifying further, we get:

8 sin θ / cos^2 θ = 3

Now, multiplying both sides of the equation by cos^2 θ, we have:

8 sin θ = 3 cos^2 θ

Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:

8 sin θ = 3(1 - sin^2 θ)

Expanding the equation, we get:

8 sin θ = 3 - 3 sin^2 θ

Rearranging the terms, we have:

3 sin^2 θ + 8 sin θ - 3 = 0

Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.

b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.

To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.

In this case, the equation factors as:

(3 sin θ - 1)(sin θ + 3) = 0

Setting each factor equal to zero, we have two equations:

3 sin θ - 1 = 0    or    sin θ + 3 = 0

For the first equation, solving for sin θ, we get:

3 sin θ = 1

sin θ = 1/3

Taking the inverse sine (sin^-1) of both sides, we find:

θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)

For the second equation, solving for sin θ, we have:

sin θ = -3

Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).

Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.

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Answer:

Triangle

Step-by-step explanation:

It has three side unlike the others can't have three sides

Answer:

45 degrees

Step-by-step explanation:

90 - 45 = 45

Then you can state that angle DEF is congruent to angle GHJ.

The postulate or theorem that allows you to state that angle DEF is congruent to angle GHJ is the Angle-Angle (AA) Postulate.

This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles must also be congruent.

In this case, if you have two triangles, one with angles DEF and the other with angles GHJ, and

you know that angle D is congruent to angle G and angle E is congruent to angle H, then by the AA Postulate, you can conclude that angle F is congruent to angle J.

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Answer:

Step-by-step explanation:

Let x be the cost of the bench. Then the cost of the garden table is 3x.

The combined cost of the bench and the table is 1000, so x + 3x = 1000.

Combining like terms, we get 4x = 1000.

Dividing both sides by 4, we get x = 250.

The cost of the bench is 250.

Answer:

250.

Step-by-step explanation:

Let's call the cost of the bench "x".

The cost of the garden table is then 3x.

So the combined cost of both is x + 3x = 4x = 1000

So x = 250, and the cost of the bench is 250.

The area of the sector in terms of π is 35.6π inches squared.

The area of the sector is approximately  111.6 inches square

The area of sector of a circle is the amount of space enclosed within the boundary of the sector.

Therefore,

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅ = 200 degrees

r = 8 inches

area of the sector = 200 / 360 × 8²π

area of the sector = 200 / 360 × 64π

area of the sector =12800π/  360

area of a sector = 35.6π inches squared

Let's find the area of the sector with π = 3.14

area of a sector = 35.6 × 3.14 = 111.6 inches square

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Answer:

the iqr is 42

Step-by-step explanation:

Answer:

B. x=45, y=20

Step-by-step explanation:

Angles in a quadrilateral add up to 360 degrees.

One angle is a right angle = 90 degrees.

2x + 3y + 6y + 90 = 360

2x + 9y + 90 = 360

2x + 9y = 270

Plug x as 20 and y as 45.

2(20) + 9(45) = 270

445 = 270

Wrong.

Plug x as 45 and y as 20.

2(45) + 9(20) = 270

270 = 270

Correct.

Plug x as 60 and y as 120.

2(60) + 9(120) = 270

1200 = 270

Wrong.

Plug x as 90 and y as 60.

2(90) + 9(60) = 270

720 = 270

Wrong.

Answer:

Option B is the right option.

Solution,

Shown quadrilateral is a trapezoid.

2x and the right angle are consecutive interior angles because they are on the same side of a transversal and between likes that the transversal Intersects.

Since, 2x° and the right angles are consecutive interior angles and two of the lines form these angles are parallel, then by consecutive interior angles theorem the two angles are supplementary and thus the sum of their measure is 180°

\(2x + 90 = 180\)

Subtracting 90 on both sides:

\(2x + 90 - 90 = 180 - 90 \\ 2x = 90\)

dividing both sides by 2

\( \frac{2x}{2} = \frac{90}{2} \\ x = 45\)

Also,

\(3y + 6y = 180 \\ 9y = 180\)

dividing both sides by 9

\( \frac{9y}{9} = \frac{180}{9} \\ y = 20\)

hence, The value of X and y are 45° and 20° respectively..

Hope this helps....

Good luck on your assignment....

The scale factor used to dilate triangle D to create triangle D' is 1/3. This means that each side length in triangle D' is one-third of the corresponding side length in triangle D.

To determine the scale factor used to dilate triangle D to create triangle D', we can compare the corresponding side lengths of the two triangles.

In triangle D, the side lengths are given as 18, 24, and 30. In triangle D', the corresponding side lengths are given as 6, 8, and 10.

To find the scale factor, we can divide the corresponding side lengths of D' by the corresponding side lengths of D.

Scale factor = Length of corresponding side in D' / Length of corresponding side in D

For the corresponding sides, we have:

Scale factor = 6/18 = 1/3

Please note that the scale factor can also be determined by comparing the area or perimeter of the two triangles. However, in this case, we used the corresponding side lengths to find the scale factor.

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(a). The Tanakas paid a total of $523,906.40 for the townhome.

(b). The Tanakas paid $206,906.40 in interest on their mortgage over the 15-year period.

Simple interest is the type of interest that is calculated on the principal amount only.

It is a fixed percentage of the principal amount that is charged or earned over a certain period of time, without any compounding of interest.

(a) The total amount they ended up paying for the townhome is the sum of the down payment and the total amount of the mortgage payments.

Down payment = $41,000

Total amount of mortgage payments = monthly payment x number of payments = $2675.04 x 12 months/year x 15 years = $482,906.40

Total amount paid = down payment + total amount of mortgage payments = $41,000 + $482,906.40 = $523,906.40

(b) The amount of interest paid on the mortgage can be calculated by subtracting the principal (the amount borrowed) from the total amount paid.

Principal = Total cost of townhome - Down payment = $358,000 - $41,000 = $317,000

Total interest paid = Total amount paid - Principal = $523,906.40 - $317,000 = $206,906.40

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Answer:

5

Step-by-step explanation:

1.25+1.25+1.25+1.25=5

Answer:

Step-by-step explanation:

11

angle2=180-152=28

angle3=28

angle4=152

angle5=152

angle6=28

angle7=28

angle8=152

The values of the marked angles: angle 2, angle 3,  angle 4,  angle 5,  angle 6,  angle 7,  angle 8 are 28°, 28°, 152°, 152°, 28°, 28°, 152°.

When two lines or rays meet at a point, then the geometrical figure is formed, is called an angle.

Given, angle 1 = 152°

We know, angle 1 + angle 2 is 180°.     (supplementary angles)

Therefore, angle 2 = (180° - 152°) = 28°.

Again, angle 2 = angle 3.             (opposite angles)

Therefore, angle 3 = 28°.

Similarly, angle 1 = angle 4

Therefore, angle 4 = 152°.

Now, angle 1 = angle 5        (corresponding angle)

Therefore, angle 5 = 152°.

Now, angle 2 = angle 6        (corresponding angle)

Therefore, angle 6 = 28°.

Now, angle 3 = angle 7        (corresponding angle)

Therefore, angle 7 = 28°.

Now, angle 4 = angle 8        (corresponding angle)

Therefore, angle 8 = 152°.

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The complete values of the table for time taken to sign the diploma are: Seconds | 30 | 90 | 150 | 210; Diplomas | 4 | 12 | 20 | 28.

Two ratios are said to be equal when a proportion is stated. Ratios, which can be written as a fraction or a colon, are used to compare two objects or values. For instance, a class might have a boy to girl ratio of 2:3 or 2/3. A percentage is an equation proving the equality of two ratios. The formula is a/b = c/d, where a, b, c, and d are all numerical values or variables. Numerous branches of mathematics, science, and daily life, including banking, engineering, and cookery, require proportions.

Given that, it takes the principal 30 seconds to sign 4 diplomas.

Setting the proportion we have:

30 seconds / 4 diplomas = x seconds / y diplomas

x = 7.5y

Substituting the values of x and y from the table we have:

For y = 12

x = 7.5(2) = 90

Similarly, for y = 20:

x = 7.5(20) = 150

For x = 210:

210 = 7.5y

y = 28

The complete values of the table for time taken to sign the diploma are: Seconds | 30 | 90 | 150 | 210; Diplomas | 4 | 12 | 20 | 28.

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The complete question is:

Answer:

A

Step-by-step explanation:

Answer:

t = 15

Step-by-step explanation:

t - 12 = 3

t = 3 + 12

t = 15

Answer:

The probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

Step-by-step explanation:

Let the random variable X represent the time it takes to wash the dishes.

The random variable X is uniformly distributed with parameters a = 10 minutes and b = 15 minutes.

The probability density function of X is as follows:

\(f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b\)

Compute the probability that washing dishes will take between 12 and 14 minutes as follows:

\(P(12\leq X\leq 14)=\int\limits^{12}_{14} {\frac{1}{15-10} \, dx\)

                           \(=\frac{1}{5}\int\limits^{12}_{14} {1} \, dx \\\\=\frac{1}{5}\times [x]^{14}_{12}\\\\=\frac{1}{15}\times [14-12]\\\\=\frac{2}{15}\\\\=0.1333\)

Thus, the probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

288 ounces of water are left in the water tank.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots

Here, we have

Given: Tom has a water tank that holds 5 gallons of water. tell me this is water for my footing to fill six bottles they each hold 16 ounces and a picture that holds one over 2 gallons.

1 gallon = 128 ounces, 2 gallon = 256 ounces

6 bottles × 16 ounces = 96 ounces

2 gallon + 96 ounces = 256 + 96 ounces = 352 ounces

5 gallon = 5 × 128 = 640 ounces

= 640 - 352 = 288 ounces

Hence,  288 ounces of water are left in the water tank.

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Answer:

1

Step-by-step explanation:

4-3=1. Because both numbers are positive, the absolute value has no effect.

Answer:

1

Step-by-step explanation:

The  |  | sign is used to get an absolute figure.

For example: |3 - 4| = 1

Under normal circumstances, 3 - 4 = -1 but the |  | sign changes whatever is in it to a positive value.

Hence, |p - 4| when p = 4:

|4 - 3| = 1

4 - 3 = 1 under normal circumstances so the | | sign won't affect anything

9514 1404 393

Answer:

  392 7/50

Step-by-step explanation:

The fraction part is fourteen hundredths, or 14/100. Removing a common factor of 2 from numerator and denominator reduces this to 7/50. Then the mixed number is ...

  392.14 = 392 7/50

Answer:

Step-by-step explanation:

a) The volume of a rectangular boxlike bag is given by the formula V = lwh, where l is the length, w is the width, and h is the height. In this case, we know that the length is three times the width, or l = 3x. The height is not given, but we can express it in terms of x and the other dimensions. Since the total dimensions of the bag must not exceed 44 inches, we have:

l + w + h ≤ 44

Substituting l = 3x and rearranging, we get:

h ≤ 44 - l - w

h ≤ 44 - 3x - x

h ≤ 44 - 4x

Therefore, the volume of the bag is:

V = lwh = (3x)(x)(44 - 4x) = 132x^2 - 12x^3

b) To graph the function y = V(x), we can plot points for different values of x and connect them with a smooth curve. Here is a possible set of points:

x V(x)

0 0

5 3300

8 5376

10 6600

12 7128

15 6750

20 4800

We can plot these points and connect them with a smooth curve to obtain the graph of y = V(x). The graph should have a maximum point, which represents the maximum volume that the bag can have while still meeting the airline's requirements. This maximum volume occurs at x = 11/3 inches, and its value is V(11/3) = 8000/27 cubic inches.

Answer:

Step-by-step explanation:

Answer:

Domain: 5, 6, 7, 8

Range: 0, -2, 10, -3

The relation is a function because each x-value has its own y-value.

Step-by-step explanation:

Domain: Set of all first elements in relation

Range: Set of all second elements in relation

How to determine if the relations is a function:

1. Identify the input values.

2. Identify the output values.

3. If each input value leads to only one output value, classify the relationship as a function.

Suppose H (x)=(2x+4)⁶. Find two functions ƒ and g such that (f°g)(x) = H (x). One of the possible solution is

f(x) = (2x + 4)^3

g(x) = x^2

(f°g)(x) = f(g(x)) = f(x^2) = (2x^2 + 4)^3

One possible solution is to set f(x) = (2x + 4)^3 and g(x) = x^2.

f(x) = (2x + 4)^3

g(x) = x^2

Then, (f°g)(x) = f(g(x)) = f(x^2) = (2x^2 + 4)^3

And, (2x^2 + 4)^3 = (2(x^2) + 4)^3 = (2x^2 + 4)^3 = H(x).

Note that this is just one of the possible solutions. There could be other functions ƒ and g that would satisfy the equation (f°g)(x) = H (x).

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