The sum of the speeds of two trains is 720.4 miles per hour. If the speed of the first train is 9.6 mph faster than that of the second​ train, find the speeds of each.

The amount Niko earns than Miley in one week is estimated to be $210

the exact amount is $209.85

The estimated amount is solved using subtraction operation.

The weekly amounts of Niko and Miley will be compared and the difference is the amount that Niko earn more than Miley.

From the chart Niko's weekly earning is $650.35 and Miley's weekly earning is $44.50

difference of the two earnings

= Niko's weekly earning - Miley's weekly earning

= 650.35 - 440.50

= 209.85

Niko earns $209.85 more than Miley this could be estimated to be $210

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The value of x is 36 degrees which states that two angles are supplementary.

The given problem can be solved using the formula for supplementary angles,  (that is, their sum is 180 degrees) if their measures add to 180 degrees.

In this case, we are given two angles: (x + 35) degrees and (3x + 1) degrees. We know that the sum of these two angles must be 180 degrees, so:

x + 35 + 3x + 1 = 180

4x + 36 = 180

4x = 144

x = 36

Therefore, the value of x is 36 degrees.

To calculate this, we first added the two angles together to get 4x + 36 = 180. We then subtracted 36 from both sides of the equation to get 4x = 144. Finally, we divided each side of the equation by 4 to get x = 36.

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The value of x is 17

In this question we ahve been given that two lines intersects each other at one point, making an angle of measure (x+35) degrees whose opposite angle measures (3x+1) degrees.

We need to find the value of x.

We know that opposite angles are the angles that are opposite each other when two lines intersect each other at one point.

Also the opposite angles are congruent means they have the same measurement.

So, x + 35 = 3x + 1

We solve above equation to find x.

x + 35 = 3x + 1

x + 35 - 1 = 3x + 1 - 1

x + 34 -x = 3x - x

34 = 2x

2x/2 = 34/2

x = 17

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From the equation A = 1 + prt. solving for r will result to (A - 1) / pt

Using the expression A = 1 + prt solving for r involves making r the subject of the formula this is achieved by taking r to be at one side of the equation

The side is usually at the left hand side of the equation, making r the subject of the formula in the question is done as follows

A = 1 + prt

subtract  to both sides of the equation

A - 1 = 1 + prt - 1

A - 1 = prt

divide both sides of the equation by pt

(A - 1) / pt = prt / pt

(A - 1) / pt = r

rearranging the equation

(A - 1) / pt = r

r = (A - 1) / pt

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The equation of the line is y = (1/4)x - 10 that parallel to y=(1/4)x+2 and passes through (4,-9).

The slope of the line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. Since the line is parallel to y=(1/4)x+2, it has the same slope, m = 1/4.

To find the y-intercept of the line that passes through (4,-9), we can substitute the point's coordinates into the equation and solve for b.

So the equation would be:

y = (1/4)x + b  ....(i)

Substitute the point (4,-9) in it

-9 = (1/4) × 4 + b

Solving it

b = -9 - (1/4) × 4 = -9 - 1 = -10

Substitute the value of b = -10 in equation (i),

y = (1/4)x - 10

Therefore, the required equation of the line is y = (1/4)x - 10.

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Answer: m∠C=45°     AB=12.4 units     AC=15.9 units

Step-by-step explanation:

Given: m∠A=20°     m∠B=115°     BC=6 units

Find: 1) m∠C=?       2)  AB=?  AC=?

1)

m∠C=180°-(m∠A+m∠B)

m∠C=180°-(20°+115°)

m∠C=180°-135°

m∠C=45°

2)

We use the sine theorem to find the length of a side of a triangle:

[tex]\displaystyle\\a)\ \frac{BC}{sin20^0} =\frac{AB}{sin45^0} \\\\AB=\frac{BCsin45^0}{sin20^0}\\\\AB=\frac{6*0.707}{0.342} \\\\AB\approx12.4 \ units\\[/tex]

[tex]\displaystyle\\b )\ \frac{BC}{sin20^0} =\frac{AC}{sin115^0}\\\\AC=\frac{BCsin115^0}{sin20^0} \\\\AC=\frac{6*0.906}{0.342} \\\\AC\approx15.9\ units[/tex]

Answer:

y = 0.25x + 1

Step-by-step explanation:

so, the coordinates are (0, 1) and (4, 2)

The slope formula is: change in y over change in x

which is: (2 - 1) / (4 - 0) = 0.25

the y-intercept formula is: the y value when x is equal to 0

which is: 1

So we group them together:

the slope-intercept form is y = mx + b

m = slope

b = y-intercept

which is: y = 0.25x + 1

To prove [tex]\triangle XYZ \sim \triangle MNO[/tex] using SSS, you need to know that [tex]\frac{XZ}{MO}=\frac{YZ}{NO} \implies \boxed{XZ=17.5}[/tex]

Now that you know the length of [tex]XZ[/tex], you need to know that angle [tex]O[/tex] is congruent to [tex]\boxed{\angle Z}[/tex] to prove [tex]\triangle XYZ \sim \triangle MNO[/tex] using SAS.

The 98% confidence interval for the mean repair cost for the stereos is; (83.653, 99.987)

A confidence interval is defined as the mean of the estimate plus and minus the variation in that estimate.

For this population, the confidence interval is given by the formula;

CI = x' ± z(s/√n)

where;

x' is sample mean

s is standard deviation

n is sample size

z is z-score at confidence level

We are given;

x' = 91.82

s = 16.84

n = 23

Confidence level = 98%

The z-score at 98% confidence level is 2.326. Thus;

CI = 91.82 ± 2.326(16.84/√23)

CI = 91.82 ± 8.167

CI = 83.653, 99.987

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Answer:

1, 2 and 5

Step-by-step explanation:

angle 10 = 180 - angle 9 = angle 4 + angle 6

angle 7 = 180 - angle 6 = angle 4 + angle 9

angle 3 = 180 - angle 4 = angle 6 + angle 9

Answer:

The answer to your question is 2555

Step-by-step explanation:

365 x 56 = 20440

20440 ÷ 8 = 2555

I hope this helps and have a wonderful day!

The circumference of the circle is 44 unit.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

radius=r=7

i.e. circumference

=2πr

=2*22/7*7

=44

hence,  The circumference of the circle is 44 unit.

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The number of terms for the following sequence:

90, 98, 86,....16, 14 is 39

Sequence is defined as defined as an array of numbers in a particular order of arrangment.  It can be AP or GP.

But the sequence given in this question is an AP with the following

Last term = 14,

First term = 90,

Common difference = -2

The nth term of a sequence (AP) when the last term is given is denoted by

L=a + (n-1)d

14= 90 + (n-1)*-2

14=90-2n+2

Rearrange the equation to have

14-90-2=-2n

122=-2n

Making n the subject to get

Therefore number of terms is =61

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The exact length of the apothem in this case is 4.33 units.

The apothem of a regular polygon is a line segment that extends from the centre of the polygon to the midpoint of one of its sides. In a regular polygon with side length s and radius r, the apothem has a length of a = r * cos(180/n), where n is the number of sides in the polygon.

In the case of a regular polygon with a radius of 5 units, we can use the formula above to calculate the length of the apothem. If the polygon is a regular hexagon (n = 6), then the apothem has a length of a = 5 * cos(180/6) = 5 * cos(30) = 5 * 0.866 = 4.33 units.

Alternatively, we could use the formula a = r * (1 - cos(180/n))/sin(180/n) to calculate the apothem. This formula also gives us a result of a = 4.33 units.

So, the exact length of the apothem in this case is 4.33 units.

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As per the given radius, the exact length of the apothem is 4.33 units.

Here we have given that Circle a has a radius with the length of 5 units.

And we need to find the exact length of the apothem,

Here let us consider that the regular hexagon can be divided into 6 equal equilateral triangle.

Then the ΔAED is an equilateral triangle.

=> ∠A = 60°

Then the an equilateral triangle, the altitude bisects the angle is calculated as,

=> ∠DAH = 60/2 = 30°

Now, according to the given radius the apothem is calculated as,

=> cos 30 = AE/AH

=> cos 30 = AE/5

Here we know that the value of cos 30 = √3/2, then the value of the apothem AE is calculated as.

=> AE = √3/2 x 5

=>  AE = 4.33

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The first random sample is example of Stratified Sampling technique. The other one is an example of simple sampling technique.

Some following sampling techniques are examples of probabilistic sampling.

Stratified Sampling is defined as the partition of population into groups based on a factor that may influence/differentiate the variable that is being measured.

We have a random sample of 72% from a list of male legislators and 28% of a sample from a list of female legislators. As we see there are two different groups with different percent of people's based on gender legislators. So, it is an example of Stratified Sampling.

In other example, a friend who homeschools her children about her opinion on state education policy, then collect the other information to find more participants for this study. It is an example of simple sampling technique.

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Answer:

Step-by-step explanation: First add all the different hours of speed he made each week together.

* 15.5 + 17.75 + 20.35 = 53.6

Then divide your answer by the overall amount of weeks he traveled

* 53.6 / 3 = 17.83 recurring

Hope I answered this correctly and I hope it helps.

If Anton wants to make 5 lb of syrup, he will need 1 lb of sugar and 4 lb of water.

Syrup is a frequent ingredient in cookery. It is a condiment that is a thick, viscous liquid that is mostly made up of a sugar solution in water. It has a lot of dissolved sugars but has a low tendency to crystallize.

It has a consistency akin to molasses. The many hydrogen bonds between the dissolved sugar's numerous hydroxyl (OH) groups are what cause the viscosity.

In order to balance the acidity of various juices utilised in the drink recipes, a range of beverages ask for sweetening. Cold beverages or ethyl alcohol do not readily dissolve granulated sugar in them.

Let x = pounds of sugar to make 20% syrup.

Given,

[tex]\frac{x}{5}=0.20\\ \\= > x=0.20 X 5\\= > x=1 lb[/tex]

Therefore, If Anton wants to make 5 lb of syrup, he will need 1 lb of sugar and 4 lb of water.

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To make a 20% sugar syrup of 5lb, Anton would need 4 lbs of water and 1 lb of sugar.

Let the amount of sugar Anton need be x and amount of water be y in pounds. The ratio of sugar to water for a 20% sugar syrup is

x/(x +y) × 100 = 20, that is

[tex]\frac{x}{x+y}\ 100 = 20[/tex]

Dividing by 100 and multiplying by (x + y) on both sides

x = 0.20(x + y)

x = 0.2x + 0.2y

0.8x = 0.2y

Multiplying by 5

4x = y

y = 4x

Also we know that the weight of sugar syrup is 5lb, that is

x + y = 5

Substituting y = 4x

x + 4x = 5

5x = 5

Dividing by 5

x = 1

Solving for y

y = 4x = 4

Amount of water need is 4 lb.

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The standard form of the quadratic function whose graph is a parabola will be;

⇒ y = 1/3 (x² - 4x + 1)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

Vertex coordinate = (-3, 4)

And, A point on the graph = (0, 13)

Since, We know that;

The vertex form of a quadratic equation is given by;

⇒ y = a(x - h)² + k

Where h, k are the coordinates of the vertex.

Hence, At point (5, 2) at the vertex of (2, -1), we have;

⇒ 2 = a (5 - 2)² + (-1)

⇒ 2 = a × 9 - 1

⇒ 2 + 1 = 9a

⇒ 9a = 3

⇒ a = 3/9

⇒ a = 1/3

Since, The equation y = a(x - h)² + k is the vertex form,

Let us put the vertex values for h and k as well as the value of a to get the quadratic equation;

⇒ y = 1/3(x - 2)² - 1

⇒ y = 1/3 (x² + 4 - 4x) - 1

⇒ y = 1/3x² + 4/3 - 4/3x - 1

⇒ y = 1/3x² - 4/3x + 1/3

⇒ y = 1/3 (x² - 4x + 1)

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The property for ∠A ≅ ∠B, ∠B ≅ ∠C, then ∠A ≅ ∠C is c. transitive property.

The transitive property is when the property of A is congruent to the property of B and the property of B is congruent to the property of C, so the property of A also congruent to the property of C.

In mathematics, the transitive property can be written as below,

[tex]{\displaystyle \forall a,b,c\in X:(aRb\wedge bRc)\Rightarrow aRc.}[/tex]

Option a is wrong because reflexive property is only congruent to itself.

Option b is wrong because symmetric property is only congruent to two property.

Option d is wrong because addition property is not for angle.

Thus, the correct option si c. transitive property.

Your question is incomplete, but most probably your full question was

What property is illustrated in: If ∠A ≅ ∠B, ∠B ≅ ∠C, then ∠A ≅ ∠C.

a. Reflexive Property

b. Symmetric Property

c. Transitive Property

d. Addition Property

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An extraneous solution is a solution that is obtained when solving an equation, but is not a valid solution to the original equation. This can happen when solving certain types of equations, such as rational equations, where taking the square root or other inverse operations can produce solutions that are not valid for the original equation.

For example, if you have the equation (x+3)/(x-2) = 2, and you solve for x, you will find that x = 5 is a solution. However, if you substitute x = 5 back into the original equation, you will find that it is not a valid solution. This is because the denominator (x-2) would be zero, which is not allowed in a fraction. So, x = 5 is an extraneous solution.

Generally when solving an equation we need to check our solution back in original equation. in rational equation checking the solution back in original is necessary step as it can have multiple solution or extraneous solution.

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Answer:

4π-8

Step-by-step explanation:

area of top semicircle - area of triangle = answer

triangle is a 45 45 90 triangle, so the hypotenuse = one leg * √2 = 4 * √2

the hypotenuse (side opposite right angle) = the diameter

area of top semicircle = πr²  (area of whole circle) /2

radius = diameter / 2 = 2√2

area of top semicircle = 8π /2 = 4π

area of triangle = one leg ² /2 = 4²/2 = 8

thus, final area = 4π-8

The gradient vector field of f(x, y) = tan(3x − 5y) is (3sec^2(3x - 5y), -5sec^2(3x - 5y))

A gradient vector is a mathematical object that describes the direction of the steepest increase of a scalar function. In other words, it is a vector that points in the direction of the greatest rate of change of a scalar field.

To find the gradient vector field of f(x, y) = tan(3x − 5y), we first need to find the partial derivatives of f with respect to x and y.

The partial derivative of f with respect to x is:

df/dx = 3sec^2(3x - 5y)

The partial derivative of f with respect to y is:

df/dy = -5sec^2(3x - 5y)

The gradient vector field of f is then given by the vector function:

Grad f(x,y) = <df/dx, df/dy> = <3sec^2(3x - 5y), -5sec^2(3x - 5y)>

So the gradient vector field of f(x, y) = tan(3x − 5y) is (3sec^2(3x - 5y), -5sec^2(3x - 5y)).

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The graph that represents Mai's distance from home is given below.

The two points on the graph are (20, 1) and (25, 1).

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Mai walks at a constant speed for 20 minutes.

This means,

The graph is a straight line for 20 minutes.

The red line represents the constant speed.

5 minutes break will represent a horizontal green line on the graph.

The two points on the graph below are:

(20, 1) and (25, 1)

Thus,

The graph is given below.

The two points are (20, 1) and (25, 1).

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The value of x given as x + 2 > 3x - 8 in the inequality is x < 5.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Here, they are denoted by the symbols ≥ < > ≤.

It was given that we should solve the inequality using the algebraic approach: x + 2 greater-than 3 x minus 8.

From the information, the inequality is given as:

x + 2 > 3x - 8

In this case, it is important to collect the like terms

Collect the like terms

x - 3x > - 8 - 2

-2x > -10

Then we have to divide through by 2 in order to get the value of x.

Divide

x < 10 / 2

x < 5

Therefore, the calculation shows that x is less than 5.

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Answer:

Step-by-step explanation:

the answer is 64 because 126-62 is 64

The first number or term that appears in both sequences is equals to the sixteen.

We have two sequences, for first sequence rule is subtract 8 starting from 72. The second sequence rule is subtract 6 starting from 58. We can see that both are arithmetic sequence, which defined as a sequence (list of numbers) that has a common difference (a positive or negative constant) between the consecutive terms. Now, First number in sequence 1ˢᵗ , a₁

= 72

common difference, d₁ = 8

Similarly, for 2ⁿᵈ sequence, aₙ = 58 - 6n

First number in sequence, b₁ = 58

common difference, d₂ = 6

We have to locate the number which appears in both sequences.

The nᵗʰ term of the 1ˢᵗ sequence,aₙ = a₁+ (n-1)d₁

The nᵗʰ term of 2ⁿᵈ sequence, bₙ = b₁ +(n−1)d₂

For the same number to appear on both sequence, the nᵗʰ term must be equal, so

a₁ + (n-1)d₁ = b₁ +(n−1)d₂

=> 72 + (n-1)8 = 58 +(n-1)6

=> 8n - 8 + 72 = 58 + 6n - 6

=> 8n - 6n = 52 - 64 = - 12

=> n = -6

plugging the value of n ,

72 + (-6- 1)8 = 72 - 56 = 16

58 +(-7)6 = 58 - 42 = 16

Therefore, 16 is the first common term/ number appears in both sequences.

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Answer:hard how did you find this??

Step-by-step explanation:

Your pay for the first week of January, given that you worked 10 hours of overtime is option a. $550

To solve this problem, we need to do the calculation for your total pay for the first week of January.

We will multiply the normal working hour by hourly wages:

For the first 40 hours, you would earn a total of

40 * $10.00 = $400=400.

For the 10 hours of overtime, you would earn a total of

10 * $10.00 * 1.5 = $100*1.5=150,

since you get the time and a half for anything over 40 hours. Therefore, your pay for the first week of January would be

$400 + $150 = $400+150=550.

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For the first week of January your pay was $550

The correct answer is an option a. $550

In this question we have been given that hourly wage is $10.00 per hour.

And you get time and a half for anything over 40 hours.

Since the deadline is approaching for a project at work and you are asked to put in more than the normal 40 hours of work for the first week of January.

We need to find the total pay for the first week of January.

Given that,  you get time and a half for anything over 40 hours.

This means, for overtime pay:

per hour regular pay + half of regular pay

= 10 + 5

= $15

So, the overtime wage is $15.00 per hour.

Your hourly wage is $10.00 per

Using unitary method, for the first 40 hours, you would earn a total of:

40 * $10.00

= $400

For the 10 hours of overtime, you would earn a total of

10 * $15

= $150

So, your pay for the first week of January would be

$400 + $150

= $550.

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Quartiles divide data sets in fourths.

The numbers that separate a sorted data set into four (almost) equal sections are known as quartiles. When the number of data values is a multiple of four, the set can be evenly partitioned into four sections.

You can divide the data into three equal groups called quartiles. The first quartile (Q1) separates the bottom 25 percent of the data. The middle point is located in the second quartile (Q2). In statistics, the top 25% of results are separated into the third quartile (Q3) as the upper quartile. In sales and survey statistics, quantiles are frequently used to divide populations into groups.

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The accelerations of each car are given as follows:

The velocities are given as follows:

The acceleration is obtained as the change in the velocity by the change in time, with the change in time having squared units, as velocity is given by change in distance divided by change in time.

A race car accelerates on a straight track from 0 to 100 km/h in 6 s, hence it's acceleration is given as follows:

a = 100/6 = 16.67 km/s².

For the second car, it accelerates from 0 to 100 km/h in 5 s, hence it's acceleration is given as follows:

a = 100/5 = 20 km/s².

The velocity equation for each car is defined as follows:

v(t) = at.

As the velocity is obtained integrating the acceleration.

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Answer:

The perimeter of a rectangle is equal to the sum of all four sides. If the length of the rectangle is 3 more than the width, we can express the perimeter as 2width + 2(width+3). This simplifies to 2width + 2width + 6, which is equal to 58. This can be simplified to 4width + 6 = 58, or 4width = 52. Dividing both sides by 4 gives us width = 13.

Since the width of the rectangle is 13 cm, the length is 3 more than this, or 13+3 = 16 cm. So the dimensions of the rectangle are 13 cm by 16 cm.

Step-by-step explanation: