Jane and Peter leave their home traveling opposite directions on a straight road. Peter
drives 15 mpb faster than Jane. After 3 hours, they are 225 miles apart. What is Jane's rate
in miles per hour?

The answer is 100π cm².

Since we are given the volume, equate it to the formula of a sphere to find the radius.

Now, substitute this in the formula to find surface area.

The value of A has been illustrated, computed and proven based in the triangle given.

It should be noted that that a triangle is a shape that has three sides and the value of the addition of all the angles are equal to 180°.

Based on the information that's given, it should be noted that the value of angle A, angle B, and angle C will be equal to 180°.

In this case, the following can be deduced:

A = 5x

B = 90°

C = x + 10°

Therefore, A + B + C = 180° (sum of angles in a triangle)

5x + 90 + x + 10 = 180°

6x = 180° - 90° - 10°

6x = 80°

x = 80/6

x = 13 1/3

Therefore, the value of A will be:

= 5x

= 5 × 13 1/3

= 66 2/3

Therefore, A is 66 2/3.

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Answer:

No

Step-by-step explanation:

Am irrational number is a number that can't be expressed by a ratio (fraction). 1/11 is a fraction so it is rational, not irrational.

The Kernel Function K (x,x') written as a function of the dot product x *x' is  K (x, x') = Z². See the working below.

A kernel function is a way for taking input data and transforming it into the needed form of processing data.

The term "kernel" refers to a collection of mathematical functions used in Support Vector Machine to provide a window to alter data.

Given x = [x₁, x₂][tex]^{T}[/tex]

β(x) = [x²₁, √2 x₁ x₂, x²₂]

K (x₁, x') = β(x)[tex]^{T}[/tex] β(x')[tex]^{T}[/tex]

Hence, X' =  [x₁, x₂][tex]^{T}[/tex]

→ β(x') = [x'²₁, √2 x'₁ x'₂, x'²₂]

K (x, x') = [x²₁, √2 x₁ x₂, x²₂][tex]^{T}[/tex]  [x'²₁, √2 x'₁ x'₂, x'²₂]

K (x, x') = [x²₁, [x'²₁ + 2x₁ x₂ x'₁ x'₂ + x²₂ x'²₂

Because Z = x · x' (dot product of x·x')

= x₁ x'₁ + x₂x₂'

Expressing K (x,x') as a function of Z, we have

K (x₁, x') =  x²₁ x'²₁ + 2x₁x₂ x'₁ x'² + x²₂ x'²₂

Simplified, we have

(x₁ x₁¹ + x₂x¹₂)² =  Z²; and

[(a+b)² = a²+2ab+b₂] = z x₁x₁¹ + x₂x₁²

Therefore,

K (x, x¹) = Z²

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Answer:

C

Step-by-step explanation:

You have a total of 6 outcomes (1,2,3,4,5,6).  That is your numerator.  Out of those numbers, you only want 2 of them (4 or 5), so the fractions would be 2/6 or 1/3 which can also be written 1:3

Answer:

Can i have the graph? THis doesn't make sense

Step-by-step explanation:

The graph of (f+g)(x) is on the coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5).

The graph of a parabolic equation is a curved U-shape graph from where the domain, the range, x-intercept(s), and the y-intercept(s) can be determined.

Given that:

f(x) = -x² + 3x + 5

g(x) = x² + 2x

To find (f + g)(x), we have:

(f + g)(x) = (-x² + 3x + 5)+(x² + 2x)

(f + g)(x) = -x² + 3x + 5 +x² + 2x

(f + g)(x) = 3x + 2x + 5

(f + g)(x) = 5x + 5

Use the Slope-intercept form: We are to find the graph of y = 5x + 5

y = 5x + 5

Here:

Therefore, we can conclude that on the coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)

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Using the combination formula, the coach can make 5,005 different groups.

The position does not matter, hence the combination formula is used.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 6 students are taken from a set of 15, hence the number of groups is:

[tex]C_{15,6} = \frac{15!}{6!9!} = 5005[/tex]

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Answer: 19/25

Step-by-step explanation:  50 candies total. 28 are red, 10 are blue 8 are green, and 4 are yellow. We want to calculate the probability of choosing a candy and either getting blue or red. The total candies that are blue or red are 28+10 = 38. So, 38/50. We can simplify by dividing by 2 to get 19/25. 19 is a prime number so that is as simple as we can get,

Answer:

(-4, -2).

(0, 0).

Step-by-step explanation:

Both coordinates will be negative or (0.0).

It's these followings:

□(-4,-2)

□(0,0)

Hope this helps!

Answer:

C. 21°C

Step-by-step explanation:

Substitute 69.8 for F in the equation, [tex]69.8=\frac{9}{5}C+32[/tex]. This becomes [tex]37.8=\frac{9}{5} C[/tex]. Divide both sides by [tex]\frac{9}{5}[/tex] to get [tex]21=C[/tex].

Answer:

21

Step-by-step explanation:

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Considering the proportions given in the table, the superhero is most likely to be the favorite is Superman.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Looking at the table, the proportions associated with each superhero is given as follows:

As it has the highest proportion, the superhero is most likely to be the favorite is Superman.

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Answer:

volume = 840 cubic cm

(3.2/100)×840= 26.88 per day

after 4 days = 26.88×4=107.5

answer is 107.5

The volume (in cubic centimeters) after 4 days, given that the initial volume of the ball was 840 cubic centimeters, is 732.5 cubic centimeters

First, we shall determine the volume lost per day. Details below:

Volume lost per day = 3.2% × Initial volume

= 3.2% × 840

= (3.2 / 100) × 840

= 26.88 cubic centimeters

Now, we shall obtain the volume after 4 days. Details below:

Volume after 4 days = Initial volume - Volume lost in 4 days

= 840 - 107.52

= 732.5 cubic centimeters

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Answer:

32

Step-by-step explanation:

The length of segment AB is the average of XY and WZ.

(22 + x)/2 = 27

22 + x = 54

x = 32

Here, Given

h= 8ft

a=144 * ft^2

then,

A=L*H

144=L*8 or 144/8 =L

L=18

now, P=2(L+H)

P=2(18+8)

P=52m

Perimeter and area are two important and basic mathematical subjects. They help quantify the physical space and also provide a more advanced foundation of mathematics in algebra, trigonometry, and calculus. Perimeter is a measure of the distance around a shape, and area indicates how much area the shape covers.

The perimeter of a 2D shape is the distance around the shape. You can imagine wrapping a string around a triangle. The length of this cord is around the triangle. Or, if you're traveling outside the park, take a route that goes around the edge of the park.

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We would reach our office by 7:34 a.m.

The average speed is given as 30 miles per hour.

Let us convert this into miles per minute.

30 miles/1 hour = 30 miles/60 minutes

= 0.5 miles per minute

The distance between the house and the office is 12 miles.

Therefore, we can find what it would take to reach the office by dividing the distance by the average speed:

Time taken = distance/average speed

= 12 miles/0.5 miles per minute

= 24 minutes

The time is given to be 7:10 a.m. Therefore we would reach our office by 7:34 a.m.

Therefore, we would reach our office by 7:34 a.m.

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Answer:

Step-by-step explanation:

 yes I believe it is an quartic binomial

Answer:

yes

Step-by-step explanation:

If because it has two terms, it is a binomial, therefore it also qualifies as a polynomial.

Hope this helps

The percentages of 67 of 98 is 68.36%

Fractions are written as a ratio of two integers. According to the question we are to determine the percentage of 67 that is 98.

Fraction of 67 of 98 = 67/98

Percentage = 67/98 * 100

Percentages = 6700/98

Percentages = 68.37%

Hence the percentages of 67 of 98 is 68.36%

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We use the chi-square distribution when making inferences about a single population variance.

Short Description of Chi-Square Distribution

The continuous probability distribution known as the chi-square distribution. The number of degrees of freedom (k) a chi-square distribution has determines its shape. This type of sampling distribution has a variance of 2k and a mean equal to its number of degrees of freedom (k). The range is of a chi-square distribution is from 0 to ∞.

Variance plays a key role in the analysis of risk and uncertainty. The sample variance, an unbiased estimator of population variance, is expressed by the following formula of core statistic for a sample size 'n' and Y' as the sample mean:

S² = ∑(Yₓ - Y') / (n-1)

The formula, (n-1)S² / σ² has the central chi-square distribution as χ²ₙ₋₁. Here (n-1) represents the degrees of freedom.

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The system of equations best represents the number of apples a and the number of garonia bars g be a+b=60, 0.75x+0.15y=21.

Given that cost of 1 apple is $0.75, cost of 1 gargonia bars be $0.15 ,total things are 60 and total money paid be $21.

Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be a linear equation,quadratic equation, cubic equation.

Because we have been told that there are 60 total things and a represents the number of apples and g represents number of garonia represents the number of garonia bars.

a+b=60--------1

Money paid by consumers is cost per units*number of units

So,

0.75a+0.15b=21

Hence the system of equations best represent the number of apples and the  number of garonua bars g are a+b=60, 0.75a+0.15b=21.

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Answer:

x/2>5

x>5*2

x>10.....equation 1

3x≥9

x≥9/3

x≥3.....equation 2

so by combining of the two equation we get

x>10 because it is the intersection of the. . two equations.

The answer will the Third

The vectors are linearly independent if and only if k ≠ -11

In mathematics, the definition of a vector is a quantity that is made up of both magnitude and also have direction. This type of quantity is not one that is considered based on its position. A very good example of such a quantity with magnitude and direction is acceleration.

Vectors are used to represent items such as position, velocity, physical quantities and others in mathematics and in physics.

In this question,

We have 2v - 3w

We have to multiply 2 by the values of v and multiply 3 with the values of w

this would produce

[2,6,8]-[6,6,12]

subtract w from v

= [-4, 0, -4]

We u as -1, 0 and 10+k

It is not possible to -1 = 10 + k

-11 = k

Hence we have to conclude that they are linearly independent if and only if k ≠ -11

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Two triangles are similar but not congruent if they have three congruent angles but the side lengths are not equal.

What is the congruency of triangles?

To show how can the triangles be proven similar by the SSS similarity theorem:

The two triangles can be shown to be similar given that the ratios of the corresponding sides ΔWUV and ΔYXZ are constant

Reason:

Known parameters are:

ΔWUV and ΔXZY are shown:

∠VUW ≅ ∠YXZ

∠UWV ≅ ∠XZY

∠UVW ≅ ∠ZYX

Length of side VW = 60

Length of side VU = 50

Length of side UW = 40

Length of side  ZY = 48

Length of side  YX = 40

Length of side  XZ = 32

The ratio of the sides are:

[tex]\frac{VW}{ZY} =\frac{60}{48} =\frac{5}{4} \\\frac{VU}{YX} =\frac{50}{40} =\frac{5}{4} \\\frac{UW}{XZ} =\frac{40}{32} =\frac{5}{4}[/tex]

Therefore, given that  the angles of ΔWUV and ΔXZY are all congruent, and the sides of triangle ΔWUV and ΔXZY have a constant proportion, we have that the two triangles are congruent by the Side-Side-Side SSS congruency theorem,  and we have:

ΔWUV ~ ΔYXZ given that ΔYXZ is a scaled drawing of ΔWUV.

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The complete question is given here:

Triangles W U V and X Z Y are shown. Angles V U W and Y X Z are congruent. Angles U W V and X Z Y are congruent. Angles U V W and Z Y X are congruent. The length of side V W is 60 and the length of side Z Y is 48. The length of side Y X is 40 and the length of V U is 50. The length of side U W is 40 and the length of X Z is 32.

How can the triangles be proven similar by the SSS similarity theorem?

Based on the fact that the shop still made a 40% profit on the concept xi bicycle, the original listing price must have been $1,600.

assuming the list price is x, the formula would be:

800 x 1.40 = (x × 0.7)

solving gives:

1,120 = 0.7x

x = 1,120 / 0.7

= $1,600

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Step-by-step explanation:

Taking the men first: there are 5 ways to form a 4-man committee out of 5 men.

Taking the women now: There are 20 ways to form a 3-woman committee out of 6 women.

Each of the 5 possible male groups can be combined with any of the 20 possible female groups.

So: 100.

The value of the piecewise function at the domain is f(-1) = 1

The complete question is added as an attachment

At x = -1, the function is

f(x) = x^2

So, we have:

f(-1) = (-1)^2

Evaluate

f(-1) = 1

Hence, the value of the piecewise function at the domain is f(-1) = 1

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Joanna can assemble her bracelet in 30 ways.

It is given that Joanna has 6 beads and of those 6 beads, 2 are of the same color.

The rest 4 are of different colors.

Six beads can be arranged in a circle in 6!/6 ways.

This means that the six beads can be arranged in 5! ways.

Since this is a bracelet, it can be flipped around. Therefore, it can be arranged in 5!/2 ways.

5!/2 = 5*4*3*2*1/2

= 60

Now, we know that two beads are of the same color. Therefore, we must divide this by two again.

Therefore, we get:

60/2 = 30

The six beads can be arranged in 30 ways to make the bracelet.

Therefore, we have found that Joanna can assemble her bracelet in 30 ways.

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Answer: 12 sides

Step-by-step explanation:

The sum of the interior angles of a polygon is 180(n-2), where n is the number of sides

[tex]180(n-2)=1800\\\\n-2=10\\\\n=12[/tex]

Answer: Length - 20, Width - 10

Step-by-step explanation:

First we will use the formula to find area:

Area = Length * Width --- However, since it's double the length we will do 2Length.

Area = 2x*x

Given Area = 200

Next we will solve to find Width:

[tex]2x^{2} =200[/tex]

Divide by 2:

[tex]x^{2} =100[/tex]

Take square root:

[tex]x=10[/tex]

Width = 10

Now we multiply 10 by 2, as length is twice it's width:

[tex]2*10=20[/tex]

Length = 20

Final answer: Width = 10, Length = 20

I hope this helps!