Annual high temperatures in a certain location have been tracked for several years. Let
X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).

y=________
x=________

Answer:

Part 21) The distance from Football Field to the Park is [tex]10.95\ miles[/tex]

Part 22)

a) The value of a is [tex]20\ units[/tex]

b) The value of b is [tex]20.10\ units[/tex]

Step-by-step explanation:

Part 21)

Let

A -----> Football Field

B -----> Park

C -----> Home

D -----> Library

x -----> the distance from Football Field to the Park

In the right triangle ABD

[tex]cos(A)=10/x[/tex] -----> equation A

In the right triangle ABC

[tex]cos(A)=x/12[/tex] ----> equation B

equate equation A and equation B

[tex]10/x=x/12[/tex]

solve for x

[tex]x^{2}=120\\ \\x=10.95\ miles[/tex]

Part 22)

see the attached figure with letter to better understand the problem

step 1

Find the value of a

In the right triangle ABD

[tex]tan(ABD)=a/200[/tex] ----> equation A

In the right triangle ADC

[tex]tan(DAC)=2/a[/tex] ----> equation B

remember that angle ABD is congruent with angle DAC

therefore

equate equation A and equation B

[tex]a/200=2/a[/tex]

solve for a

[tex]a^{2}=400\\ \\a=20\ units[/tex]

step 2

Find the value of b

In the right triangle ADC

Applying the Pythagoras Theorem

[tex]b^{2}=a^{2}+2^{2}[/tex]

substitute the value of a

[tex]b^{2}=20^{2}+2^{2}[/tex]

[tex]b^{2}=404[/tex]

[tex]b=20.10\ units[/tex]

Final answer:

To find the height of the 7th bounce of a bouncy ball, where each bounce is 64% of the height of the previous one, use the geometric sequence formula. For the first bounce's height of 5.5 feet and a common ratio of 0.64, calculate the 6th power of 0.64, then multiply by 5.5 and round to the nearest tenth.

Explanation:

The student is asking about finding the height of the seventh bounce of a bouncy ball, which follows a geometric sequence in which each term is 64% of the previous one. To find the height of the 7th bounce, we will use the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term, r is the common ratio, and n is the term number.

The first term a1 is the height of the first bounce, which is 5.5 feet, and the common ratio r is 0.64 (since 64% is 0.64 in decimal form). Using this information, the height of the 7th bounce is calculated as follows:

Calculate the 6th power of the common ratio: 0.646

Multiply this value by the height of the first bounce: 5.5 × 0.646

Round the result to the nearest tenth

Calculating the exact value and rounding to the nearest tenth gives us the height of the seventh bounce.

Answer:

A

Step-by-step explanation:

Degree: that's the power on the x term. 2

Coefficient on the x term. That is             3

Constant term. That has no x                   -4

The minus is included.

The answer is A

Answer :

[tex]\frac{7}{15}[/tex]×[tex]\frac{2}{15}[/tex] = [tex]\frac{14}{225}[/tex]

Step-by-step explanation:

P([tex]Event_{1}[/tex]) = choosing yellow marble from paper bag = [tex]\frac{favourable outcomes}{possible outcomes}[/tex] = [tex]\frac{7}{15}[/tex]

P([tex]Event_{2}[/tex]) = choosing yellow marble from cloth bag = [tex]\frac{favourable outcomes}{possible outcomes}[/tex] = [tex]\frac{2}{15}[/tex]

∵ Resultant outcome is dependent upon both the events and both events are independent from each other, so we can apply intersection rule [ P(A∩B)=P(A)×P(B) ] here

∴ Probability ( Both marbles are yellow) = P([tex]Event_{1}[/tex]) × P([tex]Event_{2}[/tex]) = [tex]\frac{7}{15}[/tex] × [tex]\frac{2}{15}[/tex]

The probability that Tim will draw a yellow marble from both bags is found by multiplying the probability of drawing a yellow marble from each bag, giving a result of 14/225 or approximately 0.0622.

The question is asking to find the probability of Tim drawing two yellow marbles, one from each bag, so this is a question about probability.

We know that there are 7 yellow marbles out of 15 in the paper bag, so the probability of drawing a yellow marble from this bag is 7/15. In the cloth bag, there are 2 yellow marbles out of 15, making the probability of drawing a yellow marble from this bag 2/15.

To find the overall probability that both marbles Tim draws are yellow, we multiply the two independent probabilities: (7/15) × (2/15) = 14/225.

So the probability that Tim will draw a yellow marble from both bags is 14/225, or approximately 0.0622 when expressed as a decimal.

For this case we have that the area of the kite is given by the area of two triangles, the triangles share the same base of 3 + 3 = 6 meters and one has height of 2m and the other height of 4m.

So, the total area is given by:

[tex]A = \frac {1} {2} * 6 * 2 + \frac {1} {2} * 6 * 4\\A = \frac {1} {2} 12+ \frac {1} {2} *24\\A = 6 + 12\\A = 18[/tex]

Thus, the area of the kite is [tex]18m ^ 2[/tex]

ANswer:

[tex]18m ^ 2[/tex]

Answer:

80 per hour

Step-by-step explanation:

because every hour it goes up 80 every time

The speed of the car is 80 km/h.

Speed exists as the time rate at which an object exists moving along a path, while velocity exists as the rate and direction of an object's movement. Put another way, speed exists as a scalar value, while velocity is a vector.

Speed exists the rate at which an object’s position changes, measured in meters per second.

The speed of the car is 80 km/h.

Therefore, 80 km/h stands as the correct answer.

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Answer:

  B) 504

Step-by-step explanation:

They should expect 30% of 40 out of every 300 of the 12,600, so ...

  0.30 × 40/300 × 12,600 = 504

About 504 residents might be expected to join.

To estimate the number of residents that Muscles can expect to join its new branch, multiply the total number of residents within driving distance by the percentage of respondents who would actually join the gym. Muscles can expect about 1,680 residents to join its new branch.

To estimate the number of residents that Muscles can expect to join its new branch, we can multiply the total number of residents within driving distance by the percentage of respondents who would actually join the gym.

First, we need to calculate the percentage of respondents who would join the gym:

Percentage = (Number of respondents who would join the gym / Total number of respondents) * 100

Percentage = (40 / 300) * 100 = 13.33%

Next, we multiply the estimated percentage by the total number of residents within driving distance:

Number of residents who would join the gym = (Percentage / 100) * Total number of residents within driving distance

Number of residents who would join the gym = (13.33 / 100) * 12,600 = 1,678.5

Therefore, Muscles can expect about 1,680 residents to join its new branch.

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Answer:

last choice

Step-by-step explanation:

Let's look at (8,-2)

We are moving this point 7 units right and 2 units down so that becomes

(15,-4)

But you are also reflecting it across y-axis so the x becomes opposite and y stays the same so you have the final image point after the transformations is (-15,-4).

So it can only be choice D, the last choice.

Answer: se necesitan 4 medidas de B para obtener una de D

Step-by-step explanation:

Las medidas serán entendidas como unidades de.. (A , B o C)

Entonces, de esta manera

1A + 1C = 5B

1A + 1B = 1 C

1B + 1C = 1D

Para lograr el cometido debo combinar las 3 relaciones de cambio de tal manera que se cancelen totalmente las partes A y C utilizando los multiplicadores adecuados

Entonces,

Uso 5 unidades de B para conseguir una de A y una de C

5B = 1A + 1C

Con esa A y otra de B obtengo otra C

1A + 1B = 1C

Por último con esas dos unidades de C y dos unidades mas de B consigo 2 de D

2B+ 2C = 2D

En total utilicé 5 + 1 + 2 = 8 unidades de B para obtener 2 de D

Entonces para obtener una de D necesitaría 4 unidades de B

First, lets focus on finding out the other two legs of the large triangle.

To do this, we use Pythagoras' Theorem.

So the left leg = √(16² + x²)

So the right leg = √(9² + x²)

Notice, the larger triangle is also a right angled triangle, that means the sum of the two legs squared = hypotenuse squared.

Since we have just worked out the two legs, we can substitute them into:

a² + b² = c²

(√(16² + x²) )²  +  (√(9² + x²) )² = (16 + 9)²

Notice that the power of two cancels out with the squareroots so we get:

(16² + x² ) + (9² + x² ) = (25)²     (simplify and collect like terms)

256 + x² + 81 + x² = 625    

337 + 2x² = 625     (subtract 337 from both sides to isolate the x )

2x² = 288                    (divide both sides by 2)

x² = 144                        (square root both sides)

x = √144

x = 12

_______________________________________

Answer:

x = 12

_______________________________________

Note: if you have any questions, please ask and I will be more than happy to help and give further explanations!

I can confirm that the other person is right, the answer is 12.

Answer:

x = 30t cos 20 or  x = 28.19t.

y = 30t sin 20 - 4.9t^2 + 2 or y =  -4.9t^2 + 10.26t + 2.

Step-by-step explanation:

The horizontal component of the velocity = 30 cos 20  m/s so the distance at time t seconds = 30t cos 20.

The vertical component  is obtained from the equation of motion

s = ut - 1/2* 9.8t^2 + 2

u = 30 sin 20

Vertical component  =  30t sin 20 - 4.9t^2 + 2.

Answer:

x(t) = 30t cos 20 or we can get x = 28.19t. y = 30t sin 20 – 4.9t^2 +2 or y= -4.9t^2 + 10.26t +2

Step-by-step explanation:

The path the rock took can be represented by the following equation x(t) = v0 * cos(θ) * t y (t) = v0 * sin (θ) * t – 0.5 * g * t^2 + h. v0 is the initial velocity (30 m/s), θ is the angle of launch (20 degrees), g is the acceleration due to gravity (9.8 m/s^2) , h is the initial height (2m ) , and t is time. When we switch the values, we get x(t) = 30t cos 20 or we can get x = 28.19t. y = 30t sin 20 – 4.9t^2 +2 or y= -4.9t^2 + 10.26t +2

Answer:

Discriminant D = -4 , no real solution

Step-by-step explanation:

Here our equation is

[tex]x^{2}-4x+5=0[/tex]

Discriminant (D)= [tex]b^2-4ac[/tex]

where

a = coefficient of term containing [tex]x^{2}[/tex]

b= coefficient of the term containing [tex]x[/tex]

c is the constant term

hence

a=1 , b =-4 and c=5

Hence

[tex]D=b^2-4ac\\D=(-4)^2-4*1*5\\D=16-20\\D=-4\\[/tex]

Hence D is less than 0 , therefore we do not have any real solution to this quadratic equation.

Answer:

b on edge-The discriminant is −4, so the equation has no real solutions.

Step-by-step explanation:

Without a given equation or inequality to work with, it is impossible to determine the value of 'x' based on the presented information.

The provided question seems to be missing some key elements that would offer us enough information to determine the value of x. In mathematics, to find the value of a variable, such as x, you generally need some form of an equation or inequality where x is a part of and other elements present in the equation give indirect details about x. This could include clues as to its relationships with other values, or boundaries for its possible amount. Without an equation, it is impossible to ascertain the value of x based on the given question.

This reasoning is based on the fundamental principles of algebra, a branch of mathematics. For example, if given an equation like '3x + 2 = 8', we could apply algebraic principles to solve for x. However, in this case, no such equation has been provided, and so we cannot calculate the value of x. Thus, there is not enough information provided.

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Answer:

Given the function f(x) = 3x + 1, evaluation of f(a + 1) gives:  

C. 3a + 4

Step-by-step explanation:

Given function:

f(x) = 3x + 1

We have to find f(a+1).

For this purpose, we will take x = a+1 and

substitute it in the function f(x) = 3x+1:

f(x) = 3x + 1

f(a+1) = 3(a+1) +1

f(a+1) = 3(a) + 3(1) +1

f(a+1) = 3a+3+1

f(a+1) = 3a + 4

So the function f(a+1) is equal to option C. 3a + 4.

the answer is

3a + 4

Answer:

Im positive the answer is A: x^3-3x+2

Answer:

a     x^3-3x+2

Step-by-step explanation:

f(x) = -3x+2

g(x)= x^3

(f+g)(x)= -3x+2+x^3

          = x^3-3x+2

Answer:

6π ft

Step-by-step explanation:

I believe you meant CIRCUMFERENCE, the distance around the outer edge of this circle.  The appropriate formula for the circumference is C = 2πr, where r is the radius.  In the illustration we see that line segment PA has length 3 ft.  Thus, the circumference of this circle is C = 2π(3 ft) = 6π ft (the next to last answer choice).

Answer:

=6π ft

Step-by-step explanation:

The circumference of a circle is calculated using the formula C=2πr where r is the radius and C the circumference of the circle.

In the circle provided r= 3ft

C= 2π × (3ft)

=6π ft

We do not use the approximate value of pi as the question demands us to leave pi unsolved.

Answer:

914 and 916

Step-by-step explanation:

let the first integer be x

The next largest consecutive even integer is hence x+2

given that the 2 integers add up to 1830,

x + (x+2) = 1830

2x + 2 = 1830

2x = 1828

x = 914

Hence the first number is 914

the second number is 914 + 2 = 916

Check Answer:

914 + 916 = 1830 (verified)

[tex]2n+2n+2=1830\\4n=1828\\n=457\\\\2n=914\\2n+2=916[/tex]

914 and 916

Answer:

  (B) only I and II

Step-by-step explanation:

An odd relation is symmetrical about the origin. All of the relations are odd.

An even relation is symmetrical about the y-axis. Only the first two relations are even.

_____

The graph shows the first relation is that of a circle. It is symmetrical about its center at the origin and about any diameter, including the y-axis.

The second relation is a degenerate hyperbola. It graphs as the pair of lines y=x and y=-x. It is symmetrical about both the origin and the y-axis. (It also has other lines of symmetry.)

The third relation is a line with slope -1 (represented by dots). It is symmetrical about the origin, but not the y-axis. It is only an odd relation.

Answer:

180.07 rev / min

Step-by-step explanation:

Diameter (D) of each wheel =28 inches

Circumference (C) =  π x 28 = 28π inches

Conversions:

1 mile = 63,360 inches

1 hour = 60 min

Hence 15 miles / hour

= (15)(63,360) inches / hour

= (15)(63,360) / 60  inches / min

= 15,840 inches per min

Number of revolutions per min = Number of inches per min ÷ circumference in inches

=15,840 inches/min ÷ 28π inches

= 180.07 revolutions per min

To find the number of revolutions per minute a bicycle's wheels make, convert the speed from miles per hour to inches per minute, calculate the wheel's circumference, and divide the traveling speed in inches per minute by the circumference. A bicycle with 28-inch diameter wheels going 15 miles per hour makes approximately 180 revolutions per minute.

To determine how many revolutions per minute the wheels of a bicycle with a 28-inch diameter are turning when traveling at 15 miles per hour, we first need to convert the speed to inches per minute. There are 5280 feet in a mile and 12 inches in a foot, so first we calculate:

15 miles/hour * 5280 feet/mile * 12 inches/foot = 950400 inches/hour

Since there are 60 minutes in an hour, we then convert to inches per minute:

950400 inches/hour / 60 minutes/hour = 15840 inches/minute

Next, we need to find out the circumference of the bicycle wheel, as this will tell us how far the bike travels with each revolution. The formula for the circumference (C) of a circle using the diameter (d) is:

C = π * d

For a wheel with a diameter of 28 inches:

C = π * 28 inches ≈ 87.96 inches

Now, to find the number of revolutions per minute, we divide the traveling speed in inches per minute by the circumference:

15840 inches/minute / 87.96 inches/revolution ≈ 180 revolutions per minute (rounded to the nearest whole number).

For a system of linear equations to have a solution, it means that they would cross over at some point, thus if we are looking for a system of linear equations that do not have a solution (ie. they do not cross over), we are looking for two parallel lines.

Now for two lines to be parallel, they must have the same gradient. Thus, we must find the value of a for which both the equations have the same gradient. In order to do this, we should first write both equations in the form y = mx + c, where m is the gradient and c the y-intercept.

1) Equation 1:

(1/2)x - (2/3)y = 7

(3/4)x - y = 21/2 (Multiply both sides by 3/2)

(3/4)x = 21/2 + y (Add y to both sides)

(3/4)x - 21/2 = y (Subtract 21/2 from both sides)

Thus, the first equation may be written as y = (3/4)x - 21/2

2) Equation 2:

ax - 8y = -1

(a/8)x - y = -1/8 (Divide both sides by 8)

(a/8)x = -1/8 + y (Add y to both sides)

(a/8)x + 1/8 = y (Add 1/8 to both sides)

Thus, the second equation may be written as y = (a/8)x + 1/8

Now that we know the equations of the two lines, we can compare their gradients.

Equation 1: m = 3/4

Equation 2: m = a/8

Remember, for the two lines to be parallel, their gradients must be the same. Thus, we must equate the two gradients above to find the value of a:

3/4 = a/8

24/4 = a (Multiply both sides by 8)

6 = a

Therefor, if the system of linear equations has no solution, and a is a constant, the value of a is 6 (answer D).

Answer:

C

Step-by-step explanation:

You have a vertex of (-2,2) since -b/(2a)=-12/(2*3)=-12/6=-2

and then plug it in for the y-coordinate 3(-2)^2+12(-2)+14=2

So you have a vertex of (-2,2).

The parabola is open up since 3 is positive.

So far it looks like the choice is C because it is the only one that says the vertex is (-2,2) and it does have that it is open up.

Let' s look at (-3,5) and (-1,5).

So if we plug in -3 into 3x^2+12x+14 we get 3(-3)^2+12(-3)+14=5 check mark

what about x=-1?  3(-1)^2+12(-1)+14=5

Bingo! C checks out!

Answer:

(x+1)^2+(y-7)^2=8

Step-by-step explanation:

You should try the next one and I can check work or tell you if it is right.  

The diameter length can be found be computing the distance that (-3,5) is to (1,9) which is sqrt(4^2+4^2)=sqrt(32).

The radius is half the diameter so it is sqrt(32)/2.

The center of the circle is the midpoint of a diameter. So compute the (Average of x, average of y)=(-1,7)

So plug into (x-h)^2+(y-k)^2=r^2 we get

(x+1)^2+(y-7)^2=32/4

simplifying gives

(x+1)^2+(y-7)^2=8

(I had to type this twice; my cat jump on my keyboard)

ANSWER

[tex]{(x + 1)}^{2} + {(y - 7)}^{2} = 8[/tex]

EXPLANATION

The given circle has P(-3,5) and Q(1,9) as its diameter.

The center can be obtained using the midpoint rule.

[tex]( \frac{ - 3 + 1}{2} , \frac{5 + 9}{2} )[/tex]

[tex]( - 1,7)[/tex]

The radius is obtained using the distance formula,

[tex]r = \sqrt{( - 1 - - 3 )^{2} + {(7 - 5)}^{2} } [/tex]

[tex]r = \sqrt{( 2)^{2} + {(2)}^{2} } = \sqrt{8} [/tex]

The equation is given by

[tex] {(x - h)}^{2} + {(y - h)}^{2} = {r}^{2} [/tex]

We substitute the center and radius to get:

[tex]{(x - - 1)}^{2} + {(y - 7)}^{2} = { (\sqrt{8}) }^{2} [/tex]

[tex]{(x + 1)}^{2} + {(y - 7)}^{2} = 8[/tex]

Answer:

127% markup

Step-by-step explanation:

So we need to plug in 31 into each

R(31)=160(31)=4960

C(31)=71(31)-.02(31)^2=2181.78

So the selling price is 4960 for 31 stereos.

The total cost for making 31 stereos is 2181.78.

So that is a markup for sure.

So you find the difference and then divide it by the total cost.

(4960-2181.78)/2181.78=1.27 approximately

so there is 127% markup

Answer:

f(x)=4x

Step-by-step explanation:

In order to make the graph of f(x)= 4x we will find out few coordinates first and then plot them on the graph. In order to find the coordinates we will find the values of f(x) for random values of x .

Let us see:

x=1 ; f(x) = 4(1) = 4

x=2 ; f(x) = 4(2)=8

x=0 ; f(x) = 4(0)=0

x=-1 ; f(x)= 4(-1) = -4

x=-2 ; f(x)=4(-2)= -8

Hence our coordinates are

(-2,-8) ; (-1,-4) ; (0,0) ; (1,4) ; (2,8)

Now we plot those coordinates on x - y plane and join them to make our line. Please see the graph in the attachment.

Answer:

  (-7, 5)

Step-by-step explanation:

Comparing the equation to the standard form equation of a circle of radius r centered at (h, k):

  (x -h)² +(y -k)² = r²

you see that h=-7 and k=5.

The center of the circle has coordinates (-7, 5).

_____

Like a lot of math, it's about pattern matching.

Answer:

132 m².

Step-by-step explanation:

What's the surface area of each lateral face of this pyramid?

Each lateral face of this pyramid is a triangle, with

The base of this pyramid is a square. As a result, all four lateral sides are congruent. The area of each of these triangle is thus

[tex]\displaystyle \frac{1}{2}\times \text{Base}\times \text{Height} = \rm \frac{1}{2} \times 6 \times 8 = 24\; m^{2}[/tex].

The base of this pyramid is a square. The length of a side of this square is 6 meters. The area of the base will be

[tex]\text{Side}^{2} = \rm 6^{2} = 36\; m^{2}[/tex].

Put the five faces together to get the total surface area of this square pyramid:

[tex]\rm 4\times 24 + 36 = 132\; m^{2}[/tex].

Answer:

Step-by-step explanation:

try using the equation of y=mx+b

Answer:

V = (π/4)s³

Step-by-step explanation:

The volume of a cylinder can be found using the formula ...

V = πr²h

In this problem, we have r=s/2 and h=s. Filling in these values, the volume is ...

V = π(s/2)²·s = (π/4)s³

Answer:

Its A

Step-by-step explanation:

V= 1/4 pi S^3