for a field trip a bus company charges a flat fee plus an additional fee per student. for 25 students, the total cost is $200, if there are 30 students, the total cost is $230. write an equation in point slope form,where y repersents a cost for any given number of x students

Answer:

Sides: a = 9.165   b = 4   c = 10

Step-by-step explanation:

Is that check mark supposed to be square root?

Answer:

\((4^{2} +(\sqrt{84} ^{2} )\\=100\)

Step-by-step explanation:

The first error in Jan'ai's work in determining the considered function is given by: Option D: She incorrectly determined the x-coordinate of the vertex.

For a quadratic function of the form \(y = ax^2 + bx + c\), its vertex form is obtained as:

\(y = ax^2 + bx + c\\y =a(x^2 + bx/a) + c\\y = a(x^2 + 2(b/2a)x + (b/2a)^2 -(b/2a)^2 )+ c\\y = a(x^2 + 2(b/2a)x + (b/2a)^2) -a \times (b/2a)^2 + c\\\\y = a(x+b/2a)^2 - a \times (b/2a)^2 + c\)

For the form \(y = a(x-h)^2 + k\), the vertex has coordinates (h, k)

Thus, for the obtained equation \(y = a(x+b/2a)^2 - a \times (b/2a)^2 + c\), we get the coordinates of vertex as:

\(h = -b/2a\), \(k = c - a\times(b/2a)^2\)

Thus, the coordinates of vertex of  \(y = ax^2 + bx + c\) is:

\((h,k) = (-b/2a, c - a \times (b/2a)^2 )\)

The missing steps of work of Jan'ai are:

\(y = 5x^2-20x-25\)

\(y = 5(-2)^2-20(-2)-25\)

\(y = 35\)

so (-2,35) is the coordinate of the vertex, which denotes the minimum.

So, as we see, in the 5th step, Jan'ai had the quadratic function \(f(x) = 5x^2-20x-25\),

Comparing this to \(f(x) = ax^2 + bx + c\), we get a = 5, b = -20, c = -25

The vertex's x-coordinate will be on -b/2a = -(-20)/ 2(5) = 20/10 = 2

But Jan'ai didn't putted that negative sign before b. in the 6th step.

Thus, the first error in Jan'ai's work in determining the considered function is given by: Option D: She incorrectly determined the x-coordinate of the vertex.

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Answer:

The answer is D on edge

Step-by-step explanation:

Answer:

\(\sqrt{13}\)

Step-by-step explanation:

d = √(7-4)²+(3-1)²

= √3²+2²

= √9+4

= √13

The area of the entire sector is \((\pi)(6^{2}) \left(\frac{60}{360} \right)=6\pi\)

The area of the triangle OAB is \(\frac{\sqrt{3}}{4}(6^{2})=9\sqrt{3}\).

So, the area of the segment is \(\boxed{6\pi-9\sqrt{3}}\)

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Let the original price of the item be X.

In one week, the price is halved and becomes (1/2)X.

In two weeks, the price is halved again and becomes (1/4)X, which is only 75% off.

First, let's determine what (1/3) to the power of 4 is:

1/3 x 1/3 x 1/3 x 1/3 = 1/81

(1 x 1 x 1 x 1 = 1; 3 x 3 x 3 x 3 = 81)

1/81

Now what is 3 as a decimal?

We have to use the same denominator as 1/81 to be able to do a subtraction:

81 x 3 = 243

3 = 243/81

243/81 - 1/81 = 242/81

The answer is D.

Hope this helps! :) If you have any questions, let me know.

False. We would anticipate the second-year GPA to be slightly higher than the 40th percentile based on the regression impact.

How does your GPA translate?

Given this,

 A student who has a first-year GPA in the 40th percentile

is likely to have a second-year GPA in the same range.

The scatter plot is shaped like a football.         ————— (False)

If the scatter diagram is shaped like a football, then all of the data points are drawn in a circle. As a result, the data does not fit well.

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Answer:

9-16y

Step-by-step explanation:

9-x^2y when x=4

plus in 4: 9- (4)^2y

=9-16y

Each of the blanks should be completed as follows;

A steep line has a bigger slope than a flat line.

Equally steep lines have equal slopes.

Lines that go up from left to right have positive slopes.

Lines that go down from left to right have negative slopes.

In Mathematics, a slope is sometimes referred to as rate of change and it is typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.

Generally speaking, a slope simply refers to a measure of the steepness of a straight line. This ultimately implies that, slope equals rise divided by run for any two (2) points that are located on a straight line.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

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Answer:The length of the rope between the boat and the dock is 30 feet.

What are trigonometric ratios?

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Given that, a rope is used to tie a boat to a dock.

The boat is 25.17 feet above the ocean floor.

Let the length of rope be x.

So, tanθ= Perpendicular/Base

⇒ tan40°= 25.17/x

⇒ 0.839= 25.17/x

⇒ 0.839x= 25.17

⇒ x= 25.17/0.839

⇒ x= 30 feet

Therefore, the length of the rope is 30 feet.

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

because if you divide what you said its will have a sum

The measure of three angles are : x, 60 & 100

Sum of all angles in a triangle is 180 degree

So, x + 60 + 100 = 180

x + 160 = 180

x = 180 -160

x = 20

Answer : x = 20

Answer:

(6,2)

Step-by-step explanation:

Answer:

1. 560+0.08x > 700$

2.1750$

3. Below

Step-by-step explanation:

In the third step, 10 is the mass of the dog. As such, it should have been substituted to w and not to m.

Answer:

its c/third step

Step-by-step explanation:

trust -w-

Answer:

factor out 3

\(3(4x {3}^{2} y + 12 \sqrt{x {?}^{6} } y {}^{5} \sqrt{6} \)

that's it

Answer:

The formula for the area of a circle is A = πr^2, where r is the radius of the circle.

We know that the diameter of the circle is 10 ft, so the radius is half of that:

r = 10 ft ÷ 2 = 5 ft

Now we can plug in this value for r into the formula:

A = π(5 ft)^2

A = π(25 ft^2)

A ≈ 78.54 ft^2

Rounding this to the nearest whole number, we get:

A ≈ 79 ft^2

Therefore, the area of the circle to the nearest whole number is 79 square feet.

Answer:

79ft^2

Step-by-step explanation:

diameter=10ft

radius=5ft

5^2=25ft

25×π=25π

25π= 78.539....

to nearest whole number =79ft^2

The explicit differentiation and implicit differentiation both yield consistent results so that the statement is true.

If we have an equation x = ye^y, we can find dx/dy using explicit differentiation as follows:

x = ye^y

Differentiating both sides with respect to y:

dx/dy = (d/dy) (ye^y) = e^y + ye^y

On the other hand, to find dy/dx using implicit differentiation, we differentiate both sides of the equation x = ye^y with respect to x:

d/dx (x) = d/dx (ye^y)

1 = (dy/dx) e^y + y (d/dx) (e^y)

1 = (dy/dx) e^y + y e^y (dy/dx)

(dy/dx) (e^y + y e^y) = 1

dy/dx = 1 / (e^y + y e^y)

We can see that these two expressions for the derivatives, dx/dy and dy/dx, are consistent. We can substitute y = ln(x) in the expression for dy/dx to get:

dy/dx = 1 / (e^(ln(x)) + ln(x) e^(ln(x))) = 1 / (x + ln(x))

We can verify that this is equal to dx/dy by substituting y = ln(x) in the expression for dx/dy:

dx/dy = e^y + ye^y = e^(ln(x)) + ln(x) e^(ln(x)) = x + ln(x)

Therefore, we can conclude that the explicit differentiation and implicit differentiation both yield consistent results.

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The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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main answer : the normal distribution of given graduate record  exam is 1,A(1)=0.3413

supporting answer:Because of its flared shape, a graphical representation of a normal distribution is sometimes referred to as a bell curve. The precise shape varies depending on the population distribution, but the peak is always in the middle and the curve is always symmetrical. The mean, mode, and median of a normal distribution are all the same.

body of the answer: given that x₁=mean+standard deviation

                                     given mean₁=462

                                                standard deviation =119

  x₁=462+119=581

  z₁=581-462/119=1

  A(1)=0.3413

given mean₂=584

        standard deviation=151

x₂=584+151

   =735

z₂=735-584/151

  =1

A(1)=0.3413

final answer:there fore both scores are normal

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The normal distribution of given graduate record exam is 1,A(1)=0.3413

What is population distribution?

Because of its flared shape, a graphical representation of a normal distribution is sometimes referred to as a bell curve. The precise shape varies depending on the population distribution, but the peak is always in the middle and the curve is always symmetrical. The mean, mode, and median of a normal distribution are all the same.

body of the answer: given that x₁=mean + standard deviation

                                    given mean₁=462

                                   standard deviation =119

 x₁=462+119=581

 z₁=581-462/119=1

 A(1)=0.3413

given mean₂=584

standard deviation=151

x₂=584+151

  =735

z₂=735-584/151

 =1

A(1)=0.3413

There fore both scores are normal.

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Joe can afford a car loan of approximately $12,944.

To determine the loan amount Joe can afford, we need to calculate the present value of the continuous monthly payments he can make. Joe can pay $360 per month for 4 years, which amounts to a total of 4 * 12 = 48 payments.

The formula to calculate the present value of continuous payments is given by:

PV = (PMT / r) * (1 - e^(-rt))

Where:

PV is the present value of the continuous payments,

PMT is the monthly payment amount,

r is the annual interest rate, and

t is the loan term in years.

Substituting the given values, we have:

PMT = $360,

r = 0.125 (12.5% expressed as a decimal),

t = 4.

Plugging in these values, we can calculate the present value:

PV = (360 / 0.125) * (1 - e^(-0.125 * 4))

Using a calculator or spreadsheet, we find that the present value is approximately $12,944. Therefore, Joe can afford a car loan of approximately $12,944 and still make monthly payments of $360 for 4 years.

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4. There is no enough information.

5. ΔPEF ≅ ΔREF are congruent by SAS.

6. ΔKMO ≅ ΔOLK are congruent by SSS.

7. No enough information.

8. ΔPAN ≅ ΔKLC are congruent by SSS.

9. ΔABC ≅ ΔDEF are congruent by SSS.

The SSS and SAS are theorems of triangle congruence that can be used to prove that two triangles are congruent. To prove that two triangles are congruent by SSS, both triangles must have three pairs of corresponding lengths that are congruent, while SAS is used when the two triangles have two pairs of congruent sides that are corresponding, and a pair of congruent included angles.

4. There is no enough information to prove triangles HNJ and RDF are congruent by neither SAS nor SSS.

5. Triangles PEF and REF are congruent by SAS.

6. Triangles KMO and OLK are congruent by SSS.

7. No enough information.

8. Triangles PAN and KLC are congruent by SSS.

9. Triangles ABC and DEF are congruent by SSS.

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Answer:

96/4= $24 dollars per person

Step-by-step explanation:

Answer:

The y-intercept is 4

Step-by-step explanation:

in y=mx+b, the b will always be your y-intercept

Answer:

It's going to take you 17 min to travel 12 miles

assuming you are going with mph

Step-by-step explanation:

I looked at a speed calculator and calculated that to go 25 miles in 35 min, you were going 42 mph. so I changed the imput to 12 miles and I got my answer.

Answer:

B

Step-by-step explanation:

By following these steps, you should be able to find the number of counties in Texas with childcare programs offering nighttime care for children.

To answer your question about how many of the 254 counties in Texas have child care programs that state they provide nighttime care for children, we would need to access current data on child care programs in Texas. Unfortunately, I do not have that specific data at the moment. However, I can guide you on how to find this information.
Begin by visiting the Texas Health and Human Services website (https://hhs.texas.gov) as they are responsible for overseeing child care licensing in the state. Look for information on licensed child care facilities that provide nighttime care.
Utilize websites such as Child Care Aware (https://www.childcareaware.org) or Child Care Finder (https://childcarefinder.com), where you can search for child care programs in Texas by county, and filter your search to include only programs offering nighttime care.
You may also want to check with local county websites or contact the County Clerk's office for information on child care programs within their jurisdiction, specifically those offering nighttime care.
Compile the data gathered from the above sources to determine how many of the 254 Texas counties have child care programs providing nighttime care for children.
By following these steps, you should be able to find the number of counties in Texas with child care programs offering nighttime care for children.

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Answer:

D) \(-\sqrt[3]{x-1}\)

Step-by-step explanation:

-the function is the cube root

-the cube root of zero is zero

- the graph is at 0 when x = 1, thus "x-1" must be part of answer

- the cube root of -8 is -2, at -8 the graph is +2. so the function is negated

\(-\sqrt[3]{x-1}\)

Josue needs to invest $688.23 for the value of the account to reach $1,170 in 13 years

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

The formula for compound interest compounded quarterly is,

A = P(1 + (r/4)/100)⁴ⁿ.

Therefore, From the given information,

1170 = P(1 + (3.1/4)/100)⁶⁸.

1170 = P(1.7).

P = $688.23.

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