The entrance fee to the national park is $15. The campsite fee is $25 per night.
a. Write an equation that represents this situation.
b. Explain what each component of the equation represents.
i. Define the variables. (x = ?, y = ?)
ii. Interpret the slope and y-intercept.
C. Use the equation to find the total cost for 3 nights.

Answer:

13.6 inches

Step-by-step explanation:

We can use Pythagorean theorem: \(c=\sqrt{a^{2} +b^{2} }\)

Let c be the diagonal length, a for length, and b for width.

Substitute the values.

\(c=\sqrt{11^{2}+8^{2} }\)

c=13.6 inches

Answer:

20%.

Step-by-step explanation:

A sum of money will triple itself in ten years at an annual interest rate of 20%.

Answer: D) 7 3/4

Step-by-step explanation:

With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4

Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses

29 = 21 1/4 + x

Now we can isolate x by subtracting 29-21 1/4

so

x = 7 3/4 thus the answer is D

Answer:

D) 7 3/4

Step-by-step explanation:

Let x = amount of last feeding.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4

4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x

28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x

29 = 20 10/8 + x

(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)

29 = 21 2/8 + x

29 = 21 1/4 + x

x = 29 - 21 1/4

x = 28 4/4 - 21 1/4

x = 7 3/4

Answer: 7 3/4

The experimental probability of members of Chris's class ending up with heads is about 3/5 or 0.6 (60%).

The experimental probability is one that can be calculated by:

dividing the number of favorable outcomes (the number of heads) by the total number of outcomes (the total number of students).

So, the number of heads recorded was 18, and the total number of students was 30.

Experimental probability = Number of heads / Total number of students

= 18 / 30

So one can simplify the fraction by:

Experimental probability = 3 / 5

Therefore, the experimental probability of members of Chris's class ending up with heads is 3/5 .

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In the figure, the length of any line segment in the image is longer the length of the corresponding line segment in the preimage. The scale factor of the dilation is 2

The scale factor of dilation is defined as the change in size of a figure. Thus, a scale factor that is greater than 1 is referred to as an enlargement while a scale factor that is greater than 0 but less than 1 is referred to as a reduction.

Now, we are told that ΔABC has been dilated from center D to form ΔRST, This means that the lengths in ΔRST are longer than the lengths in ΔABC.

Secondly, by close inspection we can see that it was dilated by a scale factor of 2.

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Answer:

\(x=750m\)

Step-by-step explanation:

\(Assuming\) \(That\):

\(1m=3.3ft\)

We can make the conversion from feet per second to meters per second with this procedure:

\((165 \frac{ft}{s} ) (\frac{1m}{3.3ft} )=50\frac{m}{s}\)

Let \(x\) be the amount of meters the parachutist will fall during 15 seconds of free fall

Having that in 1 second the parachutist falls 50 meters, we can calculate \(x\) :

\(x=(50\frac{m}{s} )(15s)\)

\(x = 750 m\)

Brainliest?!

​

Answer:

220

Step-by-step explanation:

Area = length · width

Area = 22 · 10

Area = 220

Note:

Please mark as Brainliest! <3

9514 1404 393

Answer:

  D. None

Step-by-step explanation:

If one of these is true for all values of k, we can see it for k=1.

 r = 1² +3·1 +9 = 13

This value is not even, not divisible by 3, and not the square of an integer.

None of the offered statements about r is true.

Answer:

256x * 16

Step-by-step explanation:

\((4x^{2} * 4)^{2}\)

(4x * 4x * 4) * (4x * 4x * 4 )

(16x * 4 ) * ( 16x *4)

16x * 16x = 256x

4 * 4 = 16

256x * 16

hope this helped a little

* = multiply

The given expression without exponent is

\(4 \cdot 4 \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x\)

Given :

\((4x^4)^2\)

Explanation

We need to write the given without exponents

outside exponent is 2 . so we multiply the parenthesis twice

\((4x^4)^2\\4x^4 \cdot 4x^4\\16 \cdot x^4 \cdot x^4\\ 16 \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x\\4 \cdot 4 \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x\)

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His potential scores are higher than 78 because he cannot achieve a number high enough to average over 85. (to 100)

The study of possibility is a math discipline that focuses on calculating the possibility or chance that an event will occur. It is a means to put a number on the uncertainty that is always present. A number among 0 and 1, where 0 denotes the event's impossibility and 1 denotes its certainty, is used to describe the likelihood of it happening. For instance, if you flip a coin, the likelihood of getting heads is 0.5, which means that you have a 50% probability of obtaining heads and a 50% probability of obtaining tails. Numerous disciplines use probability, such as statistics, finance, engineering, physics, and computer programming. It is an effective instrument for predicting outcomes, evaluating risks, and making choices based on speculative data.

given

462 grades are needed to achieve 77. (6 x 77).

510 points are needed to achieve 85. (6 x 85).

462<79 + 85 + 75 + 66 + 79 + x < =510

462 < 384 + x < = 510 Completely subtract 384 from the total.

78 < x <=126

His potential scores are higher than 78 because he cannot achieve a number high enough to average over 85. (to 100)

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9514 1404 393

Answer:

  A.

Step-by-step explanation:

If you can find the given points (pounds, dollars) = (2, 3.50), (3, 5.25), and (4, 7.00) on the graph, then it is an appropriate graph. If the graph label matches the value it shows for 1 pound, then that graph and label are the one you want.

Graph A meets these requirements. It shows the cost of 1 lb to be $1.75, as the label says.

Answer:49 miles per hour

Step-by-step explanation: 14 miles times 35 miles = 490

but the 0 will not matter so steve was going 49 miles per hour

HOPE THIS HELPS YOU:)

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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Answer:

26.875 = 26.88

86km = 60 minutes

86km/2=

43

43/1.6(kilometers in miles)

26.88

hope this helps uwu

Answer:

foreal

Step-by-step explanation:

The given system of simultaneous equations has no solutions.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given is the system of simultaneous equations as -

y = 3x + 9

6x − 2y = 6

Refer to the graph of the equations attached. The value of {x} and {y} for which both the equations are true is given by the point of intersection of both lines. Since both lines are parallel, there is no point of intersection and hence no solution.

Therefore, the given system of simultaneous equations has no solutions.

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Answer:definition of midpoint, angle BCA is congruent to angle DCA

The triangles ΔABC and ΔADC are congruent triangles by

a) definition of mid-point

b) measure of ∠ACB = measure of ∠ACD = 90°

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔADC

Now , the side AC is the common bisector of both the triangles such that

C is the midpoint of BD

So , the measure of side BC = measure of side CD

And , the perpendicular bisector is right angle

So , the measure of ∠ACB = measure of ∠ACD = 90°

And , the measure of AC = measure of AC ( reflexive property )

Therefore , the triangles are congruent by SAS theorem

Hence , the triangles are congruent

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Point located at each location: 1) A  2) I 3) W 4) H 5) X 6) G 7) J 8) N 9) U 10) M 11). Ordered pairs are:  B(2,8) 12) E(0,0) 13) T(3,3) 14) Q(8,7)  15) Y(7,6) 16) R( 9,8) 17)  F(9,0) 18) S(3,6) 19) C(6,7)

Describe Ordered pair?

An ordered pair is a pair of mathematical object elements, such as numbers or other mathematical elements, where the order in which the object elements are listed is important. The ordered pair is usually written in the form (a, b), where 'a' represents the first element or coordinate, and 'b' represents the second element or coordinate.

In the context of the Cartesian coordinate system, an ordered pair represents a point in two-dimensional space, where the first element or coordinate represents the horizontal position on the x-axis and the second element or coordinate represents the vertical position on the y-axis. The order of the elements in an ordered pair is crucial because (a, b) is different from (b, a) and represents a different point in two-dimensional space.

Point located at each location is:

1) A

2) I

3) W

4) H

5) X

6) G

7) J

8) N

9) U

10) M

The ordered pair for given points is:

11) B(2,8)

12) E(0,0)

13) T(3,3)

14) Q(8,7)

15) Y(7,6)

16) R( 9,8)

17)  F(9,0)

18) S(3,6)

19) C(6,7)

The graph for remaining is questions is attached below.

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Answer:

The ratio of blue balloons to the total number of balloons is 1:2.

so we know that θ is between π and 3π/2, which is another of saying that θ is in the III Quadrant, and obviously its cosine will be negative.

we also know that cos(θ/2) is negative, well, that rules out the I and IV Quadrants, so most likely θ/2 is on the II Quadrant, since is smaller than θ anyway, and on the II Quadrant as we know, the sine or "y" value is positive.

\(\stackrel{\textit{Half-Angle Identities}}{ sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \qquad\qquad cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}}} \\\\[-0.35em] ~\dotfill\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+\left(-\frac{1}{9} \right)}{2}}\implies cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-\left(\frac{1}{9} \right)}{2}}\)

\(cos\left(\cfrac{\theta}{2}\right)=-\sqrt{\cfrac{~~ \frac{8}{9} ~~}{2}}\implies cos\left(\cfrac{\theta}{2}\right)=-\sqrt{\cfrac{4}{9}}\implies cos\left(\cfrac{\theta}{2}\right)=-\cfrac{2}{3} \\\\[-0.35em] ~\dotfill\)

\(sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-\left( -\frac{1}{9} \right)}{2}}\implies sin\left(\cfrac{\theta}{2}\right)=+ \sqrt{\cfrac{~~\frac{10}{9}~~}{2}}\implies sin\left(\cfrac{\theta}{2}\right)=+\cfrac{\sqrt{5}}{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{~~~a_1~\hfill a_2~~~}{\left( -\cfrac{2}{3}~~,~~ \cfrac{\sqrt{5}}{3}\right)}~\hfill\)

Answer:

  (-2/3, (√5)/3)

Step-by-step explanation:

We can use the half-angle identities to find the values of the sine and cosine of the desired angle. The desired angle is a 2nd-quadrant angle, so the sine is positive, and the cosine is negative.

  \(\sin{\left(\dfrac{\theta}{2}\right)}=\sqrt{\dfrac{1-\cos{(\theta)}}{2}}=\sqrt{\dfrac{1-(-1/9)}{2}}=\sqrt{\dfrac{5}{9}}=\dfrac{\sqrt{5}}{3}\\\\\cos{\left(\dfrac{\theta}{2}\right)}=-\sqrt{\dfrac{1+\cos{(\theta)}}{2}}=-\sqrt{\dfrac{1+(-1/9)}{2}}=-\sqrt{\dfrac{4}{9}}=-\dfrac{2}{3}\)

The coordinates of the terminal point are ...

  \((a_1,a_2)=\left(\cos{\dfrac{\theta}{2}},\sin{\dfrac{\theta}{2}}\right)=\left(-\dfrac{2}{3},\dfrac{\sqrt{5}}{3}\right)\)

Answer:50 minutes

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

first multiply both sides by 12

collect like terms

x/12×12+3×12<=7×12

x+36<=84

x<=84-36

x<=48

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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The correct answer is option D which is 0.798

The complete question is given below:-

For an exponential regression equation in the form y=ab^x which of the following values of b will cause y to get smaller as x gets larger?

a.) 1.526

b.) 1.798

c.) 2.526

d.) 0.798

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Since we know that an exponential function is in the form:y= ab\(.^x\) where,

a= Initial value,

b = For growth b is in form (1+r), where r is the rate in decimal form.

b = For decay or regression b is less than 1 and in form (1-r), where r is the rate in decimal form.

Upon looking at our given choices we can see that options a, b and c are in form 1+r, while the choice provided in option d is less than 1 and in form 1-r, therefore, option d is the correct choice.

Therefore the correct answer is option D which is 0.798

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Answer:

12%

Step-by-step explanation:

A percent is any fraction with 100 as a denominator. So \(\frac{12}{100}\) is the same as 12% and 4 over 100 is the same as 4%

Here's an easy was to remember, there are 100 pennies to make a dollar that like per-CENT it's out of 100.

Hope that helps and have a great day!

Answer:

12%

Step-by-step explanation:

your question isn't giving me an option to answer but do 12 divided by 100 and you get a decimal, then multiply it by 100 which will give you the percentage. In this case is would be 12%

I hope this helps:)