Kevin wants to hike the Pacific Crest Trail, which is 2,653 miles long. If Kevin wants to
finish the hike in 7 months, how many miles should he hike each month?
miles

The required graph is attached below.

Given that,

Quarterback Susie has a bad attitude and often gets fined for bad sportsmanship.

And the table of cost is given,

Cost of fine       Number of fines

    1                              1

    2                             4

    3                              1

We know that,

A graph is a form of figure used to show accumulated data. This data might be quantitative or qualitative, which means that graphs can be utilized for a variety of purposes.

This is why there are numerous sorts of graphs, such as bar graphs, line graphs, area graphs, pictographs, and others.

To plot this data,

Label number 0, 1 , 2, 3, 4... on a number line

Which represents the cost of fine in thousands of dollars.

And plot the graph according to the given data.

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Answer:

Quotient = x^ -1 and the remainder: 0

Step-by-step explanation:

Constant to the left with the opposite sign and coefficients to the right:

-5 | 1 5 -1 -5

Make an horizontal line

Bring down the first coefficient (1) under the line.

Multiply the constant -5 times 1=-5 and add -5 to 5 = 0

Keep doing the same with the coefficients.

The given equivalent function is g(x)=(x+9)(x-2). Therefore, option B is the correct answer.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is g(x)=x²+7x-18

Now, g(x)=x²+9x-2x-18

g(x)=x(x+9)-2(x+9)

g(x)=(x+9)(x-2)

Therefore, option B is the correct answer.

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Answer:

The answer will be :-

2. AB = 31.5 in

3. AC = 5.25 in

When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.

When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.

It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.

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The value of the missing part of the triangle such as PR and ST = 8 and 5 respectively

Triangle PQS is congruent with triangle PRS

Therefore, PQ = PR

That is;

PQ = 8

PR = 2x

8 = 2x

X = 8/2 = 4

PR = 2(4) = 8

For ST;

Triangle VST = VUT

That is, TU = ST

ST = 5z

TU = 2z+3

5z = 2z+3

5z+2z = 3

z= 3/3 = 1

ST = 5(1) = 5

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Answer:

No it's not unusual

Step-by-step explanation:

That's an unusual definition for unusual if you don't mind me saying so.

There are 4 sixes in a standard deck of cards without the jokers. There are 52 cards in that deck

4/52 = 0.077

This is greater than 0.05 so it is not unusual.

Let's add the 2 jokers and see what happens.

4/54 = 0.074

That's still not going to get the situation defined as unusual.

Answer:

88

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

9.6 times 10=96

96-8 =88

The linear function y = 2x + 5 shows that Sarah charges $5 as fixed amount before she begins selling newspapers.

The table representing amount of money which Sarah charges her customers to sell newspapers.

Let us consider 'x' represents the time per hour charges taken by Sarah from customers.

In the table,

For zero hours charges are $5.

It means Fixed charges taken by Sarah to sell newspaper.

Difference between the rate per hour is,

$7 - $5 = $2

$9 - $7 = $2

It represents for Sarah charges $2 per hour.

let us consider 'y' that represents total amount charges by Sarah.

Required linear function for selling news paper and charging amount is

y = $5 + 2x

⇒ y = 2x  + 5

Therefore, the linear function y = 2x + 5 represents option 1. Sarah charges $5 before she begins selling newspapers.

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Maximum: 1, Minimum: -3, Midline y = -1, Amplitude = 4, Period = π, Frequency = 1/π,  equation -4cos(2x) + 1:

Sinusoidal Functions

It refers to the oscillating functions like the sine or cosine which range from a minimum and maximum value periodically.

The graph shown can give us all the information we need to answer these questions:

Maximum: 1

Minimum: -3

The midline goes through the center value (mean) of the max and min values, i.e.

Equation of the midline:

y = (1-3)/2

y = -1

Amplitude is the difference between the maximum and minimum values

A =4

The period is the time it takes to complete a cycle. We can see the minimum value is first reached at x=0 and next at  x = π

Thus the period is

T = π

The frequency is the reciprocal of the period:

f = 1/T = 1/π

The angular frequency is

ω = 2πf

ω = 2

The equation of the function is a negative cosine (since it starts at the minimum) or a shifted sine or cosine. We'll choose the negative cosine, knowing all the parameters:

f(x) = -4cos(2x) + 1

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Answer:

134 children and 120 adult plates were served

Step-by-step explanation:

let the children mean be x

Let the adult meal be y

If fourteen less children’s meals were served than adult meals at a barbecue, then;

y = x - 14 .... 1

IF Children plate were 1.50 each and adult plates were 2.00 each with a total of 441 in amount then;

1.5x + 2y = 441 .... 2

Substitute 1 into 2;

1.5x + 2(x-14) = 441

1.5x+2x-28 = 441

3.5x = 441+28

3.5x = 469

x = 469/3.5

x = 134

Recall that y = x - 14

y = 134-14

y = 120

Hence 134 children and 120 adult plates were served

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Lets do this step by step.

\(30x^{2\ }-\ 28x\ +\ 6\ =\ 0\)

Use the quadratic formula to find the solutions.

\(\frac{-b± \sqrt{ b^2 - 4 (ac)} }{2a}\)

Substitute the values \(a = 30, b = -28 ,\) and \(c = 6\) into the quadratic formula and solve for \(x.\)

\(\frac{28±\sqrt{( -28)^2 -4 . (30 . 6)} }{2 . 30}\)

Simplify.

__________

Simplify the numerator.

____________

Raise \(-28\) to the power of 2.

\(\frac{28±\sqrt{ 784 -4 . (30 . 6)} }{2 . 30}\)

Multiply 30 by 6.

\(x = \frac{28±\sqrt{ 784 - 4 . 180} }{2 . 30}\)

Multiply -4 by 180.

\(x = \frac{28±\sqrt{ 784 - 720} }{2 . 30}\)

Subtract 720 from 784.

\(x = \frac{28 ±\sqrt{8^2} }{2 . 30}\)

Rewrite 64 as 8^2.

\(x = \frac{28 ± 8}{2 . 30}\)

Pull terms out from under the radical, assuming positive real numbers.

\(x = \frac{28 ± 8}{2 . 30}\)

Multiply 2 by 30.

\(x = \frac{28 ± 8}{60}\)

Simplify \(\frac{28 ± 8}{60}\)

\(x = \frac{7 ± 2}{15}\)

The final answer is the combination of both solutions.

\(x = \frac{1}{3} , \frac{3}{5}\)

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

a = \(\frac{d}{b+c}\)

Step-by-step explanation:

a(b + c) = d

isolate a by dividing both sides by b + c

a = \(\frac{d}{b+c}\)

Answer: 4,588.4 cubic centimeters.

Step-by-step explanation: 20 centimeters ⋅ 14 centimeters = 280 centimeters = 4588.38 cubic centimeters = 4,588.4 cubic centimeters.

1) 3:00 to 4:00

2) 103

The required solution is 4:00 to 5:00 and  87  customers.

It is required to fill in the blanks.

The arithmetic refers to working with numbers by doing addition, subtraction, multiplication, and division. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.

Given:

According to question , Initially, there were 75 customers.

From 1:00 to 2:00, a total of 30 more people entered, meaning there were

 75 + 30 - 12

= 93 people.

From 2:00 to 3:00, a total of 14 more people entered, meaning there were

93 + 14 - 8  

= 99 people.

From 3:00 to 4:00, a total of 18 people entered, meaning there were

 99 + 18 - 30

= 87 people.

4:00 to 5:00   :  If the store does not accept any more customers except those who are already inside then, all 87 must leave between 4:00 to 5:00 in order to left from the store by 5:00.

Therefore, the required solution is 4:00 to 5:00 and  87  customers.

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Answer:

waht is your question

?

Step-by-step explanation:

The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.

From the given table;

The volume of the first gas Layla bought = 3 gallons.

The cost of the 3 gallons = 9.45

Therefore the cost of 1 gallon = ?

That is:

3 gallons = $9.45

1 gallon = X

Make X the subject of formula:

X = 9.45/3 = $3.15

Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.

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Answer:

(9, 3)  

Step-by-step explanation:

(1) 4(0.25x + 0.5 y) = 3.75 ⟶ x + 2y = 15

(2)                 4x - 8y = 12 ⟶ x  -  2y =   3

                                                   2x = 18

                                                      x = 9

                                              9 - 2y = 3

                                                  -2y = -6

                                                     y = 3

Answer:

1. The function that gives the lion population size P(t), t years from today is:

P(t) = 325(0.95)^t

2. To find the population in 4 years, we can substitute t=4 in the function:

P(4) = 325(0.95)^4

P(4) = 279.14

So the population will be approximately 279 lions in 4 years.

3. The exponential function for all three years is the same as in part 1:

P(t) = 325(0.95)^t

Two foci of the ellipse are ( 2 - √3) and moves clockwise three fourth is ( 2 + √3).

As given in the question,

Given equations are :

x = 1 + sin(t)

⇒ sin(t) = (x - 1)

y = 6 + 2cos(t)

⇒cos(t) = (y - 6)/2

We know that,

sin²t + cos²t = 1

Substitute the value of sin(t) and cos(t) we get,

(x - 1)²/ 1² + (y - 6)²/ 2² = 1

Standard Equation of the ellipse  is:

( x -h)²/b² + (y - k)²/a² = 1

Center of the ellipse = (h , k)

(h , k) = (1, 6)

here b = 1 and a = 2

'c' is the distance from focus to the center

c = √a² - b²

  = √4 -1

  = √3

Therefore , two foci for the given ellipse are ( 2 - √3) and moves clockwise three fourth is ( 2 + √3).

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The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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Answer:

1. (a)  [-1, ∞)

   (b)  (-∞, -1) ∪ (1, ∞)

2. (a)  (1, 3)

    (b)  (-∞, 1) ∪ (3, ∞)

3. (a)  9.6 m and 0.4 m

   (b)  03:08 and 15:42

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Part (a)

When x < 0, the function is f(x) = x².

Since the square of any non-zero real number is always positive, the range of the function f(x) for x < 0 is (0, ∞).

When x ≥ 0, the function is f(x) = sin(x).

The minimum value of the sine function is -1 and the maximum value of the sine function is 1.  As the sine function is periodic, the function oscillates between these values.  Therefore, the range of function f(x) for x ≥ 0 is [-1, 1].

The range of function f(x) is the union of the ranges of the two separate parts of the function.  Therefore, the range of f(x) is [-1, ∞).

Part (b)

The domain of the function g(x) = ln(x² - 1) is the set of all real numbers x for which (x² - 1) is positive, since the natural logarithm function (ln) is only defined for positive input values.

Find the values of x:

\(\implies x^2-1 > 0\)

\(\implies x^2 > 1\)

\(\implies x < -1, \;\;x > 1\)

Therefore, the domain of function g(x) is (-∞, -1) ∪ (1, ∞).

Part (a)

To determine the interval where f(x) < 0, we need to find the values of x for which the quadratic is less than zero.

First, set the function equal to zero and solve for x:

\(\begin{aligned} x^2-4x+3&=0\\x^2-3x-x+3&=0\\x(x-3)-1(x-3)&=0\\(x-1)(x-3)&=0\\ \implies x&=1,\;3\end{aligned}\)

Therefore, the function is equal to zero at x = 1 and x = 3 and so the parabola crosses the x-axis at x = 1 and x = 3.

As the leading coefficient of the quadratic is positive, the parabola opens upwards. Therefore, the values of x that make the function negative are between the zeros.  So the interval where f(x) < 0 is 1 < x < 3 = (1, 3).

Part (b)
Since the square root of a negative number cannot be taken, and dividing a number by zero is undefined, function f(x) has to be positive and not equal to zero:  f(x) > 0.

As the parabola opens upwards, the values of x that make the function positive are less than the zero at x = 1 and more than the zero at x = 3.

Therefore the domain of g(x) is (-∞, 1) ∪ (3, ∞).

Part (a)

The range of a sine function is [-1, 1]. Therefore, to calculate the maximal and minimal possible water depths of the bay, substitute the maximum and minimum values of sin(t/2) into the equation:

\(\textsf{Maximum}: \quad 5+4.6(1)=9.6\; \sf m\)

\(\textsf{Maximum}: \quad 5+4.6(-1)=0.4\; \sf m\)

Part (b)

To find the times when the depth is maximal, set sin(t/2) to 1 and solve for t:

\(\implies \sin \left(\dfrac{t}{2}\right)=1\)

\(\implies \dfrac{t}{2}=\dfrac{\pi}{2}+2\pi n\)

\(\implies t=\pi+4\pi n\)

Therefore, the values of t in the interval 0 ≤ t ≤ 24 are:

Convert these values to times:

Using conditional probability, it is found that there is a 0.7873 = 78.73% probability that Mona was justifiably dropped.

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

In this problem:

The probability of failing the test is composed by:

Hence:

\(P(A) = 0.46(0.37) + 0.63 = 0.8002\)

The probability of both failing the test and being unfit is:

\(P(A \cap B) = 0.63\)

Hence, the conditional probability is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.63}{0.8002} = 0.7873\)

0.7873 = 78.73% probability that Mona was justifiably dropped.

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Answer:

2

Step-by-step explanation:

1+1=2

Answer:

3zx-15z+12x-60

Step-by-step explanation:

first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20

then distribute the 3 to get the answer

Answer:

14 students have to retake the test

Step-by-step explanation:

to calculate the mean mark as

sum of ( product of mark and frequency ) ÷ total

mean = \(\frac{14(2)+15(10)+16(2)+17(3)+18(13)}{30}\)

        = \(\frac{28+150+32+51+234}{30}\)

       = \(\frac{495}{30}\)

      = 16.5

students who score less than 16.5 will retake the test , that is

2 scored 16 , 10 scored 15 , 2 scored 14

number who have to retake test = 2 + 10 + 2 = 14

0.60 km which I got from https://quizizz.com