Jocelyn walks her dog 5 days each week.Each Walk is 2 1/4 miles long. What is the total number of miles that Jocelyn walks her dog each week

The value of both domain and range of this exponential function is (−∞,∞).

y = 2x-9

The domain of the function can be defined as all real numbers except the ones where the expression is undefined. In the case of 2x-9, there is no real number for which this expression is undefined. Therefore, a domain of this exponential function is (−∞,∞).

The range of the function is defined as the set of all valid y values. In this case, all real numbers are valid values of y. Therefore, the range of this exponential function is (−∞,∞).

Therefore, domain of y = 2x-9 is (−∞,∞) and range is also (−∞,∞).

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Answer:

3=x

Step-by-step explanation:

multiply 5 times 2x and 4 which is 10x-20

then you have -10=10x-20

then add 20 to both aides and you'll have

30=10x then divide by 10 to get x alone

and you have

3=x

Answer:

$870.00 is the motorcycle price after a 40% discount

Step-by-step explanation:

discount = original price x discount % / 100

discount = 1450 x 40 / 100

discount = 1450 x 0.4

discount = $580.00

Final Price = Original Price - Discount

Final Price = 1450 - 580

Final Price = $870

Answer:

Step-by-step explanation:

Convert the given amount to the given unit.

6 yd; ft

The time it would take to get a sunburn when the UV rating is 10 is approximately 9 minutes.

UV rays from the sun are one of the primary causes of skin damage and sunburns. The UV rating indicates the intensity of these rays at a specific location and time. In this case, we are given that at a UV rating of 6, an average person can get a sunburn in as little as 15 minutes. Since the time it takes to get a sunburn varies inversely with the UV rating, we can use this information to determine the time for a UV rating of 10.

To calculate the time, we can set up a proportion using the inverse relationship. The proportion would be:

Time with UV rating of 6 / Time with UV rating of 10 = UV rating of 10 / UV rating of 6

Plugging in the given values, we have:

15 minutes / Time with UV rating of 10 = 10 / 6

To solve for the unknown time, we can cross multiply:

15 * 6 = 10 * Time with UV rating of 10

90 = 10 * Time with UV rating of 10

Dividing both sides by 10, we find:

9 = Time with UV rating of 10

It would take approximately 9 minutes to get a sunburn when the UV rating is 10.

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12 is the ending value of sum.

Ending value of sum=?

x = scnr.nextInt();

sum = 0;

for (i = 0; i < x; ++i) {

currValue = scnr.nextInt();

sum += currValue;

}

Input provided to the code 2 5 7 3.

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Answer:

number 1

k=12

Step-by-step explanation:

The x-value that corresponds to a z-score of 2.05 is approximately 130.75.

To find the x-value that corresponds to a given z-score, we use the formula:

x = μ + zσ

Where:

x is the corresponding value in the distribution,

μ is the mean of the distribution,

z is the z-score,

σ is the standard deviation of the distribution.

In this case, the mean (μ) is 100, the z-score (z) is 2.05, and the standard deviation (σ) is 15.

Substituting the values into the formula, we have:

x = 100 + 2.05 * 15

Calculating this, we get:

x = 100 + 30.75

x = 130.75

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Answer:

Choice 'D' (10x + 9) (10x-9) is the correct answer

Step-by-step explanation:

100x^2 - 81

This is a difference of squares...

therefore = (10x + 9) (10x - 9)

Answer:

As a fraction = \(\dfrac{30}{100}\)

As a decimal = 0.3

Step-by-step explanation:

Recall that: The total yard of a football field = 100 yards

Tritan played in a football game he caught the ball at the goal line and ran forward 30 yards before he was tackled,

As a fraction;

Tristan run can be represented as = number of run from goal-line/ total length of the field

= \(\dfrac{30}{100}\)

As a decimal= 0.3

Hey there!

-4 + y + 4y - 5x + 2x - 3

COMBINE the LIKE TERMS

= (-5x + 2x) + (y + 4y) + (-4 - 3)

= -3x + 5y - 7

Answer: -3x + 5y - 7

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

a) The graph of the object's velocity versus time can be seen below. The x-axis is labelled "time (s)" and the y-axis is labelled "velocity (m/s)". The important points on the graph are when the velocity is 0 (t = 0, 3, and 10 s) and the maximum velocity (t = 5 s).
b) The object's change in velocity over the first 3 seconds of its motion is 20 m/s.
c) The object is instantaneously at rest at t = 0, 3, and 10 s.
d) The object's total displacement over the first 10 seconds of its motion is 100 m.

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26.32 is the result when the number 28 is decreased by 6%.

What is percent decrease?

Calculate the % of the amount to be increased or decreased, and then either add the result to the amount to make it larger or subtract it to make it smaller.

First to calculate the 6% of 28.

Multiply 28 by 6%,

\(28(0.06) = 1.68\)

Now subtract this amount from 28,

\(28 - 1.68 = 26.32\)

Therefore, 26.32 is the result when the number 28 is decreased by 6%.

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The probability of a randomly selected student completing the test in 45 minutes or less is 15.87%.

The probability of a randomly selected student completing the test in 95 minutes or less is 84.13%.

Using the standard normal distribution to standardize the values:

z = (x - μ) / σ

where:

For 45 minutes or less:

z = (45 - 70) / 25

z = -1

Using a calculator, we can find that the probability of a z-score less than or equal to -1 is approximately 0.1587.

For 95 minutes:

z = (95 - 70) / 25

z = 1

Using a calculator, the probability of a z-score less than or equal to 1 is approximately 0.8413.

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Lenny's total wage is $7000

In this question, Lenny works a basic week of 32 hours. His basic rate of pay is $1,750. During a certain week he worked 9 hours overtime for which he was paid triple time.

32 hours of work = $1750

In a certain week, we work 9 hours as over time

For this overtime which he was paid triple time.

1750 * 3 = $5250

So, Lenny's total wage would be,

$1,750 +  $5250 = $7000

Therefore,  Lenny's total wage is $7000

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The expression which represents either the length or width is (x+3). The correct answer is option (c).

Given that the area of a rectangle which is given as x²+5x+6.

We have to find which expression represents either the length or width.

We are given an expression for the area. But we also know that the area of a rectangle is length times width. So the expression we were given, x²+5x+6 must be equal to the length of the rectangle times its width.

So, will find the factoring the expression we can see expressions for the length and the width.

Factoring x²+5x+6 we get (x+2)(x+3).

One of these factors is the width and the other is the length.

Hence, the expression represents either the length or width of the rectangle when the area of a rectangle is given as x²+5x+6 is (x+3).

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Answer:

B

Step-by-step explanation:

In the equation it states there is a one-time fee charge so we would add this when writing it in an expression. Since the expressions is: T = 15n + 12; and the only number being added is 12, we can assume the number 12 represents the service fee cost.

The limit of \((e^{2x} - 1)^x\) as x approaches 0 is 2.

What is L'Hopital's rule?

L'Hopital's rule is a mathematical technique used to evaluate the limit of an indeterminate form (such as 0/0 or infinity/infinity) that arises in calculus. The rule states that if the limit of the ratio of the derivatives of two functions f(x) and g(x) exists as x approaches a certain value (usually 0 or infinity), then the limit of the original function f(x)/g(x) is equal to this same value. This rule can be useful in cases where other methods of finding limits are inconclusive or difficult to apply. However, it should be used with caution and only after checking that the conditions for its applicability are met.

We can use L'Hopital's rule to evaluate this limit:

lim \(x- > 0 (e^{(2x) }- 1)^x\)

= lim x->0 [exp(x ln\((e^{(2x)} - 1))]\)

= exp[lim x->0 x ln\((e^{(2x)}\) - 1)]

= exp[lim x->0 (ln\((e^{(2x) }- 1))/(1/x)]\)

Now applying L'Hopital's rule again, we get:

= exp[lim x->0 \((2e^{(2x)})/(2x/(e^{(2x)} - 1))]\)

= exp[lim x->0 \((e^{(2x)} - 1)/x]\)

= exp[lim x->0 2\(e^{(2x)}\)]

= 2

Therefore, the limit of \((e^{2x} - 1)^x\) as x approaches 0 is 2.

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Answer:

Two expressions for the area are;

i) x/3 + 2·y + 6

ii) (1/3) × (x + 6·y + 18)

Step-by-step explanation:

The given dimension of the rectangle are;

The height of the rectangle, h = 1/3

The width of the smallest rectangle, w₁ = x

The width of the med sized rectangle, w₂ = 6·y

The width the large rectangle, w₃ = 18

The area, 'A', of the entire rectangular figure, the big rectangle, can be expressed as follows;

A = A₁ + A₂ + A₃

Where;

A₁ = The area of the smallest rectangle

A₂ = The area of the mid sized rectangle

A₃ = The area of the large rectangle

∴ A = (1/3) × x + (1/3) × 6·y + (1/3) × 18 = x/3 + 2·y + 6

The area of the big rectangle. 'A', can also be found as follows;

A = (1/3) × (x + 6·y + 18)

Therefore, two expressions for the area of the big rectangle are;

x/3 + 2·y + 6 and (1/3) × (x + 6·y + 18).

Answer:

5/12, $10

Step-by-step explanation:

Lea earned $24 babysitting. She spent ⅔ of that amount on a gift for her bestie, ¼ on snacks. What fraction of her earning is left? How much money does she have left?

Let the total amount earned be 1

Given

Amount on snacks = ¼

Amount on babysitting = ⅔

Required

Fraction left

Fraction left = Total -(snacks+babysitting)

Fraction left = 1-(1/4+2/3)

Fraction left = 1-(3+4/12)

Fraction left = 1-7/12

Fraction left = 5/12

Amount of money she has left = 5/12 × 24 = 5×2 = $10

Hence she has $10 left

Answer:

3990 miles

Step-by-step explanation:

570 miles per hour

7 hours

570x7=3990

a. The linear equation that models the temperature T as a function of the number of chirps per minute N is: T(N) = (1/9)N + 60

b. If the crickets are chirping at 155 chirps per minute, the estimated temperature is approximately 77.22 degrees Fahrenheit.

a. Let's first find the slope of the line using the formula:

slope (m) = (y2 - y1) / (x2 - x1)

where (x1, y1) = (117, 73) and (x2, y2) = (180, 80).

slope = (80 - 73) / (180 - 117)

= 7 / 63

= 1/9

Now, let's use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Using the point (117, 73):

T - 73 = (1/9)(N - 117)

Simplifying the equation:

T - 73 = (1/9)N - (1/9)117

T - 73 = (1/9)N - 13

Now, let's rearrange the equation to solve for T:

T = (1/9)N - 13 + 73

T = (1/9)N + 60

Therefore, the linear equation that models the temperature T as a function of the number of chirps per minute N is: T(N) = (1/9)N + 60

(b) If the crickets are chirping at 155 chirps per minute, we can estimate the temperature T using the linear equation we derived.

T(N) = (1/9)N + 60

Substituting N = 155:

T(155) = (1/9)(155) + 60

T(155) = 17.22 + 60

T(155) ≈ 77.22

Therefore, if the crickets are chirping at 155 chirps per minute, the estimated temperature is approximately 77.22 degrees Fahrenheit.

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The calculated value of the test statistic is approximately 6.40.

To test the hypothesis that job satisfaction is the same at Baruch College and Brooklyn College, we can use a two-sample t-test.

The null hypothesis (H0) assumes that the means of the two populations are equal, while the alternative hypothesis (Ha) assumes that the means are not equal.

H0: μ1 = μ2 (Mean job satisfaction at Baruch College is equal to mean job satisfaction at Brooklyn College)

Ha: μ1 ≠ μ2 (Mean job satisfaction at Baruch College is not equal to mean job satisfaction at Brooklyn College)

We can calculate the test statistic using the formula:

t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes.

Given the data:

Baruch College: mean job satisfaction score (x1) = 83.0, standard deviation (s1) = 15, sample size (n1) = 150.

Brooklyn College: mean job satisfaction score (x2) = 73.0, standard deviation (s2) = 12, sample size (n2) = 100.

Calculating the test statistic:

t = (83.0 - 73.0) / sqrt((15^2 / 150) + (12^2 / 100))

t = 10 / sqrt(1 + 1.44)

t ≈ 10 / sqrt(2.44)

t ≈ 10 / 1.561

t ≈ 6.40

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A situation in which conclusions based upon aggregated crosstabulation are different from unaggregated crosstabulation is known as Simpson's paradox.

Simpson’s Paradox is an example of statistics that can be wrong. The paradox is defined as averages that can be silly and misleading. Sometimes they can be just plain baffling.

It is also called the Yule-Simpson effect which is an effect that occurs when the marginal association between two categorical variables is qualitatively different from the partial association between the same two variables after controlling for one or more other variables.

This result is often encountered in social science and medical science statistics and is particularly problematic when frequency data are unduly given causal interpretations.

It is a statistical phenomenon where an association between two variables in a population emerges or reverses when the population is divided into subpopulations.

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The combined area of the four removed triangles is 48 sq.units. Answer: 48

We need to find out the combined area of the four removed triangles, in square units. Given: AB = 12 units.

Let's consider the given square, and let's draw an altitude BD and also draw perpendiculars to BD from the three vertices A, C and D.

Let AB = x cm. Area of square = x² sq.cm.

Now, we are cutting a triangle with base x and height x, which is a right-angled triangle. Hence, area of each removed triangle = (1/2) * x * x = (x²/2) sq.cm.

Now, BD = x/√2. Area of rectangle = AB * BD = 12 * 12/√2 = 72√2 sq.cm.

Now, area of 4 triangles = (x²/2) + (x²/2) + (x²/2) + (x²/2) = 2x² sq.cm.

We know that, Area of rectangle = Area of 4 triangles + Area of square => 72√2 = 2x² + x² => 72√2 = 3x² => x² = 24√2 cm² => x = √(24 * 2) cm = √(48) cm = 4√3 * √2 cm.

Area of 4 triangles = 2x² sq.cm = 2 * 24 cm² = 48 sq.cm.

Hence, the combined area of the four removed triangles is 48 sq.units. Answer: 48.

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Answer:

g(-1)=-16

Step-by-step explanation:

g(x)=6x-10

Let x=-1

g(-1)=6(-1)-10

=-6-10

g(-1) =-16

Answer:

16x2-78x+88

Step-by-step explanation:

2(2x-4)2 - 7(2x-4)-4

16x2-64x+64-14x+28-4

16x2-78x+88