Pamela drove her car
99
9999 kilometers and used
9
99 liters of fuel. She wants to know how many kilometers
(
k
)
(k)left parenthesis, k, right parenthesis she can drive with
12
1212 liters of fuel. She assumes the relationship between kilometers and fuel is proportional.
How many kilometers can Pamela drive with
12
1212 liters of fuel?

Answer:

62

Step-by-step explanation:

775 steps divided by 12.5 minutes is 62 steps per minute.

The common factor for 13%, 0.125, 1/5, and 10% is that they can be expressed as fractions with denominators of 100.

All of the numbers can be converted to fractions with a denominator of 100.

To convert 13% to a fraction with a denominator of 100, we need to divide 13 by 100, which gives us 0.13.

To convert 0.125 to a fraction with a denominator of 100, we multiply both the numerator and denominator by 100 to get 12.5/100.

To convert 1/5 to a fraction with a denominator of 100, we multiply the numerator and denominator by 20, which gives us 20/100.

To convert 10% to a fraction with a denominator of 100, we divide 10 by 100, which gives us 0.1.

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The dependent variable in this study is the number of times the students got out of their seats over the course of 2 hours.

The independent variable is the variable that is being manipulated or controlled by the researcher.

It is the variable that is expected to cause a change in the dependent variable which is the variable being measured as the outcome or response to the manipulation of the independent variable.

In the given scenario, the independent variable is the group assignment based on the scores on the sensation-seeking test.

The researcher has divided the students into two groups based on their scores, and this grouping is being used as a way of manipulating or controlling the students' level of sensation-seeking behavior.

The researcher is interested in how this manipulation affects the students' behavior in terms of getting out of their seats.

The dependent variable is the number of times the students got out of their seats over the course of 2 hours.

This variable is expected to vary depending on the level of the independent variable, which is the group assignment based on the sensation-seeking test scores.

The researcher will measure the dependent variable for each group separately and then compare the results to determine if there is a significant difference between the two groups.

In summary,

The independent variable is the grouping of the students based on their scores on the sensation-seeking test and the dependent variable is the number of times the students got out of their seats over the course of 2 hours.

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Answer:

\(\frac{-19}{8}\)

Step-by-step explanation:

\(\frac{-3}{4}-\frac{13}{8}\)

\(-\frac{3}{2^2}-\frac{13}{2^3}\)

\(\frac{2(-3)+(-13)}{2^3}=\frac{-19}{8}\)

hope it helps u

Answer:

Step-by-step explanation:

If we look at the picture,we can see that n<22

So the correct answer will be 22

Answer:

x=-18

Step-by-step explanation:

Answer:

The answer is -18

Step-by-step explanation:

STEP 1:

\(3 \times \frac{2}{3} (x + 6) = 3( - 8)\)

2(x+6) = -24

______________________________________

STEP 2:

Divide both sides by 2:

\( \frac{2(x + 6)}{2} = \frac{ - 24}{2} \)

________________________________

STEP 3:

Simplify:

\(x + 6 = - 12\)

Subtract 6 from both sides:

\(x + 6 - 6 = - 12 - 6\)

________________________________

STEP 4:

\(x = - 18\)

Therefore, your answer is -18.

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Using the given exponential function,

The rate of the disease spreading is approx. 140 peoples per day affected.

let P be the number of people's that are contacting a new disease.

given exponential function about the new disease modeled by population is

P(t) = 3725/(1 +1.72 e⁻⁰·⁵²ᵗ) ---(1)

where t is time measured in days

we want to calculate the rate of diseases spreading on day 4 i.e t = 4

putting the value t = 4 in above formula, we get

P(t=4) = 3725/(1 + 1.72 e⁻⁽⁰·⁵²⁾⁴)

=> P( t= 4) = 3725 / (1 + 1.72× e⁻⁰·²⁸)

=> P(t=4) = 3725/(1 + 1.72× 0.124)

=> P(t = 4) = 3725/(1+ 0.2148)

=> P(t=4) = 3725/1.2148

=> P(t = 4) = 3066.14

Hence, after 4 days of diseases spread , total 3066 people's are affected from it .

rate of diseases spreading per day is equal to (3725-3066)/4 = 659/4 = 139.75

so, rate of spreding diseases is 139.75 ~ 140 peoples per day .

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D. 25

This is the answer

Answer:

D. 25

Step-by-step explanation:

You can solve this by saying that he gained 2 points 13 times, and lost half a point two times.

2 * 13 - 0.5 * 2

= 26 - 1

= 25

So his final score was 25.

Answer:

For the outside square, the diagonal is 7√2, or about 9.9 units.

For the inside square, the diagonal is 5√2, or about 7.1 units.

The best-predicted value of Modifying Above y with caret given that the twin born first has an IQ of 104​ is 106.2.

The dependent variable's predicted value in basic linear regression is given by the equation = b0 + b1x.

In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b0 + b1X. (the error is the difference between the predicted value and the actual value of y).

Use regression equation

ŷ=14.68+0.88x​

plug in IQ, which is x

y = 14.68 + 0.88(104)

 = 106.2

Hence, the answer is 106.2

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Answer:

(12,-7)

Step-by-step explanation:

The required ordered pair of the pre-image of D'(4, -3) is D(12, -7).

Given that,
To determine the preimage of the ordered pair of D'(4, -3) by the translation, (x, y)  to (x – 8, y+4).

Coordinate, is represented as the values on the x-axis and y-axis of the graph.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the ordered pair of the preimage be (x, y)
Now,

according to the question,
x - 8 = 4
x = 12
y + 4 = -3
y = -7

Thus, the required ordered pair of the pre-image of D'(4, -3) is D(12, -7).

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Answer:

m=-1

Step-by-step explanation:

3-7/2-(-2)

-4/2-(-2)

-4/2+2

-4/4

-1

Answer:

slope = -1

Step-by-step explanation:

gradient = (difference in y)/(diffidence in X)

m = (7-3)/(-2-2)

m = 4/-4

m = -1

Answer:

10 km/h

Step-by-step explanation:

First, convert 150 minutes to hours:

150/60

= 2.5 hours

Then, to find his speed, divide the km by the number of hours:

25/2.5

= 10 km/h

Answer:

10 km / hr

Step-by-step explanation:

We want to find the average speed in kilometers per hour.

We know that Andre cycled 25 kilometers in 150 minutes.

First, we have the convert 150 minutes to hours.

There are 60 minutes in 1 hour, so we can divide 150 by 60.

150/60= 2.5

Next, find the average speed in kilometers per hour.

Divide the kilometers traveled by the hours.

speed = kilometers / hours

Andre cycled 25 kilometers in 2.5 hours.

speed= 25 km /2.5 hrs

speed = 10 km/hr

Andre’s average speed was 10 kilometers per hour.

Answer:

Step-by-step explanation:

area of triangle=base*height/2

=8*3/2

=24/2

=12 m^2

Answer:

Janice travelled 6 miles.

Step-by-step explanation:

23 -5=18

18/3=6

so Janice travelled 6 miles.

a. At values of x=1 and x =3 the local maximum and minimum values of g occur

b. The absolute maximum value of g(x) is approximately 0.76 and occurs at x = 4.

c. On the intervals [0, 1) and (3, 4] g concave downward

Since g(x) is defined as the definite integral of f(t) from 0 to x, we can use the First Fundamental Theorem of Calculus to find g'(x) in terms of f(x):

g'(x) = f(x)

Similarly, we can use the Second Fundamental Theorem of Calculus to find g''(x) in terms of f'(x):

g''(x) = f'(x)

(a) The local maximum and minimum values of g occur at critical points of g(x), which are values of x where g'(x) = f(x) = 0 or is undefined. From the graph of f(x), we see that f(x) = 0 at x = 1 and x = 3, so these are possible candidates for critical points of g(x). We also see that f(x) is undefined at x = 2, so this is another possible critical point. Evaluating g'(x) and g''(x) at each of these values, we have:

g'(1) = f(1) = 0, g''(1) = f'(1) < 0, so g(x) has a local maximum at x = 1.

g'(2) is undefined, so x = 2 is not a critical point of g(x).

g'(3) = f(3) = 0, g''(3) = f'(3) > 0, so g(x) has a local minimum at x = 3.

Therefore, the local maximum of g(x) occurs at x = 1, and the local minimum of g(x) occurs at x = 3.

(b) To find the absolute maximum value of g(x), we need to examine the values of g(x) at the endpoints of the interval [0, 4]. We have:

g(0) = 0

g(4) = R 4 0 f(t)dt = the area under the curve of f(x) from x=0 to x=4.

From the graph, we can see that the absolute maximum value of g(x) occurs when x is in the interval [1, 3], so we can evaluate g(x) at the critical points found in part (a) and the endpoints of the interval to find the absolute maximum value of g(x):

g(1) = R 1 0 f(t)dt ≈ 0.72

g(3) = R 3 0 f(t)dt ≈ 0.65

g(4) = R 4 0 f(t)dt ≈ 0.76

Therefore, the absolute maximum value of g(x) is approximately 0.76 and occurs at x = 4.

(c) The function g(x) is concave downward on an interval if its second derivative, g''(x), is negative on that interval. From part (a), we know that g''(x) = f'(x), so we need to find where f'(x) is negative. From the graph of f(x), we can see that f'(x) is negative on the intervals [0, 1) and (3, 4]. Therefore, g(x) is concave downward on the intervals [0, 1) and (3, 4].

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For a random sample of 155 observations results in 62 successes.

a) A 90% confidence interval for the population proportion of successes is equals to the (0.335 , 0.465).

b) A 90% confidence interval for the population proportion of failure is equals to the (0.535 , 0.665).

We have a random sample of 155 observations results in 62 successes. So,

Observed value, x = 62

Sample size,n = 155

Population Proportion, p = x/n

= 62/155

= 0.4

a) We have to determine 90% confidence interval for the population proportion of successes. Using the distribution table, for 90% confidence interval, z-score value is equals to 1.6. Consider Confidence interval formula with proportion, CI \(= p ± z×\sqrt\frac{p(1-p)}{n}\)

substitute all known values in above formula, \(= 0.4 ± 1.64\sqrt\frac{0.4(1- 0.4)}{155}\)

= 0.4 ± 0.0645

= (0.4 - 0.0645 , 0.4 + 0.0645)

= (0.335 , 0.465)

b) Now, we have to determine a 90% confidence interval for the population proportion of failures.

Now consider, here failure observed values, x = 155 - 62

= 93

proportion, p = x/n

= 93/155 = 0.6

Consider the confidence interval formula, CI \(= p ± z×\sqrt\frac{p(1-p)}{n}\)

substitute values, \(= 0.6 ±1.64×\sqrt\frac{0.6(1-0.6)}{155}\)

= 0.6 ± 0.0645

= (0.6 - 0.0645 , 0.6 + 0.0645)

= (0.535 , 0.665)

Hence, required value is (0.535 , 0.665).

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a = 18°

we have opposite angles =>

=> 6a + 11 = 2a + 83

6a - 2a = 83 - 11

4a = 72

a = 72 : 4

a = 18°

Answer:

0.00976

Step-by-step explanation:

Answer: 0.00976

10^{-3}  = 0.001

9.76 times 0.001 = 0.00976

The wind speed for the flight is 2 miles per hour.

Let's assume the wind speed is represented by "w" miles per hour.

When the drone flies with the wind, its effective speed is the sum of its own speed and the wind speed, so it travels at 5 + w miles per hour. Therefore, the time it takes to fly 35 miles with the wind is given by:

time = distance / speed

time = 35 / (5 + w)

Similarly, when the drone flies against the wind, its effective speed is the difference between its own speed and the wind speed, so it travels at 5 - w miles per hour. The time it takes to fly 15 miles against the wind is given by:

time = distance / speed

time = 15 / (5 - w)

Since the flight time is the same for both scenarios, we can set the two expressions for time equal to each other:

35 / (5 + w) = 15 / (5 - w)

Now, we can solve this equation to find the value of "w," the wind speed.

Cross-multiplying:

35(5 - w) = 15(5 + w)

175 - 35w = 75 + 15w

Combining like terms:

50w = 100

Dividing both sides by 50:

w = 2

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Answer:

0.5

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This function starts at point (1, 2), so 2 is inclusive. Therefore the range of this function is:

\(y \geq 2\)

Answer:

4

Step-by-step explanation:

Using the rule of exponents

\(a^{0}\) = 1

Then

4\((57ab)^{0}\) = 1 and

4\((57ab)^{0}\) = 4 × 1 = 4

Answer:

4

Step-by-step explanation:

since 57ab has power 0 it is equal to 1

1×4 is 4

Answer:

-x+11

Step-by-step explanation:

5(x+1)-6(x-1)=

Multiply the x+1 by 5 and x-1 by -6

5x+5-6x+6=

Combine like terms

-x+11

Answer:

The total distance the students ran in the race would be 5 1/2 km.

Step-by-step explanation:

2/4 + 3/4 + 2 2/4 + 1 3/4 = 3 10/4 = 5 2/4 = 5 1/2 (Simplified)

By using the formula of curved surfaced area of cylinder, it can be calculated that-

Height of the cylinder = 3.18 cm

What is curved surface area of cylinder?

Curved surface area of cylinder is the space occupied by the curved surface of the cylinder.

If r is the radius of the cylinder and h is the height of the cylinder, then curved surface area of cylinder is calculated by the formula

Curved surface area of cylinder = 2\(\pi\)rh

Let the height of the cylinder be h cm

Radius = 5 cm

Curved surface area = 2\(\pi\)rh

                                  = \(2\times \frac{22}{7}\times 5 \times h\)

                                  = \(\frac{220}{7}h\)

By the problem,

\(\frac{220}{7}h = 100\)

\(h = \frac{100 \times 7}{220}\)

h = 3.18 cm

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The value of f(0) is -1

A function can be defined as an expression, law or rule that explains the relationship between two variables; a dependent and an independent variable.

Given the function;

f(x)= -x - 1

To determine f(0), we substitute the value of x as 0 in the function

So, we have;

f(0) = -(0) - 1

f(0) = -0 - 1

f(0) = -1

Thus, the value of f(0) is -1

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