Nora has to drive 245 miles to visit a friend. she drives 95.68 miles and then stops for lunch. how many more miles will she have to drive

Therefore, the probability that a randomly selected athlete uses a stairclimber for less than 17 minutes is 0.3336. Therefore, the probability that a randomly selected athlete uses a stairclimber for between 20 and 27 minutes is approximately 2.3891/100, or 0.0239. Therefore, the probability that a randomly selected athlete uses a stairclimber for more than 30 minutes is 0.0764.

(a) To find the probability that a randomly selected athlete uses a stairclimber for less than 17 minutes, we need to find the area under the normal curve to the left of 17. We can standardize the value 17 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation. Substituting the values we get:

z = (17 - 20) / 7 = -0.43

Using a standard normal table or calculator, we find that the area to the left of z = -0.43 is approximately 0.3336.

(b) To find the probability that a randomly selected athlete uses a stairclimber for between 20 and 27 minutes, we need to find the area under the normal curve between 20 and 27. We can standardize the values 20 and 27 using the same formula:

z1 = (20 - 20) / 7 = 0

z2 = (27 - 20) / 7 = 1

Using a standard normal table or calculator, we find that the area to the left of z = 1 is approximately 0.8413, and the area to the left of z = 0 is 0.5. Therefore, the area between z = 0 and z = 1 is:

0.8413 - 0.5 = 0.3413

To convert this area back to the original units of measurement (minutes), we need to multiply by the standard deviation and add the mean:

0.3413 * 7 = 2.3891

(c) To find the probability that a randomly selected athlete uses a stairclimber for more than 30 minutes, we need to find the area under the normal curve to the right of 30. We can standardize the value 30 using the formula:

z = (30 - 20) / 7 = 1.43

Using a standard normal table or calculator, we find that the area to the right of z = 1.43 is approximately 0.0764.

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Answer: The slope of parallel lines are the same

Step-by-step explanation:

There are not triangles in the image, but instead two lines creating a corner, they want you to connect the opposite corners of each of these sets of lines to create a triangle.

The bigger set of lines is up 2 right 8. slope is rise/run so the slope is 2/8 or if we simplify 1/4

The smaller set of lines is 1 up 4 right. slope is rise over run so the slope is 1/4.

The problem tries to confuse you by not connecting those lines and by having the bigger one go up first then right, and then the smaller one go right first and then up.

But as you can see the parallel lines both have a slope of 1/4

the only difference between parallel lines is the 'b' in the equation y=mx+b

The pair which is at the same level of structural organization is: D. S and X which are brain and leaf respectively.

The brain and the leaf are in the organ level of organization. The brain is an organ in human body which carries out most activities in the body. It controls all functions of the body and also interprets information from the outside world. The brain is the seat of intelligence, emotion, creativity and memory.

The leaf in plants is a collection of tissues. It enables photosynthesis to occur. The leaf traps sunlight and carbon dioxide which are used during photosynthesis to manufacture food for plants.

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The area of ​​the playgrounds are,

⇒ Area of playgrounds = 2,178 m²

We have to given that;

The school plans to add 2 new playgrounds.

And, Each play area will be in the shape of a 33m by 33m squared.

Now, We know that;

Area of square = side²

Hence, We get;

⇒ Area of playgrounds = 2 × (side)²

⇒ Area of playgrounds = 2 × 33²

⇒ Area of playgrounds = 2,178 m²

Thus, The area of ​​the playgrounds are,

⇒ Area of playgrounds = 2,178 m²

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Answer:

17 miles

Step-by-step explanation:

Let's start by using algebra to solve the problem.

Let's use "L" to represent the length of the land, and "W" to represent the width of the land. We know that the land is 4 1/4 miles wide, which we can write as a mixed number:

W = 4 1/4We also know that the length is 4 times the width:

L = 4WNow we can substitute the first equation into the second equation:

L = 4(4 1/4)

Simplifying the right side of the equation:

L = 4(4) + 4(1/4)

L = 16 + 1L = 17Therefore, the length of the land is 17 miles.

Answer:16 1/4

Step-by-step explanation:

4 1/4 * 4 = 16 1/4

The relation displayed in the table is

The relation in the table is compared by identifying how a coordinate point are expressed as ordered pair and how they are expressed as a table

For instance, say (b, c) is represented in a table as

x    y

a    b

Using this instance and writing out the values in the table we have

(3, 3), (-1, 1), (2, -2), and (-3, 2)

This is similar to option B making option B the appropriate option

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Answer:

it's more than 90°

A telescoping series is a series where most of the terms cancel out, leaving only a few terms that cannot be simplified.

The name "telescoping" comes from the idea that if you align the terms of the series, they resemble the tubes of a telescope, with most of the terms "collapsing" or "canceling out" like a collapsing telescope leaving only a few terms at the beginning and end of the series.

Telescoping series are often used in calculus to evaluate infinite series, as the cancellation of terms makes the computation much easier. In order to evaluate a telescoping series, it is often necessary to rewrite the terms in a way that allows for the cancellation of terms.

We can rewrite the given series as:

∑[infinity]n=3(1√n−1√n+2) = [(1/√2) - (1/√3)] + [(1/√3) - (1/√4)] + [(1/√4) - (1/√5)] + ...

Notice that most of the terms cancel out, leaving only the first and last terms:

[(1/√2) - (1/√3)] + [(1/√3) - (1/√4)] + [(1/√4) - (1/√5)] + ...

= (1/√2) - (1/√5)

Therefore, the sum of the telescoping series is:

(1/√2) - (1/√5) = (√5 - √2)/(√10)

So the answer is (√5 - √2)/(√10).

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The correct answer is (a) both the mean and median will decrease, but the median will decrease by more than the mean. Choice B) Both the mean and median will decrease, but the mean will decrease by more than the median.

The mean and median will both decrease with the addition of the 4th kitten. The median will decrease more than the mean because it is the middle value, and the new weight is much smaller than the other weights.

Explanation:
Before the 4th kitten was born, the weights of the kittens were between 147g and 159g. Let's denote the three weights as x, y, and z, where 147 ≤ x < y < z ≤ 159.

Mean (before 4th kitten) = (x + y + z) / 3
Median (before 4th kitten) = y (since the weights are arranged in ascending order)

After the birth of the 4th kitten, which weighed 57g, the new weights are 57g, x, y, and z.

Mean (after 4th kitten) = (57 + x + y + z) / 4
Median (after 4th kitten) = (x + y) / 2 (since there are now an even number of kittens)

Comparing the means, we see that the mean has decreased after the birth of the 4th kitten because:

(57 + x + y + z) / 4 < (x + y + z) / 3

For the medians, we can see that the median has also decreased because:

(y + x) / 2 < y

Therefore, both the mean and median have decreased. However, since the 4th kitten's weight is significantly lower than the other three kittens, the mean will be affected more and will decrease by more than the median.

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The Aztec Empire was much larger than the state of Ohio, with an estimated area of around 80,000 square miles at its peak.

This vast empire encompassed much of central Mexico and included cities such as Tenochtitlan, the capital of the Aztec Empire. The area of Ohio is approximately 44,825 square miles, not 4,000 square miles. At its peak, the Aztec Empire covered an area of about 80,000 square miles. To compare the two:

1. Note the area of Ohio: 44,825 square miles
2. Note the area of the Aztec Empire at its peak: 80,000 square miles
3. Compare: The Aztec Empire was larger, covering nearly 1.78 times the area of Ohio.

In conclusion, the Aztec Empire was significantly larger than the state of Ohio at its peak, with an area estimate of around 80,000 square miles.

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The area of the circle is 16π = 50.265 square cm

the perimeter of the circle is 25.133 cm

Area of a circle is solved using the formula

= π r^2

where

π is a constant term

r is the radius of the circle

r = diameter / 2 = 8 cm / 2 = 4cm

plugging in the value

= π 4^2

= 16π = 50.265 square cm

Perimeter is solved using the formula

= 2 π r

= 2 x  π  x 4

= 8 π

= 25.133 cm

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The area of the quadrilateral is 176.6 square meters, rounded to one decimal place.

Triangle ABC is approximately 14.1 meters tall.

Triangle ACD is roughly 2.6 meters tall.

We can now calculate the area of triangle ACD:

Area(ACD) = (1/2) * AD * height Area(ACD) = (1/2) * 7.8 * 2.6 Area(ACD) = (1/2) * 7.8 * 2.6

Finally, we may sum the areas of the two triangles to get the quadrilateral's area:

Area(quadrilateral) equals Area(ABC) + Area(ACD).

166.5 + 10.1 = 176.6

The area of the quadrilateral is roughly 176.6 square meters, rounded to one decimal place.

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The amplitude of v(t) at steady-state is (a) Amplitude = KFc. This is because the amplitude of the response in a linear system is proportional to the amplitude of the forcing function, and the constant of proportionality is the system gain, K.

In this case, the forcing function has an amplitude of Fc, and the system gain is K, so the amplitude of the response at steady-state is K times Fc, or KFc. The amplitude of v(t) at steady-state can be found by considering the relationship between the system gain (K) and the forcing function f(t). Given the forcing function f(t) = Fc * sin(100t/τ), we can determine the steady-state response by taking the amplitude of the sinusoidal forcing function and multiplying it by the system gain K. Hence, the amplitude of v(t) at steady-state is: Amplitude = K * Fc Therefore, the best answer is: a. Amplitude = KFc.

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The function rule for the statement "The output is the cube of the input" is given as follows:

f(x) = x³.

The standard definition of a function rule is given as follows:

y = f(x).

In which:

The cube is represented by the third power = x³ operation, hence the function rule for the statement "The output is the cube of the input" is given as follows:

f(x) = x³.

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The equation of the line shown, in slope-intercept form, is expressed as:

y = -1/4 + 2.

The line shown is given in the attachment below, which shows a straight line. To find the equation of this line, we would have to find its slope and also determine the y-intercept.

Slope of a line (m) = rise / run = -1/4

Th y-intercept is the point where the straight line crosses the y-axis, which is b = 2.

To write the equation of the line, substitute m = -1/4 and b = 2 into y = mx + y:

y = -1/4x + 2.

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To calculate the standard error of the proportion, we can use the formula:

Standard Error = sqrt((p*(1-p))/n)

where p is the proportion of young adults in Generation Y who pay their monthly bills on time (which is given as 0.58), and n is the sample size (which is 210).

Plugging in these values, we get:

Standard Error = sqrt((0.58*(1-0.58))/210)
              = sqrt((0.2436)/210)
              = 0.031

Therefore, the standard error of the proportion is 0.031.

It's worth noting that the standard error is a measure of the variability of the sample proportion from one sample to another. It tells us how much we can expect the sample proportion to vary if we were to take multiple random samples of the same size from the population. In this case, a standard error of 0.031 indicates that we can expect the sample proportion of young adults in Generation Y who pay their monthly bills on time to vary by around 3.1 percentage points from one sample to another.

In conclusion, if we take a random sample of 210 people from Generation Y, the standard error of the proportion of young adults who pay their monthly bills on time is 0.031.

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Answer:

-2/3

Step-by-step explanation:

3x -2y = 14

-2y = -3x + 14

y = 3/2x - 7

m = 3/2

The equation of a perpendicular line to y = 3/2x − 7 must have a slope that is the negative reciprocal of the original slope.

m perpendicular = - [tex]\frac{1}{\frac{2}{3} }[/tex]

So, the answer is m perpendicular = -2/3

If the choir director tries to maintain a ratio of 5 altos for every 7 sopranos, with 21 sopranos, there must be 15 altos.

The ratio refers to the relative size of one quantity, value, or number compared to another quantity, value, or number.

Ratios are the quotients of two groups of values or quantities.

We can express ratios as fractions, decimals, percentages, or in standard form (:).

The ratio of altos to sopranos = 5:7

The sum of ratios = 12 (5 + 7)

The number of sopranos in the choir = 21

The number of altos that must be present to keep the ratio = 15 (21/7 x 5)

Thus, there must be 15 altos and 21 sopranos to maintain a ratio of 5:7, respectively.

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Answer:

Step-by-step explanation:

The diameter of a circle is twice the radius. Therefore, if the diameter is 8cm, the radius is 8cm/2 = 4cm.

The area of a circle is given by the formula A = πr^2, where π is the mathematical constant pi, and r is the radius of the circle. Substituting the value of r=4cm, we get:

A = π(4cm)^2 = 16π cm^2

Therefore, the area of the circle is 16π cm^2.

The circumference of a circle is given by the formula C = 2πr. Substituting the value of r=4cm, we get:

C = 2π(4cm) = 8π cm

Therefore, the circumference of the circle is 8π cm.

Answer:

8 cm

Step-by-step explanation:

you do circumference with diamer

The required points D and E of the partitions AB and AC are (4, 3) and (8/3, 5) respectively.

The section formula is a formula used in geometry to find the coordinates of a point that lies on a line segment between two given points.

The coordinates of point P can be found using the section formula:

x = (nx₂ + mx₁)/(m+n)

y = (ny₂+ my₁)/(m+n)

Here, x and y are the coordinates of the point P, and m+n is the total length of the line segment between (x₁, y₁) and (x₂, y₂). The ratio of the lengths of the two parts is given by m:n.

Substitute the value of coordinates of endpoints of AB for D,
D = (x,  y) = ((10×1 + 1×2)/3, (3×1+2×3)/3)
D = (4, 3)

Similarly,
E = (8/3, 5)

Thus, the required point D and E of the partitions AB and AC are (4, 3) and (8/3, 5) respectively.

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The pieces of wires that can be cut from this is 16.4

From the question, we have the following parameters that can be used in our computation:

This means that

Number of pieces = Length/Each piece

Substitute the known values in the above equation, so, we have the following representation

Number of pieces = (30 2/3)/(1 7/8)

Evaluate

Number of pieces = 16.4

Hence, the number of pieces is 16.4

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Answer:

both question 5 and question 6 are answered...

The surface area of solid B is calculated as:

1,384 square inches.

Regardless of the type of solids (e.g. Solid A and Solid B), if they are similar to each other, the following proportion would be true:

Surface area of solid A / surface area of solid B = (side length of solid A)² / (side length of solid B)²

Given the following:

Surface area of prism A = 346 in.²

Surface area of prism B = ?

Side length of prism A = 17 in.

Side length of prism B = 34 in.

Plug in the values:

346 /  surface area of solid B = 17²/34²

Cross multiply:

Surface area of solid B = (34² * 346) / 17²

Surface area of solid B = 1,384 square inches.

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The margin of error for the 95% confidence interval used to estimate the population proportion is 0.0598.

The formula for the margin of error for a proportion is:

E = zsqrt(p(1-p)/n) where z is the critical value for the desired confidence level, p is the sample proportion, and n is the sample size.

In this case, the sample size is n = 192, the sample proportion is p = 129/192 = 0.6719 (rounded to four decimal places), and the desired confidence level is 95%, which corresponds to a critical value of z = 1.96.

Substituting these values into the formula, we get:

E = 1.96sqrt(0.6719(1-0.6719)/192) = 0.0598 (rounded to four decimal places)

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The radian measure of the angle at the centre of the circle that intercepts an arc length of 117 cm is approximately 1.918 radians.

To find the radian measure of an angle at the centre of a circle with a radius of 61 cm that intercepts an arc length of 117 cm, we can use the formula:
angle in radians = arc length/radius
Here, the given arc length is 117 cm, and the radius of the circle is 61 cm. Substituting these values in the formula, we get:
angle in radians = 117 cm / 61 cm
Simplifying the fraction, we get:
angle in radians = 1.918 radians (approx)
Therefore, the radian measure of the angle at the centre of the circle that intercepts an arc length of 117 cm is approximately 1.918 radians.
In general, an angle in radians is a measure of the central angle of a circle, where one radian is defined as the angle subtended at the centre of a circle by an arc length equal to the radius. The centre of a circle is the point that is equidistant from all points on the circumference of the circle. The radius of a circle is the distance from the centre to any point on the circumference. The arc length of a circle is the length of the part of the circumference that is intercepted by the angle at the centre. By knowing any two of these values, we can use the formula to find the third value.

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we expect there to be one pair of consecutive zeroes in a random bit string of length 5

To find the expected value of the random function x that counts the number of pairs of consecutive zeroes in a random bit string of length n, we need to consider all possible bit strings of length n and count the number of pairs of consecutive zeroes in each one.

Let's first consider the case of a bit string of length 2. There are four possible bit strings: 00, 01, 10, and 11. Only the first-bit string has a pair of consecutive zeroes, so x(00) = 1, while x(01), x(10), and x(11) are all 0. Therefore, the expected value of x for a bit string of length 2 is:

E(x) = (1/4)*1 + (1/4)*0 + (1/4)*0 + (1/4)*0 = 1/4

Now let's consider a bit string of length 3. There are eight possible bit strings: 000, 001, 010, 011, 100, 101, 110, and 111. The bit strings that have pairs of consecutive zeroes are 000 and 100, so x(000) = 1, x(001), x(010), x(011), x(100) = 1, and x(101), x(110), and x(111) are all 0. Therefore, the expected value of x for a bit string of length 3 is:

E(x) = (1/8)*1 + (1/8)*0 + (1/8)*0 + (1/8)*0 + (1/8)*1 + (1/8)*0 + (1/8)*0 + (1/8)*0 = 2/8 = 1/4

We can continue this process for bit strings of longer lengths, but we can also see a pattern emerging. For any bit string of length n, there are n-1 possible pairs of consecutive bits, and each pair has a probability of 1/4 of being a pair of consecutive zeroes. Therefore, the expected value of x for a random bit string of length n is:
   
E(x) = (n-1)*(1/4) = (n-1)/4

So for example, if we have a random bit string of length 5, the expected value of x would be:

E(x) = (5-1)/4 = 1

This means that we expect there to be one pair of consecutive zeroes in a random bit string of length 5.

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Answer: No.

Step-by-step explanation:

A triangle's angles add up to 180 degrees.

         180° - 100° - 35° = 45°

         180° - 100° - 55° = 25°

These triangles are not similar because their angles are not congruent.

Ricky had 176 cookies initially.

Let Ricky has x number of cookies

Cookies left after he ate 1/8 of his cookies and additional 14 cookies:

x - (1/8x + 14)

Cookies left after he ate 3/10 of the remaining cookies and an additional 24 cookies on Saturday:

x - (1/8x + 14) - 3/10(x - (1/8x + 14)) + 24)

Cookies left after he ate 40 more cookies on Sunday

x - (1/8x + 14) - 3/10(x - (1/8x + 14)) + 24) - 40 ------(1)

Cookies left with him at the end = 34

Therefore, equating equation (1) with 34

(7/10)((7x/8) - 14) - 64 = 34

x = 176

Thus Ricky had 176 cookies intially

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complete question:

Ricky has some cookies. he ate 1/8 of his cookies and an additional 14 cookies on friday. he then ate 3/10 of the remaining cookies and an additional 24 cookies on saturday. he ate 40 cookies on sunday and had 34 cookies left. how many cookies did ricky have at first?

The answer is (B): One of the vectors is in the span of the other vectors, and in this case it is vector w that is in the span of vectors u and v.

To determine if one of the given vectors is in the span of the other vectors, we need to check if the vectors are linearly dependent. If they are, then we can express one of the vectors as a linear combination of the others, and that vector is in the span of the others. If they are not linearly dependent, then none of the vectors are in the span of the others.

To check if the vectors are linearly dependent, we can put them into a matrix and row reduce:

[tex]\left[\begin{array}{ccc}1 & 7 & 8 \\-1 & 3 & -5 \\4 & 8 & 6\end{array}\right] \rightarrow\left[\begin{array}{ccc}1 & 7 & 8 \\0 & 10 & 3 \\0 & 0 & -26\end{array}\right][/tex]

We see that the third row is a scalar multiple of the second row, so the vectors are linearly dependent. Therefore, we can express one of the vectors as a linear combination of the others.

Since the third row is a scalar multiple of the second row, we can express the third vector as:

[tex]w--\frac{26}{10} v--\frac{13}{5}\left[\begin{array}{c}-1 \\3 \\-5\end{array}\right][/tex]

So we can express vector w as a linear combination of u and v, and therefore w is in the span of u and v.

Therefore, the answer is (B): One of the vectors is in the span of the other vectors, and in this case it is vector w that is in the span of vectors u and v.

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