3 Dave can drive from Abdet to Bentall by two routes. The old route goes in roughly a straight line while the new faster route is 26% longer. Dave's average speed on the new faster route is 40% higher than his average speed on the old route. (a) By what percentage is Dave's journey time reduced by taking the new route compared to the old? [2]

Answer:

300

Step-by-step explanation:

25 choose 2 (exactly how it sounds like)

= (25*24)/(2*1)=600/2=300

Answer:

8h=p

Step-by-step explanation:

Answer:

8h = p

or

p = 8h (this is how i wrote it and it was right)

Step-by-step explanation:

The value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

According to the given question.

We have an equation

2x + 2/y = 4w + 2

Since, we have to find the value of x for the given equation

2x + 2/y = 4w + 2

Thereofore,

2x + 2/y = 4w + 2

⇒ 2(x + 1)/y = 2(2w + 1)    (taking 2 common from both the sides)

⇒ (x + 1)/y = 2w + 1

⇒ (x + 1) = y(2w + 1)         (multiplying both the sides by y)

⇒ x + 1 = 2yw + y

⇒ x = 2yw + y - 1         ( subtracting 1 both the sides)

Hence, the value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

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The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, \(P(X = k) = (1 - p)^{k-1}p\)

For  k = 2,

\(P(X = 2) = (1 - 0.25)^{2-1}\times 0.25\)

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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Answer:

x = 4

Step-by-step explanation:

In this equation, x is being cubed to equal 64. When x is being cubed, it means that x is multiplied by itself 3 times to get 64. Thus, we have to find which number to the power of three = 64.

Therefore, x = 4.

Equation: 3√64 = x

In case you needed it

This so happens to be a perfect cube

Cube = A number raised to the power of 3

1 x 1 x 1 = 1

2 x 2 x 2 = 8

3 x 3 x 3 = 27

4 x 4 x 4 = 64

So therefore, x = 4

Hope this helped you!

Answer: 7w - 28

7*w - 7*4

7w - 28

Brainliest pwease if the answer is correct! <3

Answer:

1 intercept and 2 intercepts

Step-by-step explanation:

there is only one x-intercept for the first graph, which is (0,0)

for the second equation there are two: (-sqrt7,0) and (sqrt7, 0)

the transormation that occured from f(x) to its image g(x) is g(x) = -7 + f(x)

Answer:

the answer is 9

Step-by-step explanation:

x=3 so its 6+3

Answer:

9

Step-by-step explanation:

Bru simple math

The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

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

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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The anti-derivative in other words integration of the inverse of sine function i.e 1/sinx is

x sin⁻¹x + √(1 - x²) + C.

Integration of a function is the inverse process of differentiation. The integral is just the inverse derivative. The inverse integral of sin is written as

x sin⁻¹x + √(1 - x²) + C.

where ∫ --> the sign of integration, dx --> that the integration of sine inverse with respect to x, C --> the constant of integration.

Integral of Sin Reverse proof by integration by parts :

f(x) = sin⁻¹x, g(x) = 1

d(sin⁻¹x)/dx = 1/√(1 - x²)

Using these equations and facts,

∫sin⁻¹x dx = ∫sin⁻¹x.1 dx

= sin⁻¹x ∫1dx - ∫[d(sin⁻¹x)/dx × ∫1 dx] dx

= x sin⁻¹x - ∫[1/√(1 - x²) × x] dx

= x sin⁻¹x - ∫x/√(1 - x²) dx

= x sin⁻¹x + (1/2) ∫-2x/√(1 - x²) dx [multiplication and division by 2]

= x sin⁻¹x + (1/2) ∫(-2x)(1 - x²)-1/2 dx

= x sin⁻¹x + (1/2) [(1 - x²)-1/2 + 1/ (-1/2 + 1)] + C {using the formula ∫[f(x)]nf'(x)dx=[f(x)]n +1/(n + 1) +C}

= x sin⁻¹x + (1/2) [(1 - x²)1/2/ (1/2)] + C

= x sin⁻¹x + (1 - x²)1/2 + C

= x sin⁻¹x + √(1 - x²) + C

Therefore the inverse derivative of 1/sinc is x sin⁻¹x + √(1 - x²) + C.

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Answer:

19/20

Step-by-step explanation:

380÷ 20= 19

400÷20= 20

The probability of drawing 2 yellow markers and 2 red markers is approximately 0.2697.

To find the probability of drawing 2 yellow markers and 2 red markers, we need to calculate the total number of ways to draw 4 markers from the bag, as well as the number of ways to draw 2 yellow and 2 red markers.

The total number of ways to draw 4 markers from the bag is:

¹⁴C₄ = (14!)/(4!*(14-4)!) = 1001

This is because there are 14 markers in total, and we are choosing 4 of them.

To find the number of ways to draw 2 yellow and 2 red markers, we can use the combination formula again. The number of ways to choose 2 yellow markers from 4 yellow markers is:

⁴C₂ = (4!)/(2!*(4-2)!) = 6

Similarly, the number of ways to choose 2 red markers from 10 red markers is:

¹⁰C₂ = (10!)/(2!*(10-2)!) = 45

Therefore, the number of ways to draw 2 yellow and 2 red markers is:

6 * 45 = 270

Now we can find the probability of drawing 2 yellow and 2 red markers by dividing the number of ways to draw 2 yellow and 2 red markers by the total number of ways to draw 4 markers:

P(2 yellow and 2 red) = 270/1001 = 0.2697 (rounded to four decimal places)

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The probability of drawing 2 yellow marker and 2 red markers 15/1078

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty an event will occur is 1 which is equivalent to 100%.

Probability = sample space / total outcome

for the first draw ;

probability of picking yellow = 2/14 = 1/7

second draw;

probability of picking yellow = 1/13

third draw;

probability of picking red = 10/12 = 5/6

fourth draw;

probability of picking red = 9/11

Probability of picking two yellow = 2/14 × 1/7 = 2/98 = 1/49

probability of picking two reds = 5/6 × 9/11 = 45/66 = 15/22

probability of picking 2 yellow and 2 red = 1/49 × 15/22 = 15/1078

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The width of the pool is approximately 0.67 feet or 8 inches. To find the width of the pool, we can use the given information about the volume of water it holds and the relationship between volume and dimensions.

First, we calculate the volume of the pool using the formula: Volume = length × width × height. Since the length is given as 5 feet and the height is 6 feet, we can substitute these values into the formula: Volume = 5 × width × 6.

Next, we convert the volume from gallons to cubic feet by dividing by the conversion factor of 7.5 gallons per cubic foot: (150 gallons) / (7.5 gallons per cubic foot) = 20 cubic feet.

Now we can set up the equation: 20 = 5 × width × 6.

To solve for the width, we divide both sides of the equation by (5 × 6): width = 20 / (5 × 6).

Evaluating the expression, we find that the width of the pool is approximately 0.67 feet or 8 inches.

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Answer:

Let's define the variable "d" to represent the number of days after Student X starts studying when both students will have studied the same number of hours.

Student X will study for d days, and since they study 2 hours each day, they will have studied a total of:

2d hours

Student Y will start studying 4 days after Student X, so by the time Student Y starts studying, Student X will have already studied for d + 4 days.

Student Y will study for d days, and since they study 3 hours each day, they will have studied a total of:

3d hours

To find the number of days when both students will have studied the same number of hours, we can set the two expressions for total hours equal to each other and solve for d:

2d = 3d - 12

Adding 12 to both sides:

2d + 12 = 3d

Subtracting 2d from both sides:

12 = d

Therefore, both students will have studied the same number of hours 12 days after Student X starts studying.

Step-by-step explanation:

Answer: Let's define the variable t as the number of days after Student X starts studying.

Then the equation that represents the total number of hours each student has studied in terms of t is:

For Student X: Hx = 2t

For Student Y: Hy = 3(t-4)

Note that we subtract 4 from t for Student Y since they start studying 4 days after Student X.

To find the number of days after Student X starts studying when both students will have studied the same number of hours, we can set the two equations equal to each other and solve for t:

2t = 3(t-4)

2t = 3t - 12

t = 12

Therefore, it will take 12 days after Student X starts studying for both students to have studied the same number of hours.

Step-by-step explanation:

If a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1

The mean of the normal distribution = 4

Standard deviation of the normal distribution = 1.5

The value of x = 5.5

The z-score of the normal distribution = The mean of the normal distribution / Standard deviation of the normal distribution

Substitute the values in the equation

The z-score of the normal distribution  = (5.5 - 4) / 1.5

Substract the terms

= 1.5 / 1.5

= 1

Hence, if a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1

The complete question is:

suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x = 5.5

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Answer:

5 × \(10^{-3}\)

Step-by-step explanation:

A number in standard form is

a × \(10^{n}\)

where 1 ≤ a > 10 and n is an integer

Given

0.005 ← express as a number between 1 and 10

= 5 ×\(10^{n}\)

n is the value required to move the decimal point back to its original position

A move to the right is +

A move to the left is -

Here we require to move the decimal point back 3 places to the left

Thus

0.005 = 5 × \(10^{-3}\)

\(\\ \sf\Rrightarrow 0.005\)

\(\\ \sf\Rrightarrow 0.05\times 10^{-1}\)

\(\\ \sf\Rrightarrow 0.5\times 10^{-2}\)

\(\\ \sf\Rrightarrow 5\times 10^{-3}\)

Yes, it is possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity].

Explanation:

We can approximate f(x) as a Fourier series, as follows:

\($$f(x) = \sum_{n=0}^{\infty}a_n\cos\left(\frac{n\pi x}{L}\right)+\sum_{n=1}^{\infty}b_n\sin\left(\frac{n\pi x}{L}\right)$$\)

If f(x) is an odd function, the cosine terms are gone, and if f(x) is an even function, the sine terms are gone.

We can create an approximation for f(x) using only the first n terms of the Fourier series, as follows:

\($$f_n(x) = a_0 + \sum_{n=1}^{n}\left[a_n\cos\left(\frac{n\pi x}{L}\right)+b_n\sin\left(\frac{n\pi x}{L}\right)\right]$$\)

For any continuous function f(x), the Fourier series converges uniformly to f(x) on any finite interval, as given by the Weierstrass approximation theorem.

However, if f(x) is discontinuous, the Fourier series approximation does not converge uniformly.

Instead, it converges in the mean sense or the L2 sense. The L2 norm is defined as follows:

\($$\|f\|^2 = \int_{-L}^{L} |f(x)|^2 dx$$\)

Hence, it is possible for a plot of a partial expansion of f(x) to share ink with the plot of f(x) all the way from -[infinity] to + [infinity].

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Answer:

A.

Step-by-step explanation:

The y-intercept starts at -5.

Using the rise over run method, we count 6 up and 2 to the right.

6/2 = 3.

y = 3x - 5

Answer:

30

Step-by-step explanation:

The arc length of the sector is 10π inches, and the area of the sector is 60π square inches.

What is the arc length and area of the sector of a circle?

Arc length = \( \frac{ \theta}{ {360}^{o} } \times 2\pi \: r\)

Area of sector = \( \frac{ \theta}{ {360}^{o} } \times \pi \: {r}^{2} \)

Where r is the radius of the circle, angle is the central angle in degrees, and π is the mathematical constant pi (approximately equal to 3.14159).

Given that the angle is 150° and the radius is 12 inches, we can substitute these values into the formulas to get:

Arc length

\(= \frac{150}{360} \times 2π(12) \\ = \frac{5}{12} \times 2π(12) \\ = 10π \: inches\)

Area of sector

\(= \frac{150}{360} \times π(12)^2 \\ = \frac{5}{12} \times π(144) \\ = 60π \: square \: inches\)

Therefore, the arc length of the sector is 10π inches, and the area of the sector is 60π square inches.

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Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

Answer:

-29a - 6b + 59c

Step-by-step explanation:

First, keep in mind that only like terms can be combined.

5a + 7b - 12a + 6c - 13b - 22a + 53c

You can rearrange them to make it easier:

5a - 12a - 22a + 7b - 13b + 6c + 53c

-29a - 6b + 59c

From the data given, the two-way frequency table below shows the categories of the data from size to flavor and frequency in which they occur.

One method for displaying frequencies for two distinct categories gathered from a same group of individuals is a two-way table. The rows indicate one category, while the columns represent another.

A two-way frequency table that will represent the given data is;

Size                                   Flavor                                     Frequency

Large                           Grape                                         40

Large                           Cherry                                       55

Large                           Watermelon                               30

Small                           Grape                                       17

Small                           Cherry                                       35

Small                           Watermelon                               23

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Answer:

\(a=4; b=2\)

Step-by-step explanation:

1. The unmarked angle is 30° (since unmarked, +60°, a right angle will add to 180°)

2. Mirror the triangle over the known side. The triangle you get is an equilateral triangle. This allows us to say 2b = a

At this point, pythagorean theorem:

\(a^2 = b^2+(2\sqrt3)^2 \rightarrow a^2= b^2+12 \rightarrow\\(2b)^2=b^2+12 \rightarrow 4b^2-b^2 = 12\rightarrow 3b^2=12\\b^2=4 \rightarrow b=2 \implies a=4\)

Only the positive solution is taken since it's a length of a segment.

Same result can be obtained with trigonometry if you are allowed to use higher grade math. In particular

\(tan 60\° = \frac{2\sqrt3}b \rightarrow b= \frac{2\sqrt3}{\sqrt3} = 2\\sin 60\° = \frac{2\sqrt3}a\rightarrow a = \frac{2\sqrt3}{\frac{\sqrt3}{2}} = 4\)

Answer:

One denominator you could use to add the two fractions 3/1 and 8/12 is 12.

Step-by-step explanation:

When adding the fractions 3/1 and 8/12, the first step is to multiply both the numerator and denominator by the same number until you end up with common denominators. Here, the best thing to do is multiply both 3 and 1 by 12 which ends in 36/12; from that point on, you just do the simple math of 36/12 + 8/12.

There are 13,992 integers between 1 and 1,000,000 with a sum of digits equal to 15.

To find the number of integers between 1 and 1,000,000 with a sum of digits equal to 15, we can use a combinatorial approach.

We need to distribute the sum of 15 among the digits of the number. We can think of this as placing 15 indistinguishable balls into 6 distinct boxes (corresponding to the digits).

Using the stars and bars method, the number of ways to distribute the sum of 15 among 6 boxes is given by the combination formula:

C(n + r - 1, r - 1)

where n is the sum (15) and r is the number of boxes (6).

Plugging in the values, we have:

C(15 + 6 - 1, 6 - 1) = C(20, 5)

Calculating this combination, we find:

C(20, 5) = 13,992

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Answer:

its 3 and 4

Step-by-step explanation:

Answer:

2 and 3

Step-by-step explanation:

Answer:

a= 6 b=4

Step-by-step explanation:

-2+6=4

3+4+7

When written in factored form, 4w² -11w-3 is equivalent to (4w+1)(w−3).

When an expression is written as a result of the multiplication of some terms, then that multiplication form is called the factored form of that expression.

Example:   6 = 3 x 2 is a factored way of writing 6.

Given expression as

4w² -11w-3

4w²- 12 w− 1w − 3

(4w+1)(w−3)

Thus, the factored form of 4w² -11w-3 is (4w+1)(w−3).

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