Un grup de ciclistes han de fer una excursió a una casa rural que es troba a 72 quilòmetres del seu poble. El primer dia recorren 2/3 del camí. El segon dia recorren 1/4 del camí i el tercer dia arriben a la casa rural. Calcula els quilòmetres que recorren cada dia.

Answer:

Step-by-step explanation:

(a+2,b)=(4,5)

Since the points are equal we can equate them to find a

Comparing a + 2 to 4

We have

a + 2 = 4

Send 2 to the right side of the equation

a = 4 - 2

We have the final answer as

Hope this helps you

Step-by-step explanation:

Here,

according to the question,

(a+2, b)=(4,5)

since, they are equal, equating with their corresponding elements we get,

(a+2)=4

or, a= 4-2

Therefore, the value of a is 2.

Also you can find value of b in same way,

b=5.

Therefore, the value of a abd b are 2 and 5 respectively.

Hope it helps...

Answer:

The new mixture is 49% peanuts.

Step-by-step explanation:

The first batch of 9 lb of mixed nuts contains 55% peanuts. This means the quantity of peanut is:

9*55/100=4.95 lb

The second batch of 6 lb of mixed nuts contains 40% peanuts. This means the quantity of peanut is:

6*40/100=2.4 lb

The total quantity of peanut in the mix is

4.95 lb + 2.4 lb =7.35 lb

There are 9 lb + 6 lb = 15 lb of mix. Thus, the percent of peanut in the mix is:

7.35 / 15 * 100 = 49%

The new mixture is 49% peanuts.

To answer the given questions you need to find the equation of the line CD.

Equation of a line (y=mx+b)

1. As the bisector CD is perpendicular to AB; if AB has a slope m, CD has a slope -1/m (opposite of the reciprocal)

Use the coordinates of points A and B to find the slope (m) of AB:

Then, the slope of CD is:

2. To find the y-intercept (b); find a point in CD.

As CD is a bisector of AB, it passes through the midpoint of AB; use the next formula to find the midpoint:

The line CD passes through the point (2,4), use it and the slope (-5/2) to find the y-intercept as follows:

3. Write the equation of the line CD: us the slope and y-intercept above

m=-5/2

b=9

4. To find the x-intercept solve x using the equation of the line when y=0:

5. Use the equation of the line and evaluate it for each of the given points to find if the line passes through it:

As you can see above the point that makes a truth math equation is (32,-71)

Answer:

The x-intercept of CD=18/5,0

Point lies  on CD=32,-71

Step-by-step explanation:

The tangent to the circle is AP and the length of side AP = 24

Given data ,

Let the center of the circle be O

And , the length of the line segment OB = 7 units

The length of the line segment BP = 18 units

Now , the length of the line AP = √ ( OP )² - ( OB )²

On simplifying the equation , we get

AP = √ ( 25 )² - ( 7 )²

AP = √ ( 625 - 49 )

AP = √576 units

AP = 24 units

Hence , the length of the tangent AP = 24 units

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The point slope form finds the equation of a straight line that passes through a given point and is inclined to the x-axis. Each point on a line must satisfy the line's equation. Two-variable linear equations symbolize lines. The point slope formula is utilized when we know the line's slope and a point. The next section explains the point slope form and how to calculate its formula.

The equation of a straight line that is inclined at a particular angle to the x-axis and passes at a given point may be found by using the point slope form. This form is used to get the equation of the line. An equation may be said to be the equation of a line if it can be shown to be fulfilled by every point along the line. This indicates that a line is represented by a linear equation that has two variables. Whereas the Point slope formula is only used in situations in which both the slope of the line and a point on the line are known. In the next part, let's get more in-depth knowledge about the point slope form as well as how to derive the formula that is used to express the point slope form.

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Hello BinibiningDel!

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Hope it'll help you!

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Given:

The equation is y = 2x.

The objective is to find which of the table values match the with a given graphs.

The general equation of straight line is,

Here, m represents the slope and b represents the y intercept.

Consider the graph A and find the slope of the equation.

Take two coordinates from the graph as,

The formula to find the slope of the equation is,

Fro mthe graph A, the value of y intercept is 0.

Substitute the obtained values in the equation of straight line.

Thus, the given equation, coordinates of the table A matches with the graph A.

Hence, option (D) is the correct ant

We can find the common ratio with the following formula:

In this case, we have the following:

we can see that the common ratio is r = 2. Then, we have the following formula for the sequence:

Now, to find the 10th term,we make n = 10:

therefore, the 10th term is 2560

The sum of the series can be calculated with the formula:

Step-by-step explanation:

2 fractions (ratios) in the form a/b and c/d are equivalent if it's verified the following relation:

a·d = b·c

Let's see!

1) 4·7 = 3·7     False. They are not equivalent.

2) 9·4 = 18·2    True. They are equivalent.

To show the formation of a sulfide ion from a neutral sulfur atom, we need to add two electrons to the sulfur atom, as sulfide ion has a charge of -2. Therefore, the equation for this process is: S + 2e- → S2-

In this equation, S represents the neutral sulfur atom, while S2- represents the sulfide ion that is formed after the addition of two electrons. This reaction is a reduction reaction, as sulfur is gaining two electrons to form a negatively charged ion.
In summary, the equation S + 2e- → S2- shows the formation of the sulfide ion from a neutral sulfur atom by adding two electrons to it. This equation highlights the importance of electron transfer in chemical reactions and how it can lead to the formation of new compounds.

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Answer:

There is a correlation between amount of time spent playing video games and memorization ability. There may or may not be causation. Further studies would have to be done to determine this.

Step-by-step explanation:

A piano instructor examined student progress. She noticed that when students spend less time playing video games, their memorization ability tends to increase. What can she conclude?

There is a correlation between amount of time spent playing video games and memorization ability. There may or may not be causation. Further studies would have to be done to determine this.

The piano instructor observes changes in the number of video games

played and its effects on the memorization ability.

Reasons:

The aim of the experiment is to check if there is a correlation between the

time students spend playing video games and their memorization ability.

The observation made following a reduction in the time the student spend

playing video games and their memorization ability is that there is no

change in the memorization ability of student following a change in the

time spent playing video games.

The conclusion that can be made is that there is no relationship between

the time the student spends playing video games and their memorization

ability.

The time spent playing video game and memorization are not correlated.

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The linear equation written in slope-intercept form is:

y = 8x + 5

A general linear equation written in slope-intercept form is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

For this case, we know that the values for these are:

slope = 8

y-intercept = 5

Replacing these values in the general formula for a line we will get the equation that we want, which is:

y = 8x + 5

That is the line.

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Answer:

94% so C

Step-by-step explanation:

I did the assignment

Hope it helps

Answer:

95%

Step-by-step explanation:

Edge 2020

(a) The fundamental matrix for the given system of equations is Φ(t) = e^(At).

Let's denote the given coefficient matrix as A:

A = [ -1 -4

      1 -1 ]

The fundamental matrix Φ(t) for the system is given by the matrix exponential of the coefficient matrix A multiplied by t:

Φ(t) = e^(At)

(b) The fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix.

Finding the fundamental matrix φ(t) satisfying φ(0) = I:

To find the fundamental matrix φ(t) satisfying φ(0) = I, we substitute t = 0 into Φ(t):

φ(0) = Φ(0) = e^(A * 0) = e^(0) = I

So, the fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix.

In summary, for the given system:

(a) The fundamental matrix Φ(t) is e^(At).

(b) The fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix, denoted as φ(t) = I.

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The solution to the inequality is x ≤ -1 or x ≥ 0, which can be written in interval notation as (-∞, -1] ∪ [0, ∞).

To solve the inequality |x+3| ≥ -7x+3 ≥ -7, we first need to isolate the absolute value on the left-hand side of the inequality. We can do this by considering two cases: when x+3 is nonnegative, and when x+3 is negative.
Case 1: x+3 ≥ 0
In this case, the absolute value becomes x+3, and we have x+3 ≥ -7x+3 ≥ -7. Simplifying this inequality, we get 8x ≥ 0, or x ≥ 0.
Case 2: x+3 < 0
In this case, the absolute value becomes -(x+3), and we have -(x+3) ≥ -7x+3 ≥ -7. Simplifying this inequality, we get x ≤ -1.

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Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

The total length of craft wire used by Samantha is 10x + 9

What is the scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Let's call the length of the smaller quadrilateral's 6-centimeter side "x".

Then the length of the corresponding side in the larger quadrilateral would be 6+3=9 centimeters, since the scale factor is 3.

To find the total length of craft wire used, we need to add up the lengths of all the sides in both quadrilaterals.

The smaller quadrilateral has four sides, each with a length of x.

The larger quadrilateral also has four sides, but only one of them has a different length (9 cm), while the other three sides are simply 3 times longer than the corresponding sides in the smaller quadrilateral.

So the total length of craft wire used by Samantha is:

4x + 9 + 3x + 3x + 3x

Simplifying this expression, we get:

10x + 9

Hence,  the total length of craft wire used by Samantha is:

10x + 9

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Explanation

Step 1

The middle number is 6 and the last number is -7.

Factoring means we want something like

We need two numbers that...

Add together to get 6

Multiply together to get -7

c

The probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.

Assuming that each die is fair and that the outcome of rolling one die does not affect the outcome of rolling the others, the probability of rolling a 6 with the red die is 1/6, the probability of rolling a 5 with the green die is also 1/6, and the probability of rolling a 4 with the blue die is 1/6.

Since the three events of rolling each die are independent of each other, we can multiply their probabilities to get the probability of all three events happening at the same time, i.e., rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die:

Probability of rolling 6 with the red die = 1/6

Probability of rolling 5 with the green die = 1/6

Probability of rolling 4 with the blue die = 1/6

Probability of rolling 6 (R), 5 (G), 4 (B) at the same time = Probability of rolling R and G and B together = Probability of R × Probability of G × Probability of B

= 1/6 × 1/6 × 1/6 = 1/216

Therefore, the probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.

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You have three dice: one red (R), one green (G), and one blue (B). When all three dice are rolled at the same time, calculate the probability of the following outcome: 6 (R), 5 (G), 4 (B)?

The initial value of the function represented by this graph will be 1. Then the correct option is A.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.

A straight line joins the ordered pair (0, 1) with the ordered pair (6, 7).

Then the value of slope (m) will be

m = [(7 - 1) / (6 - 0)]

m = 1

Then we have

y = x + c

The equation is passing through (0, 1). Then we have

1 = 0 + c

c = 1

Then the equation will be

y = x + 1

Then the initial value of the function represented by this graph will be 1.

Then the correct option is A.

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Answer:

95% confidence interval for the mean time spent on housework per week by all married women.

( 26.66 , 32.94)

Step-by-step explanation:

Step(i):-  

Given random sample size 'n' = 20

Mean of the sample (x⁻ ) = 29.8 hours

Standard deviation of the sample (S) = 6.7

Given Margin of error = 3.14

Step(ii):-

95% confidence interval for the mean is determined by

\((x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} +t_{0.05} \frac{S}{\sqrt{n} })\)

We know  that margin of error is determined by

\(M.E = \frac{t_{0.05}XS.D }{\sqrt{n} } = 3.14\)

Now 95% confidence interval for the mean time spent on housework per week by all married women.

\((29.8 - 3.14 , 29.8+3.14)\)

( 26.66 , 32.94)

Answer:

7.97%

Step-by-step explanation:

Given data

Original Salary= $32,000

Increase= $2,550.00

percent increase= increase/original *100

Percent increase= 2,550.00/32000*100

Percent increase=  0.0796875*100

Percent increase= 7.97%

Hence the increase is  7.97%

The probability that both batteries pass the test is; 11/20

Total Number of Batteries tested = 16

Number of Batteries that fail the Test = 4

Number of batteries selected at Random = 2

Probability that both batteries fail the test = (4/16) * (3/15)

Probability that both batteries passed the test = 12/16 * 11/15 = 11/20

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On solving the provided question, we can say that Considering that the test statistic inside the lower tail the rejection zone, the null hypothesis should be rejected.

A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.

\(H0:p=0.25\) (null hypothesis)

\(H0:p \neq 0.25\) (alternative hypothesis)

Do not reject the null because the test statistic\((-1.2) is >\) \(the critical value (-1.7531)\)

Considering that the test statistic is inside the lower tail of the rejection zone, the null hypothesis should be rejected.

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The distance traveled by the particle from t=0 to t=2 is e^2 - 1 units.

The particle moves in a straight line with velocity v(t) = e^t. To find the distance traveled by the particle from t=0 to t=2, we need to find the displacement of the particle in that time interval.

The displacement of the particle is given by the integral of the velocity function from t=0 to t=2:

∫v(t)dt = ∫e^tdt

Using the fundamental theorem of calculus, we can find the antiderivative of the velocity function and evaluate it at t=2 and t=0:

∫e^tdt = e^t |^2_0 = e^2 - e^0

The displacement of the particle from t=0 to t=2 is e^2 - e^0 = e^2 - 1.

Therefore, the distance traveled by the particle from t=0 to t=2 is e^2 - 1 units.

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Answer:

8

Step-by-step explanation:

========================================================

Explanation:

Let's convert the mixed number 5 & 1/3 to an improper fraction.

The formula to use is

a & b/c = (a*c + b)/c

So,

a & b/c = (a*c + b)/c

5 & 1/3 = (5*3 + 1)/3

5 & 1/3 = 16/3

Imagine you had 16 pieces of candy, and imagine you wanted to divide that up amongst 3 friends. Each friend would get 15/3 = 5 whole pieces. There would be 1 candy left over. The 5 and 1 help then form the 5 & 1/3. So this is one way to visualize how 5 & 1/3 is the same as 16/3.

Another way to see why this works is to note how 16/3 = 5.333 approximately. The '5' before the decimal point is the whole part of the mixed number 5 & 1/3; the decimal portion 0.333 is the approximate value of the fractional part 1/3.

------------------

The total length of fencing needed is 16/3 yards. Each section is 2/3 of a yard long. Since both denominators are "thirds", we can ignore them. An equivalent problem is this: "He needs 16 yards of fencing and each section is 2 yards long"

Based on the new problem without fractions involved, we can see that he'll need 16/2 = 8 sections in total.

You should find that dividing (16/3) over (2/3) will lead to 8 as well. You could say this:

(16/3) divide (2/3) = (16/3)*(3/2) = (16*3)/(3*2) = 48/6 = 8

-------------------

An alternative method:

Let's start with 2/3 of a yard. That doubles to 4/3 which is the same as 1 & 1/3. Think of it as 4/3 = (3+1)/3 = 3/3+1/3 = 1+1/3 = 1 & 1/3.

Next, we'll double 1 & 1/3 to land on 2 & 2/3. You simply multiply each '1' by 2 to end up with those '2's shown.

Now we'll double 2 & 2/3 like so:

2*(2 & 2/3) = 2*(2 + 2/3) = 4 + 4/3 = 4 + (1+1/3) = 5 + 1/3 = 5 & 1/3

The act of doubling exactly three times leads to us ultimately multiplying by 2*2*2 = 8, so he needs 8 sections that are each 2/3 of a yard long.

-------------------

Whichever method you prefer, the final answer is 8 sections.

Answer: C) 0

This is the x intercept because y = 0 here. The full location is (x,y) = (4,0)

Effectively, you draw a vertical line through x = 4 to see where it crosses the function curve. Call this point P. Then from point P, you draw a horizontal line to the y axis to see what the y coordinate of that point is. In this case, P = (4,0).

Step-by-step explanation:

2x+(-8x) +5-5

-5=0. u Wii collect like terms and if u do that that's the answer if am wrong let me know