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Answer:

30

Step-by-step explanation:

just divide 60 by 2

If the distance between Nikki's cousin and Nikki is 60 miles and covered in 2 hours then the speed of the train is 30 miles per hour.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

\(\rm Speed = \dfrac{Distance}{Time}\)

Nikki's cousin lives 60 miles away, so Nikki decided to take the train to visit him. If the trip took 2 hours. Then the speed of the train will be

\(\rm Speed = \dfrac{60}{2}\\\\Speed = 30 \ miles/hour\)

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Answer: 185.7 miles

Step-by-step explanation:

To find the total distance, add the smaller distances together.

47.8 + 72 + 65.9 = 185.7

Answer:

it is not possible

Step-by-step explanation:

6+4=10

10+8=18

so it is not possible

The amount of time till Rowan and Kennedy would have read the same number of pages is C 6 mins 40 secs.

Assume that the time they would take to read the same number of pages is x.

Rowan's reading expression is then:

= 20 + 1.5x

Kennedy is:

= 25 + 3/4x

Equate them:

20 + 1.5x = 25 + 3/4x

1.5x - 3/4 = 25 - 20

0.75x = 5

x = 5/0.75

x = 6.67 minutes

= 6 minutes 40 secs

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The Poisson distribution is a probability distribution that describes the number of independent occurrences of an event in a fixed interval of time or space.

In this case, the random variable is the number of occurrences during an interval. Therefore, the statement "the random variable is the number of occurrences during an interval" applies to the Poisson distribution. Another statement that applies to the Poisson distribution is "the probability of the event is proportional to the interval size". This means that the probability of observing k events in a fixed interval is proportional to the length of the interval. However, the statement "the probability of an individual event occurring is quite large" does not describe the Poisson distribution. In fact, the Poisson distribution assumes that the probability of an individual event occurring is small, but the number of events is large. Finally, the statement "the intervals do not overlap and are independent" is not a defining characteristic of the Poisson distribution, although it is often assumed in practical applications. In summary, the Poisson distribution is a probability distribution that models the number of independent occurrences of an event in a fixed interval. The probability of the event is proportional to the interval size, and the random variable is the number of occurrences during an interval.

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Answer:

B. 8

Step-by-step explanation:

By evaluate, they mean substitute in the values and solve.

x + 3y - n

= 10 + 3(2) - n

= 10 + 6 - 8

= 8

Please lmk if you have questions.

Answer:

It is 8!

Proof:

I took the activity.

Answer:

56 baseball's

Step-by-step explanation:

The number of baseballs were pitched to Chad in 8 minutes is 56.

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

Given that, the pitching machines pitch baseballs at a rate of 35 pitches in 5 minutes.

Number of pitches hit in 1 minute = 35/5

= 7

Chad practiced hitting for 8 minutes.

So, the number of baseballs were pitched = 7×8

= 56

Hence, the number of baseballs were pitched to Chad in 8 minutes is 56.

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The given conditions describe an ellipse with its center at (-1, 2), a vertex at (-1, 0), and a focus at (-1, 3).

The standard form equation for an ellipse with center (h, k) is:

\(\(\frac{{(x - h)^2}}{{a^2}} + \frac{{(y - k)^2}}{{b^2}} = 1\)\)

where "a" is the semi-major axis and "b" is the semi-minor axis.

Since the center is given as (-1, 2), the equation becomes:

\(\(\frac{{(x + 1)^2}}{{a^2}} + \frac{{(y - 2)^2}}{{b^2}} = 1\)\)

To find the values of "a" and "b", we consider the distance between the center and the vertex and the distance between the center and the focus.

The distance between the center (-1, 2) and the vertex (-1, 0) is equal to the semi-major axis "a". Therefore, a = 2 - 0 = 2.

The distance between the center (-1, 2) and the focus (-1, 3) is equal to "c", where "c" is the distance from the center to the focus. Therefore, c = 3 - 2 = 1.

To find the value of "b", we can use the relationship \(\(b^2 = a^2 - c^2\):\)

\(\(b^2 = 2^2 - 1^2 = 4 - 1 = 3\)\)

Thus, the equation of the ellipse is:

\(\(\frac{{(x + 1)^2}}{{2^2}} + \frac{{(y - 2)^2}}{{3}} = 1\)\)

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Answer:

unlikely

Step-by-step explanation:

If there 10 numbers, each number has a 10% chance of being chosen, and there are 3 generated number.

1/10 x 1/10 x 1/10 = 1/1000

Therefore the percent of this happening is 0.001%

That's very low.

That's why it's unlikely.

The length of each side of the square is (3x-2) units

The dimensions of the rectangle are (5x + 4y) and (5x -4y) units

From the question, we are to factor out the given expression for the area of the square

The expression is

9x² − 12x + 4

Factoring

9x² − 12x + 4

9x² −6x -6x + 4

3x(3x -2) -2(3x-2)

(3x -2)(3x -2)

Hence, the length of each side of the square is (3x-2) units

Part B:

The given expression is

25x² − 16y²

Factoring

25x² − 16y²

By difference of two squares, we get

(5x + 4y)(5x -4y)

Hence, the dimensions of the rectangle are (5x + 4y) and (5x -4y) units

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Answer:

2

Step-by-step explanation:

12:1,2,3,4,6,12

18:1,2,3,6,9,18

32:1,2,4,8,16,32

h.c.f = 2

The approximate value of ㏒(b) to the nearest hundredth is 1.23.

The other method to write exponents in mathematics is using logarithms. A number's base-based logarithm is equal to some other number. A logarithm performs exponentiation's exact opposite function. 

In Logarithms, ㏒ₐ(b) = ㏒(b)/ ㏒(a)

Given that

The two expressions below have the same value when rounded to the nearest hundredth

=> ㏒₅ (b) = ㏒₉ (48)  

As we know  ㏒ₐ(b) = ㏒(b)/ ㏒(a)

=> ㏒₅ (b) = ㏒(b)/㏒(5)

=> ㏒(b)/㏒(5) = ㏒₉ (48)  

=> ㏒(b) = ㏒₉ (48) ㏒(5)

=> ㏒(b) =  (1.7618)(0.6989)  

=> ㏒(b) = 1.23132202  

=> ㏒(b) = 1.23  

Therefore,

The approximate value of ㏒(b) to the nearest hundredth is 1.23.

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Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

I do not know

Step-by-step explanation:

Answer:

pretty sure it's b but I can't see that well can you please take a clearer picture of your question?

The area of the triangle is 3.535533, whose vertices are  (0,0,0), (1,3,−1), and (2,1,1) .

Explanation: -

To find the area of the triangle with vertices (0,0,0), (1,3,-1), and (2,1,1), you can use the formula for the area of a triangle in 3D space:

Area = 0.5 * ||AB x AC||

Here, AB and AC are the vectors representing the sides of the triangle, and "x" denotes the cross product.

STEP 1:- Find the vectors AB and AC:
AB = B - A = (1,3,-1) - (0,0,0)

     = (1,3,-1)
AC = C - A = (2,1,1) - (0,0,0)

     = (2,1,1)

STEP 2: - Compute the cross product AB x AC:
AB x AC = (3 * 1 - (-1) * 1, -(1 * 1 -(- 1 )* 2), 1 * 1 - 3 * 2)
AB x AC = (3 + 1, 3, 1 - 6)

              = (4, 2, -5)

STEP 3: - Compute the magnitude of the cross product ||AB x AC||:
||AB x AC|| = √(4² + (-3)² + (-5)²)

                  = √(16 + 9 + 25)

                  = √50

                  =7.071060

STEP 4: - Calculate the area of the triangle:
Area = 0.5 * ||AB x AC|| = 0.5 * (7.071060)

Therefore, the area of the triangle is 3.535533.

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It must change systematically when the independent variable is changed for an extraneous variable to become a confounding variable that is option D.

This is because a confounding variable is a variable that is related to both the independent and dependent variables and affects the outcome of the study, making it difficult to determine the true effect of the independent variable. In order for a variable to be considered a confounding variable, it must change systematically with changes in the independent variable.

A confounding variable is a variable that affects the outcome of a study but is not the variable of interest. This can create ambiguity in the results and make it difficult to determine if the observed effect is due to the independent variable or the confounding variable. In order for a variable to be considered a confounding variable, it must change systematically with changes in the independent variable.

This means that as the independent variable changes, the confounding variable also changes in a predictable way. Without controlling for this variable, the study may not accurately reflect the true effect of the independent variable. Therefore, it is important to identify and control for confounding variables in a study to ensure that the results are valid and reliable.

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The percentage increase in the price of petrol when increased from 12,58 per litre to 13,28 per litre is 5.56%

The change in the price of the petrol is given as

Increased from 12,58 per litre to 13,28 per litre.

This means that the change in the price is

Change = 13.28 - 12.58

Evaluate the difference

Change = 0.7

The percentage increase in the price of petrol is then calculated as

Percentage = 0.7/12.58 * 100%

Evaluate the prodcuts

Percentage = 5.56%

Hence, the change is 5.56%

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The tree's diameter is increased by 1.4/π inches and the increase in the tree's cross sectional area is 32.2 square inches.

According to the question,

We have the following information:

The diameter of a tree was 23 inches. During the following year, the circumference increased 2.8 inches.

Now, let's take the radius of the tree to be r inches.

Following formula is used to find the circumference of the circle = 2πr where r is the radius

Using differentiation, we have:

dC = 2πdr

dC = 2.8 inches

2πdr = 2.8

dr = 2.8/2π

dr = 1.4/π inches

Now, increase in the cross sectional area:

Area = \(\pi r^{2}\)

Using differentiation:

dA = 2πrdr

Radius = diameter/2

Radius = 23/2 inches

Radius = 11.5 inches

dA = 2π*11.5*1.4/π

dA = 2*11.5*1.4

dA = 32.2 square inches

Hence, the tree's diameter is increased by 1.4/π inches and the increase in the tree's cross sectional area is 32.2 square inches.

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In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

OR 1464 - 1426 = 38 seats

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The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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Answer:

7 tonnes

Step-by-step explanation:

the vehicle is x

the load is 5/2 tonnes ( i simplify this)

the load is 5/9 the vehicle

we got the equation: 5/9x = 5/2

therefore x = 4.5 so the total mass of the vehicle is 4.5 + 5/2 = 7

The value of sin D rounded to the nearest hundredth, if necessary is

What is pythagorean theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

So in this problem, we have to find the hypotenuse first, since sine is opposite over hypotenuse.

We can do this using the pythagorean theorem (you can search it if you don't know). Or, we can just remember this as one of our pythagorean triplets (9,40,41). The last side will be 41.

We have to find the value of sin(D)

opposite/hypotenuse = 9/41 = 0.2195 which is about 0.22.

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The square root function involves the square root symbol √ which is  mostly read as "square root of", the rule says that the square root of a number 'x' is a number 'y' such that y² = x.

We know that the square root of a number can be either positive or negative, but while defining the square root function, we restrict its range to be the set of all positive real numbers and hence making all square roots possible to be positive.

If the range for the square root of a number is set to be positive as well as negative it wont be a function that is why there is a restriction to the range of this set allowing only positive real numbers.

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Answer:

24

Step-by-step explanation:

3x4x2=24

When finding the answer to this problem, you times all of the options by each other.

The vertex and range of y = |x + 3| + 2 are (-3, 2) and 2 ≤ y < ∞

The function is given as

y = |x + 3| + 2

The above function is an absolute value function.

An absolute value function is represented as

y = a|x - h| + k

Where vertex is represented as

Vertex = (h, k)

This means that the vertex of y = |x + 3| + 2 is

Vertex = (-3, 2)

And, we have

a = 1

When the variable a is positive, then the vertex is a minimum

This means that the range is 2 ≤ y < ∞

Hence, the vertex and range of y = |x + 3| + 2 are (-3, 2) and 2 ≤ y < ∞

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10 is the answer for the blank

Susan has more candy in weight compared to Isabel.

To compare the candy weights between Susan and Isabel, we need to ensure that both weights are in the same unit of measurement. Let's convert Isabel's candy weight to ounces for a fair comparison.

Given:

Susan: 4 bags x 6 ounces/bag = 24 ounces

Isabel: 1 bag x 16 ounces/pound = 16 ounces

Now that both weights are in ounces, we can see that Susan has 24 ounces of candy, while Isabel has 16 ounces of candy. As a result, Susan is heavier on the candy scale than Isabel.

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