Theo has one piece of train track that is 74 millimeters long and a second piece of train track that is 97 millimeters long.

How many meters of track does Theo have in all

Thus, the total length of lap covered to get the seven different obstacles is found as: 52 units.

the Pythagorean theorem is used to calculate the distance between two locations using the distance formula. The Pythagorean theorem can be rewritten as d = √((x2 - x1)²+(y2 - y1)²)  to calculate the separation between any two locations.

Given data:

Points on  y-axis and an x-axis are given,

M(-3,5), F(8,5), G(8,2), H(3,2), I(3,-5), J(-8,-5), K(-8,-2), and L(-3,-2).

Starting and ending point is F.

Points lies between the starting and ending are-

F ,G, H, I, J, K, L, M, F

Total length = sum of all length

d = √((x2 - x1)²+(y2 - y1)²)

FG =  √((8 - 8)²+(2 - 5)²)

FG =  √9

FG =  3

GH =  √((8 - 3)²+(2 - 2)²)

GH  =  √25

GH =  5

HI =  √((3 - 3)²+(2 + 5)²)

HI  =  √49

HI  =  7

IJ =  √((3 + 8)²+(-5 + 5)²)

IJ =  √121

IJ =  11

JK =  √((-8 + 8)²+(-2 - 5)²)

JK =  √9

JK =  3

KL =  √((-8 + 3)²+(-2 + 2)²)

KL =  √25

KL =  5

LM =  √((-3 + 3)²+(-2 - 5)²)

LM =  √49

LM =  7

MF =  √((8 + 3)²+(+5 - 5)²)

MF =  √121

MF =  11

Total length = 3 + 5 + 7 + 11 + 3 + 5 + 7 + 11

Total length = 52 units

Thus, the total length of the lap covered to get the seven different obstacles is found as: 52 units.

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There are 11550 different ways that the line of marbles could be formed in this scenario.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

As a result, there are (4 + 3 + 4) spots on the line, which equals 11 spots for the 11 marbles.

Given that identical-colored marbles cannot be distinguished.

This means that, for instance, if there are four red marbles in the first, second, third, and fourth positions, moving the four red marbles around these positions won't result in a different arrangement.

Solving by combination,

The total number of ways that four spots can be assigned to red marbles is thus = ¹¹C₄ = 330 ways

The number of ways three yellow marbles can be placed in each allocation of red marbles is equal to ⁷C₃ = 35 ways

The number of ways four slots can be allocated to green marbles for each allocation of red and yellow marbles is equal to ⁴C₄ way = 1

As a result, there are (330 × 35 × 1) = 11550 different ways that the line of marbles could be formed in this scenario.

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The hypothesis test that tests H0: mu ≤ 45 versus H1: mu > 45 is a one-tailed or one-sided test because the alternative hypothesis specifies a particular direction of difference between the population parameter and the hypothesized value.

In hypothesis testing, we use statistical evidence to either support or reject a null hypothesis. The null hypothesis (H0) is the default assumption, while the alternative hypothesis (H1) is the opposite of the null hypothesis.

A one-tailed test is used when the alternative hypothesis is directional, meaning it specifies a particular direction of difference between the population parameter and the hypothesized value.

In this case, the alternative hypothesis is mu > 45, which is a directional hypothesis, indicating that we are interested in testing whether the population mean is greater than 45.

Therefore, this test is a one-tailed or one-sided test, which means that the critical region lies entirely in one tail of the sampling distribution.

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(a) The cost of 1 kg of turnips is £71.95, and

(b) The cost of 1 kg of mushrooms is £89.50.

To solve this problem, let's assign variables to the unknowns.

Let the cost of 1 kg of mushrooms be 'm' and the cost of 1 kg of turnips be 't'.

According to the given information:

Equation 1: 2m + 2.5t = 8.55

Equation 2: 3m + 4t = 13.10

We can solve these equations simultaneously to find the values of 'm' and 't'.

To eliminate the decimals, let's multiply both sides of Equation 1 by 10 and Equation 2 by 20:

20m + 25t = 85.50

60m + 80t = 262.00

Now, let's multiply Equation 1 by 12 and subtract Equation 2 multiplied by 5:

240m + 300t - (60m + 80t) = 1026.00 - 1310.00

180m + 220t = -284.00

We have a new equation:

180m + 220t = -284.00 ---(3)

Next, let's multiply Equation 1 by 18 and subtract Equation 2 multiplied by 4:

36m + 45t - (60m + 80t) = 154.35 - 524.00

-24m - 35t = -369.65

We have another new equation:

-24m - 35t = -369.65 ---(4)

Now, we have a system of linear equations with two variables. Let's solve this system by eliminating one variable.

Multiply Equation 3 by 35 and Equation 4 by 220:

6300m + 7700t = -9940.00 ---(5)

-5280m - 7700t = -81323.00 ---(6)

Adding Equations 5 and 6, we eliminate 't':

1020m = -91263.00

m = -91263.00/1020

m = -89.50

Substituting the value of 'm' back into Equation 3:

180(-89.50) + 220t = -284.00

-16110 + 220t = -284.00

220t = -284.00 + 16110

220t = 15826.00

t = 15826.00/220

t = 71.95.

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Given:

a.) He has 12 1/2 cups of milk.

b.) The chef has 3 1/2 more cups of broth than milk.

Step 1: Since it is said that the chef has 3 1/2 more cups of broth than milk, and he has 12 1/2 cups of milk, we will be adding 3 1/2 and 12 1/2 to get the actual number of cups of broth.

We get,

In adding mixed numbers, we add separately the whole numbers and fractions and add them together later on.

Therefore, the chef has 16 cups of broth.

Step 2: Let's now determine the remaining cups of broth after using 14 1/2 cups to make soup. We will be subtracting the current 16 cups of broth by 14 1/2 cups for the soup.

We get,

Let's first convert them into similar fractions before subtracting.

Let's now proceed in subtracting them,

Therefore, the chef will have a remaining 1 1/2 cups of broths after using 14 1/2 cups for the soup.

The point that is 5 units to the left of (-2,-4) is (-7,-4).


To find the x-coordinate of the new point, we subtract 5 from the x-coordinate of (-2,-4), which is -2. This gives us -2 - 5 = -7. The y-coordinate remains the same at -4. Therefore, the coordinates of the new point are (-7,-4).

To find the coordinates of the point that is 5 units to the left of (-2,-4), we need to subtract 5 from the x-coordinate. In this case, the x-coordinate is -2. So, if we subtract 5 from -2, we get -7.

The y-coordinate remains the same at -4. Therefore, the coordinates of the point that is 5 units to the left of (-2,-4) are (-7,-4). When we move to the left on a coordinate plane, the x-coordinate decreases while the y-coordinate remains the same.

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To determine the probability that Paul will not eat the pizza Chef Carl has made, we need to calculate the probability of Chef Carl selecting mushrooms as one of the toppings.

First, let's calculate the total number of possible combinations of two different toppings that Chef Carl can choose from the given options. Since order does not matter, we can use the combination formula:

C(n, r) = n! / (r! * (n-r)!),

where n is the total number of options and r is the number of choices. In this case, n = 5 (the number of toppings) and r = 2 (the number of choices).

C(5, 2) = 5! / (2! * (5-2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10.

So there are a total of 10 possible combinations of two different toppings that Chef Carl can choose.

Next, we need to calculate the number of combinations that include mushrooms. Since Paul will not eat pizza with mushrooms, we want to exclude this option.

To choose one topping from the remaining four (excluding mushrooms), there are C(4, 1) = 4 possible choices.

Therefore, the probability that Chef Carl selects a combination with mushrooms is 4/10.

Finally, the probability that Paul will not eat the pizza Chef Carl has made is the complement of this probability, which is 1 - 4/10 = 6/10 = 3/5.

So, the probability that Paul will not eat the pizza is 3/5.

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Answer:

B

Step-by-step explanation:

B. 0.0000004 metres

4÷10000000

The set of equations that corresponds to the specified function are

y = 5 - x and 5 - x = 9x².

What is linear equation in two variables?

If an equation is expressed as ax + by + c=0, where a, b, and c are all real integers and a and b, the coefficients of x and y, respectively, are not equal to zero, then it is said to be a linear equation in two variables.

The given equation is :

\(y=9x^{2}\) equation 1.

\(x+y=5\) equation 2.

From equation 2.

\(x+y=5\\y=5-x\)

substituting into 1 equation.

\(5-x=9x^{2}\)

The system of equations that is equivalent to the provided function is shown by the resulting equation, which is y = 5 - x and \(5-x=9x^{2}\)

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98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)

mean x = 16

standard deviation σ = 2.4

sample size n = 65

z score for 98% = 2.576

Interval = x±z*s/

= 16±2.576*2.4/

= 16±2.576*0.39629

= 16±1.0208

Interval = (21.0208,18.9792)

Therefore 98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).

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Step-by-step explanation:

So I didnt really understand the beginning but what I did was $325x24=$7800 payed in 24 months if we are adding the $4500 it would be

$7800+$4500=$12300

Step-by-step explanation:

So I didnt really understand the beginning but what I did was $325x24=$7800 payed in 24 months if we are adding the $4500 it would be

$7800+$4500=$12300

Answer:

Yes

Step-by-step explanation:

because it is going to keep saying LUNCH

Answer:

Step-by-step explanation:

(227-127)/4=x

"/" means divide.

Answer:

O B)   4 + 5 · (3² - 9) ÷ 3²

Step-by-step explanation:

4 + 5 · (3² - 9) ÷ 3²

4 + 5 · (9 - 9) ÷ 9

4 + 5 · 0 ÷ 9

4 + 5 · 0

4 + 0

4

Let me know if you need details

The statements that describes the effect and value of k in the functions f(x) = −x + 3 and g(x) as shown in the graph where function g(x) is a transformation of f(x), such that g(x) = kf(x) and k is a rational number, is

a. The graph of g(x) is a vertical stretch of the graph of f(x); the k value is positive and greater than 1.

A vertical stretch refers to a movement in the upward direction. A transformation that leads to a vertical stretch is as a result of multiplying by a positive number that is above or greater than 1.

The given graphs f(x) was factored and this lead to a vertical stretch to produce g(x), and the factor that leads to vertical stretch is a positive number greater that 1. Hence we say that The graph of g(x) is a vertical stretch of the graph of f(x); the k value is positive and greater than 1.

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Answer:

5x + 7

Step-by-step explanation:

Given

4x + 7 + x ← collect like terms

= (4x + x) + 7

= 5x + 7

\(\huge\text{Hey there!}\)

\(\huge\text{4x + 7 + x}\)

\(\huge\text{= 4x + 7 + 1x}\)

\(\huge\textsf{COMBINE the LIKE TERMS}\)

\(\huge\text{= (4x + 1x) + 7}\)

\(\huge\text{= 5x + 7}\)

\(\huge\text{Answer: \textsf{5x + 7}}\)

\(\huge\text{Good luck on your assignment \& enjoy your day! }\)

~\(\frak{Amphitrite1040:)}\)

Answer:

12 for each rope

Step-by-step explanation:

half of 24 is 12

Answer:

1

Step-by-step explanation:

\(cos²30° + cos²60° + cos²90°\\ + 2 cos 30° cos 60° cos 90° \\ \\ = \bigg( \frac{ \sqrt{3} }{2} \bigg) ^{2} + \bigg( \frac{ 1 }{2} \bigg) ^{2} + \bigg( 0\bigg) ^{2} \\ + 2 \times \frac{ \sqrt{3} }{2} \times \frac{ 1 }{2} \times 0 \\ \\ = \frac{3}{4} + \frac{1}{4} + 0 + 0 \\ \\ = \frac{3 + 1}{4} \\ \\ = \frac{4}{4} \\ \\ = 1\)

True, the half-life equations are an application of integrated rate laws. False, pseudo-order reaction kinetics is not a way to simplify a more complicated rate law by holding one (or more) of the reagents essentially constant. False, half-life is not the time required for the rate of the reaction to decrease by one half. The rate law equation expresses the rate of the reaction in terms of the concentrations of the reactants.

1. The half-life equations are an application of integrated rate laws: True. Half-life equations are derived from integrated rate laws to express the time required for the concentration of a reactant to decrease to half its initial value.

2. Pseudo-order reaction kinetics is a way to simplify a more complicated rate law by holding one (or more) of the reagents essentially constant: True. Pseudo-order reaction kinetics simplifies complex rate laws by considering one or more reagents to be in excess, effectively making their concentrations constant, which leads to a simpler rate law.

3. Half-life is the time required for the rate of the reaction to decrease by one half: False. Half-life is the time required for the concentration of a reactant to decrease by one half, not the rate of the reaction.

True, the half-life equations are an application of integrated rate laws. False, pseudo-order reaction kinetics is not a way to simplify a more complicated rate law by holding one (or more) of the reagents essentially constant. False, half-life is not the time required for the rate of the reaction to decrease by one half. The rate law equation expresses the rate of the reaction in terms of the concentrations of the reactants.

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Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

The number of small boxes purchased is 4.

The number of large boxes purchased is 2.

The number of nails in a small box is 50, and the number of nails in a large box is 450.

The total number of nails bought is 1100.

Let the number of large boxes be "x".

The number of small boxes is "2x".

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign.

The equation can be formed as given below :

x*450 + 2x*50 = 1100

450x + 100x = 1100

550x = 1100

x = 2

The number of small boxes purchased is 2*x = 2*2 = 4.

The number of large boxes purchased is x = 2.

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Answer:

4 boxes of small nails.

2 boxes of large nails.

Step-by-step explanation:

Define the variables:

Given information:

Create a system of equations with the given information and defined variables:

\(\begin{cases}x=2y\\50x+450y=1100\end{cases}\)

Substitute the first equation into the second equation and solve for y:

\(\implies 50(2y)+450y=1100\)

\(\implies 100y+450y=1100\)

\(\implies 550y=1100\)

\(\implies \dfrac{550y}{550}=\dfrac{1100}{550}\)

\(\implies y=2\)

Substitute the found value of y into the first equation and solve for x:

\(\implies x=2(2)\)

\(\implies x=4\)

Therefore the contractor purchased:

Answer:

Step-by-step explanation:

Construct the perpendicular bisector of the segment. Then construct the perpendicular bisector of each of the new segments. The first bisector cuts the segment into two congruent pieces. Constructing the bisector of each of those produces 4 congruent segments.

Answer:

0 is the answer

Step-by-step explanation:

The position of point P is at 0 on number line.

What is Number line?

Number line is a straight line with numbers placed at equal intervals.

Given that;

Point C is located at -4.

Point D is located at 6.

Now,

Distance between points -4 and 6 is,

6 - (-4) = 6 + 4 = 10

Since, Point P be located so that the directed line segment from C to D will be partitioned in a 2 : 3.

Let partitions are 2x and 3x.

Then,

2x + 3x = 10

5x = 10

x = 2

So, The partitions between point C and D is,

2x = 2 × 2 = 4

3x = 3 × 2 = 6

So, The ratio become = 4 : 6

Thus, Position of point P from C = - 4 + 4 = 0

Position of point P from D = 6 - 6 = 0

So, The position of point P is at 0 on number line.

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Answer:

yes

Step-by-step explanation:

Answer:

Problem 1:  HI = 12.22

Problem 2:  AB = 16.23

Step-by-step explanation:

Problem 1:

tan = opposite / adjacent

HI = x

tan 42° = 11 / x

multiply both sides of the equation by x

x (tan 42°) = 11

divide both sides of the equation by tan 42°

x = 11 / tan 42°

tan 42° = 0.90 (given)

x = 11 / 0.90

x = 12.22

Problem 2:

cosine = adjacent / hypotenuse

cos 52° = 10 / c

multiply both sides by c

c (cos 52°) = 10

divide both sides by (cos 52°)

c = 10 / cos 52°

cos 52° = 0.616 (given)

c = 10 / 0.616

c = 16.23

Answer:

Yes it is 25

Step-by-step explanation:

10 - 25 = -15

-15 + 25 = 10

Answer:

No, because the y-intercepts of lines g and h are different.

Step-by-step explanation:

Complement of angle is 70 degree.

Two angles are said to be complimentary if their sum is 90 degrees. By deducting an angle from 90, one can find its complement. For instance, 90° - 40° = 50° is the complement of 40°. Complementary angles are those whose combined angle is exactly 90 degrees.

So

We have that

3A  : 4(90 - A)  : (180 - A ) / 2   =     3   :  14   :    4

So

3A / [ 4 (90 -  A )]  =   3 /14

14* 3A   =   3 * 4 (90 - A)

42A  = 1080 - 12A

54A  = 1080

A  = 20°

The complement of A  = 70°

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