-2x - y = -9
5x - 2y = 18
Solve as a whole number.

The average speed of the Ironman winner is given by S = 15.8 mph

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the average speed of the Ironman winner be represented as S

Now , the distance of the race for swimming = 2.4 miles

The distance of the race for biking = 112 miles

The distance of the race for running = 26.2 miles

So , the total distance D = 2.4 + 112 + 26.2 = 140.6 miles

Now , the time taken for the women's race T = 8.9 hours

So , Speed = Distance / Time

And , the average speed of the Ironman winner = 140.6 / 8.9

The average speed of the Ironman winner S = 15.797 miles per hour

The average speed of the Ironman winner S ≈ 15.8 miles per hour

Hence , the average speed of the winner is 15.8 mph

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The complete question is :

The Ironman triathlon is a speed and endurance race that combines swimming ( 2.4 miles ) , biking ( 112 miles ) and running ( 26.2 miles ). One famous Ironman competition occurs each year in Hawaii , where the race began in 1978

a) What is the total distance covered in an Ironman race?

b) The best women's time for the Hawaiian Ironman race is 8.9 hours. What was the average speed of that Ironman winner?

A value of x of 4 guarantees that the angles 2 · x + 19 and x + 23 could be alternate exterior angles highlighted between two parallel lines.

If two angles are alternate exterior, then both angles have the same measure. Thus, we have the following expression:

2 · x + 19 = x + 23     (1)

Now we proceed to solve for x:

x = 4

A value of x of 4 guarantees that the angles 2 · x + 19 and x + 23 could be alternate exterior angles highlighted between two parallel lines.

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Answer:

There is no image attached

Given :

Number of gallons in the aquarium after 14 minutes = 5.6 gallons

Time taken = 14 minutes

Rate at which Jerry is filling the bucket :

Rate = 0.4 gallons per mins

Answer:

its rather 3 or 5 its prob 3

Step-by-step explanation:

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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If lidocaine is injected intra-arterially, it can quickly lead to systemic toxicity. The first signs of toxicity may include circumoral numbness and tongue paresthesia, but these symptoms may be followed by more severe manifestations such as dizziness, seizures, and cardiac arrest.

The systemic effects of lidocaine are dose-dependent, meaning that the higher the dose, the more severe the symptoms.

Lidocaine is a local anesthetic that is commonly used for minor surgical procedures or dental work. It works by blocking the nerve signals that transmit pain to the brain. However, if it is injected into an artery, it can rapidly spread throughout the body and affect other organs, leading to potentially life-threatening complications.

If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly. The first step is to stop the injection and monitor the patient closely for signs of toxicity. If the patient is experiencing severe symptoms, such as seizures or cardiac arrest, emergency treatment should be initiated immediately. Treatment may include administering medications to counteract the effects of the lidocaine or performing cardio-pulmonary resuscitation (CPR) if necessary.

In conclusion, the first signs of lidocaine toxicity may include circumoral numbness and tongue paresthesia, but more severe symptoms may follow, such as dizziness, seizures, and cardiac arrest. If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly to prevent potentially life-threatening complications.

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Answer:

D.

s + m=5

1.75 +2.5m = 11.60

Step-by-step explanation:

Equations that I have made without seeing the options:

s + m = 5

1.75s + 2.5m = $11.60

There is a option that matches my answer. that's D.

Answer:s + m=5

1.75 +2.5m = 11.60

Step-by-step explanation:

8gh x 2g2 x 3h

Simplified is 8 · 3 gghhxx ·2 · 2

and can also be:

8ghx · 2g · 2x · 3h

24g ₁ ₊ ₁ h ₁ ₊ ₁ x ₁ ₊ ₁ · 2 ₁ ₊ ₁

The value of n is 25  according to standard deviation in the question.

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

s = 30 minutes

C.I. = 99%

mean = 15 minutes

z value for 99% = 2.58

mean = z*s/√n

15  = 2.58 * 30 / √n

√n = 5.06

n = 25

Hence the value of n is 25 .

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The given matrix is an elementary matrix that represents an elementary row operation of multiplying the second row by 4k. The determinant of this matrix is determinant of the original matrix, which is 4k.

Therefore, the determinant of the given elementary matrix is 4k.

To verify this result, we can also compute the determinant using the formula for a 3x3 matrix. The matrix obtained by applying the elementary row operation to the identity matrix is:

\(\left[\begin{array}{ccc}1&0&0\\0&4k&0\\0&0&1\end{array}\right]\)

The determinant of this matrix is calculated as: det(A) = 1 * (4k) * 1 - 0 * 0 * 0 - 0 * (4k) * 0 = 4k. So, the determinant of the given elementary matrix is indeed 4k, which matches our previous result.

In summary, the determinant of the elementary matrix is 4k, and this can be verified by calculating the determinant using the formula for a 3x3 matrix.

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The required equation is 64x = 8 and the unknown variable is 1/8

Let the unknown variable be "x"

If the unknown number of 64 is 8, this can be expressed as:

x of 64 = 8

64x = 8

Divide both sides by 64

64x/64 = 8/64

x = 1/8

Hence the required equation is 64x = 8 and the unknown variable is 1/8

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The equation of the parabola is \($\dfrac{(x - 4)^2}{8(y - 1)} = 1$\)

The equation of a parabola with focus (h, k + p) and directrix y = k - p can be written as:

\($\dfrac{(x - h)^2}{4p(y - k)} = 1$\)

In this case, the focus is (4, 3) and the directrix is y = -1. Comparing this with the general equation of a parabola, we can determine the value of p.

k + p = 3 (since the y-coordinate of the focus is 3)

k - p = -1 (since the equation of the directrix is y = -1)

Adding these two equations, we get:

2k = 2

Dividing by 2, we find:

k = 1

Substituting this value back into one of the equations, we can solve for p:

1 + p = 3

p = 2

So, the value of p for this parabola is 2.

The equation of the parabola can be written as:

\($\dfrac{(x - 4)^2}{8(y - 1)} = 1$\)

This represents a parabola with focus at (4, 3) and directrix y = -1.

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Answer:

mn(5mn² + 9) ;

2mn(1 - 1/2mn²)

Step-by-step explanation:

Given:

5m²n³ +9mn

(8mn - 4m²n³ ÷ 4)​

5m²n³ + 9mn

mn(5mn² + 9)

(8mn - 4m²n³ ÷ 4)​

8mn/ 4 - 4m²n³ / 4

2mn - m²n³

2mn(1 - 1/2mn²)

Answer:

17

Step-by-step explanation:

You would make the 10.01 a 10 and the 7.07 a 7.

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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Answer:

12.34

Step-by-step explanation:

Answer:The 99% confidence interval is

To find the 99% confidence interval for the mean systolic blood pressure (SBP) level, we use the formula:

CONFIDENCE INTERVAL = Mean ± Z * (Standard Deviation / √n)

Where:

Mean is the sample mean of SBP

Z is the Z-score corresponding to the desired confidence level

Standard Deviation is the population standard deviation

Explanation:

Given that the sample size is 13 and the standard deviation is 10, we need to calculate the sample mean and the Z-score for the 99% confidence level.

First, we calculate the sample mean:

Mean = (129 + 134 + 142 + 114 + 120 + 116 + 133 + 142 + 138 + 148 + 129 + 133 + 140) / 13

= 1724 / 13

≈ 132.62

Next, we need to determine the Z-score for a 99% confidence level. The Z-score can be found using a Z-table or a statistical calculator. For a 99% confidence level, the Z-score is approximately 2.576.

Now, we can calculate the confidence interval:

Confidence Interval = 132.62 ± 2.576 * (10 / √13)

132.62 ± 2.576 * (10 / 3.6056)

≈ 132.62 ± 2.576 * 2.771

≈ 132.62 ± 7.147

Therefore, the 99% confidence interval for the mean SBP level is approximately (125.47, 139.77).

Answer:

B. Exponential

Step-by-step explanation:

Answer:

A. Linear

Step-by-step explanation:

Answer: The equation y + 6 = 3/4 (x + 4) can be solved for y to find the corresponding graph:

First, isolate x by subtracting 4 from both sides:

y + 6 - 6 = 3/4 (x + 4) - 6

y = -6 + 3/4 (x + 4)

Next, isolate y by dividing both sides by 3/4:

y = -6 + 3/4 (x + 4) ÷ (3/4)

y = -6 + (x + 4)

y = x - 2 + 10

This equation represents a line with a slope of 1 and a y-intercept of 10 - 2 = 8. The graph of this line is a line that passes through the points (0, 8) and (1, 9).

Step-by-step explanation:

ASA congruence postulate says that if the two angles and the included side of a triangle are congruent to two angles and the included side of another triangle then the triangles are congruent. ABC ≅ XYZ

Congruent triangles are those with precisely the same dimensions and appearance. Congruent has the symbol. When the dimensions of one triangle's three sides and three angles match those of another triangle's three sides and three angles, the two triangles are said to be congruent.

Angle-Side-Angle congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below.

According to the ASA criterion, ABC = XYZ because BC = YZ and B = Y and C = Z, respectively. Due to the fact that ABC = XYZ, the third angle (A) and the other two sides (A) of ABC must be equal to the equivalent angle (X) and sides of XYZ.

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Answer:

45:36:50

Step-by-step explanation:

Answer: x=6

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    72-(2*x^2)=0

Pull out like factors :

  72 - 2x2  =   -2 • (x2 - 36)

Factoring:  x2 - 36  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 36 is the square of 6

Check :  x2  is the square of  x1  

Factorization is :       (x + 6)  •  (x - 6)

A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solve  :    x-6 = 0  

Add  6  to both sides of the equation :  

                     x = 6

The population whose properties are analyzed by the data can be described as households in City A.

Given numerical information is,

58% of households in City A were online.

We have to describe what describes this numerical information.

Here, it is described that a certain percent of households in a city A are online.

So the description is about the households of the city A.

So this is the population.

Hence the best description is households in City A.

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The money bank gives to Mrs. Hilt is $50.15.

Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans. A current medium of exchange in the form of coins and banknotes.

Given that, Mrs. Hilt collected 1,003 nickels in a jar.

As 100 cents form a dollar, and 1 nickel equals five cents, we can say that 20 nickels make up a dollar.

Now, 1003/20

= $50.15

Therefore, the money bank gives to Mrs. Hilt is $50.15.

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To determine the probability that a man and woman getting married both have at least a bachelor's degree, we need to make certain assumptions.

Firstly, we must assume that the probability of a man having at least a bachelor's degree is independent of the probability of a woman having at least a bachelor's degree. Additionally, we must assume that the population of men and women with at least a bachelor's degree is representative of the population of all married couples.
Assuming these conditions are met, we can estimate the probability of a man having at least a bachelor's degree as well as the probability of a woman having at least a bachelor's degree using data from the relevant population. We can then calculate the joint probability of both events occurring simultaneously by multiplying the probabilities of each event. Without data, it is difficult to provide an exact probability. However, according to the U.S. Census Bureau, as of 2019, approximately 35% of the U.S. population aged 25 and older have at least a bachelor's degree. Therefore, assuming that the probabilities are independent, the probability of a man having at least a bachelor's degree is approximately 0.35, and the probability of a woman having at least a bachelor's degree is also approximately 0.35.
Multiplying these probabilities together, we get an estimated probability of 0.1225 or 12.25% chance that a man and woman getting married both have at least a bachelor's degree. However, it's important to remember that this is only an estimate and may not hold true for all populations or regions.

To determine the probability that a man and a woman getting married both have at least a bachelor's degree, we need to make some assumptions and use the concept of probability.
Assumptions:
1. The probability of a man having a bachelor's degree is independent of the probability of a woman having a bachelor's degree.
2. We know the probabilities of a man and a woman having a bachelor's degree in the given population.
Let P(M) be the probability of a man having a bachelor's degree, and P(W) be the probability of a woman having a bachelor's degree. To find the probability of both the man and the woman having a bachelor's degree, we simply multiply these two probabilities:
P(both have bachelor's degree) = P(M) * P(W)
So, the probability that a man and a woman getting married both have at least a bachelor's degree depends on the individual probabilities of a man and a woman having a bachelor's degree in the population under consideration.

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Let's use x to represent the cost of one orange and y to represent the cost of one lemon. We can then set up a system of two equations:16x + 13y = 9.29 19x + 6y = 9.05 These equations represent the total cost of buying a certain number of oranges and lemons in two different scenarios.

To understand why we need two equations, let's consider the first equation: 16x + 13y = 9.29

This equation tells us that if we buy 16 oranges and 13 lemons, the total cost will be $9.29. But we don't know the individual prices of oranges and lemons yet. That's where the second equation comes in: 19x + 6y = 9.05

This equation tells us that if we buy 19 oranges and 6 lemons, the total cost will be $9.05. Again, we don't know the individual prices yet.

By setting up a system of equations, we can solve for x and y, which represent the prices of oranges and lemons, respectively.

One way to solve this system is by elimination. We can multiply the first equation by 19 and the second equation by -16, which will allow us to eliminate y:

304x + 247y = 176.51
-304x - 96y = -144.8

Adding these two equations together gives: 151y = 31.71
Dividing both sides by 151, we get: y = 0.21
Now we can substitute this value of y into one of the original equations to solve for x. Let's use the first equation:
16x + 13(0.21) = 9.29
16x + 2.73 = 9.29
16x = 6.56
x = 0.41

So the cost of one orange is $0.41 and the cost of one lemon is $0.21.

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Answer:

To obtain the third side of an isosceles triangle with two sides known, use the Pythagorean theorem if it is a right triangle or provide additional information if it is no

Step-by-step explanation:

You can follow these steps:

Identify the two sides that are known. In an isosceles triangle, these will be the two equal sides, often referred to as the legs of the triangle.

Determine the length of the base. The base is the third side of the triangle, and it is the side that is not equal to the other two sides.

If the isosceles triangle is also a right triangle, you can use the Pythagorean theorem to find the length of the base. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, you can use the formula:

base^2 = (leg1)^2 + (leg2)^2

Take the square root of both sides to solve for the base:

base = √((leg1)^2 + (leg2)^2)

If the isosceles triangle is not a right triangle, you need additional information to determine the length of the base. This could be the measure of an angle or another side length.

Remember that the lengths of the two equal sides (legs) in an isosceles triangle are always equal, while the length of the base is different.

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Answer:

d = 9.9 units

Step-by-step explanation:

Picture a right triangle with one acute vertex at (1, -5) and the other at (-6, 2).  Going from one to the other, we see a change in x (run) of 7 and a change in y of 7.  Applying the Pythagorean Theorem, we find the distance between the two points as follows:

d = √(7² + 7²) = 7√2, or approximately 9.9 units.