I would use this strategy to find y.
Triangle Sum Theorem
Pythagorean Theorem
Law of Sines
Law of Cosines

Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

Answer:

  $2496

Step-by-step explanation:

You want to know the cost of carpeting a 18 ft by 24 ft room with carpet that costs $52 per square yard.

The dimensions of the room in yards are (18 ft)/(3 ft/yd) = 6 yd, by (24 ft)/(3 ft/yd) = 8 yd.

In square yards, the area is ...

  (6 yd)(8 yd) = 48 yd²

The cost of one square yard of carpet is $52, so the cost of 48 square yards will be 48 times as much.

  (48 yd²)($52/yd²) = $(48·52) = $2496

The total price to carpet the floor is $2496.

__

Additional comment

We're reluctant to call this the total price, as there are usually additional charges for tax, carpet pad, delivery, installation, removal and disposal of old flooring, and possibly additional materials such as tack strips or thresholds. Repairing mold or water damage, or leveling the floor, can also add cost.

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Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.

We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.

Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.

Therefore,  y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.

Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.

Simplifying, we have :3x = $90000 + 75 = $90075.

Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.

Therefore, Jane received $30025 and Lydia received $60000.

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62.8363 cm is the total circumference of the given circle.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

Given a circle that has an arc of 165 degrees and also given that arc has a circumference of 28.8cm

Circumference of 165 Degrees arc = 28.8cm

Circumference of 1 Degree arc = 28.8/165

Circumference of 1 Degree arc =0.17454

Since the total angle in a circle is 360 degrees

Thus from the fraction,

Circumference of 360 Degrees arc = 0.17454*360

Circumference of 365 Degrees arc = 62.8363 cm

Therefore, the total circumference of the given circle is 62.8363 cm.

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The rational zeros theorem states that the possible zeros of a polynomial can be found through the division of the factors of the constant term by the leading coefficient factors.

In this case,

the leading coefficient is: 1

The constant term is: 12

The factors for the leading coefficient are: ±1

The factors for the constant term are: ±1, ±2, ±3, ±4, ±6, ±12.

The possible roots are:

Answer:

-1, 1, -2, 2, -3, 3, -4, 4, -6, 6, -12, 12.

Answer:

75.36 cubic units

Step-by-step explanation:

The volume of a cylinder is \(V=\pi r^{2}h\) where \(V\) is the volume of the cylinder, \(r\) is the radius of the cylinder's base, and \(h\) is the height of the cylinder. This problem requires that we use 3.14 for the constant \(\pi\).

With the given information, this means that the volume of the cylinder is:

\(V=\pi r^{2}h\)

\(V=3.14(2)^{2}(6)\)

\(V=3.14(4)(6)\)

\(V=3.14(24)\)

\(V=75.36\)

Therefore, the volume of the cylinder is 75.36 cubic units

Answer:

the cafeteria is closer

Step-by-step explanation:

the scale factor from map A to the campus is 3

and for map B its 4

then you multiply the scale factor of both of em by the amount of cm which is 15.5 and 12.5 so 15.5x3 and the answer is 46.5 and 12.5x4 which is 50 therefore the cafeterias closer

Answer:

\(x = 1.212121...\)

\(-3(1.212121...) = -3.636363...\)

Answer:

Step-by-step explanation:

Hope this helps u !!

Answer: The equation used to find the value of x is 5x - 4 = 3x + 10. The value of x is determined to be 7.

Step-by-step explanation:

Four less than the product of a number (x) and 5 = 5x - 4

8 more than 2 added to 3 times the number = 3x + 2 + 8 = 3x + 10

Four less than the product of a number (x) and 5 is equal to 8 more than 2 added to 3 times the number => 5x - 4 = 3x + 10

                                                         5x - 3x = 10 + 4

                                                         2x = 14

                                                         x = 14/2

                 therefore,                      x = 7

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Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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f '(x) = 0 only when the tangent line to the curve is horizontal. This happens at the local maximum of f(x) at x = -2.

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

Hey there!

Do you remember what the Distributive property states? If not, no worries! Here's what this property states:

a(b+c)=ab+ac

In this formula, a, b, and c can be

Now that we know what this property states, let's simplify this expression.

5(x-2)

First, multiply 5 times x:

5x (5 is the coefficient of x, by the way)

Then, multiply 5 times -2 (please pay attention to the sign) :)

-10

Put both terms together.

Hence, the simplified expression is

\(\boxed{\boxed{\bold{5x-10}}}\)

Is it possible to simplify the expression any further? No.

Why? Because 5x and -10 aren't like terms, so we cannot combine them.

Hope everything is clear.

Let me know if you have any questions!

#ILoveLearning

:-)

Answer:

x = - 9

Step-by-step explanation:

2x + 7 = - 11 ( subtract 7 from both sides )

2x = - 18 ( divide both sides by 2 )

x = - 9

The answer is:

x = -9

Work/explanation:

The point of equations is to find the variable's value by isolating it step-by-step.

For this equation, the variable is x.

To isolate it, I will perform a few operations.

First, I will subtract 7 from each side:

\(\sf{2x+7=-11}\)

\(\sf{2x=-11-7}\)

\(\sf{2x=-18}\)

Divide each side by 2

\(\sf{x=-9}\)

Hence, x = -9.

\(\rule{350}{4}\)

Answer:

but I'm not sure

yes I think it is true

The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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Answer:

a. (6 - 2) × 180 = 4 × 180 = 720 degrees.

b. (23 - 2) × 180 = 21 × 180 = 3780 degrees.

2. (n - 2) × 180 = 1440

n - 2 = 8

n = 10

3. 32 × (360/32) = 32 × 11.25 = 360 degrees.

Answer:

1.

a. 720 degrees.

b. 3780 degrees.

2. decagon

3. 360 degrees

Step-by-step explanation:

1.

a. The sum of the measures of the interior angles of a hexagon can be found using the formula:

Sum of interior angles = (n-2) x 180 degrees

where n is the number of sides of the polygon. For a hexagon, n = 6, so we have:

Sum of interior angles = (6-2) x 180 degrees = 4 x 180 degrees = 720 degrees

Therefore, the sum of the measures of the interior angles of a hexagon is 720 degrees.

b. The sum of the measures of the interior angles of a 23-gon can be found using the same formula:

Sum of interior angles = (n-2) x 180 degrees

where n is the number of sides of the polygon. For a 23-gon, n = 23, so we have:

Sum of interior angles = (23-2) x 180 degrees = 21 x 180 degrees = 3780 degrees

Therefore, the sum of the measures of the interior angles of a 23-gon is 3780 degrees.

2.

The sum of the measures of the interior angles of a convex polygon with n sides can be found using the formula:

Sum of interior angles = (n-2) x 180 degrees

We are given that the sum of the measures of the interior angles is 1440 degrees. Substituting this value into the formula, we have:

1440 = (n-2) x 180 degrees

Simplifying and solving for n, we get:

n-2 = 1440/180 = 8

n = 8+2 = 10

Therefore, the polygon has 10 sides, and it is a decagon.

3.

The sum of the measures of the exterior angles of any polygon is always 360 degrees.

For a polygon with 32 sides, the sum of the exterior angles can be found using the same formula:

Sum of exterior angles = 360 degrees

Divided by the number of sides in the polygon, which is 32:

Sum of exterior angles = 360 degrees / 32 = 11.25 degrees

Therefore, the sum of the measures of the exterior angles of a 32-gon is 360 degrees, and each exterior angle of a regular 32-gon measures 11.25 degrees.

Answer:

1.6

Step-by-step explanation:

Answer is in the photo. I can only upload it to a file hosting service. link below!

linkcutter.ga/gyko

The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.

Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.

Number of tablets = Prescribed dose / Dosage strength per tablet

Number of tablets = 80 mg / 20 mg

Number of tablets = 4 tablets

Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.

Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.

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Answer:

20

Step-by-step explanation:

Initial figure times scale factor = result

10 times 2 = 20

I hope this helps!

The plot of the residuals to the area indicates that the graph that corresponds to the residuals is the second option.

Please find attached the graph of the residual plot for the data created with MS Excel

A residual plot is a tool used for assessment of statistical models, to determine how fit the model is to the data. A residual plot is a plot of the residuals to the input or x-values of the data.

The trend line for the data in the question obtained using MS Excel indicates that we get; y = 0.1128·x + 3.6158

The residuals, which is the difference between the actual values and the calculated value obtained using MS Excel are;

Area (in²)    \({}\)              Residuals

x-value

5 \({}\)                             -1.0178

10 \({}\)                           -0.2718

24 \({}\)                           0.605

46 \({}\)                           0.7874

53 \({}\)                           0.7018

78 \({}\)                           0.0758

84 \({}\)                           -0.129

100 \({}\)                         -0.7538

The above values for the areas and the residuals indicates that the residual plot is n shaped, with the first two values being below the x-axis, which corresponds to the second option

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The part of the expression which represents the discounted price before tax is x-35.

The given expression is 0.12x+(x-35).

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

a) The part of the expression represents the discounted price before tax is x-35

b) The part of the expression represent the amount of sales tax in dollars is 0.12x

Hence, the part of the expression which represents the discounted price before tax is x-35.

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Answer:

$739.55 if it is compounded

Step-by-step explanation:

470 x 1.12

ans x 1.12

ans x 1.12

ans x 1.12

Answer:

a. a = 25

b. b = 14

Step-by-step explanation:

a. a/5 + 3 = 8

a/5 = 5

a = 25

b. 3b/7 - 1 = 5

3b/7 = 6

3b = 42

b = 14

x = total amount of gumballs

let's start subtracting the balls she's giving away

\(\stackrel{total}{x}-\stackrel{\textit{to jaysen}}{\cfrac{x}{2}}\implies \stackrel{\textit{what's left}}{\cfrac{x}{2}}~\hfill \stackrel{\textit{half of what's left to Marinda}}{\cfrac{~~ \frac{x}{2}~~}{2}\implies \cfrac{x}{4}} \\\\\\ \stackrel{\textit{what was left minus Marinda's}}{\cfrac{x}{2}-\cfrac{x}{4}\implies \stackrel{\textit{what's left}}{\cfrac{x}{4}}}~\hfill ~\hfill \stackrel{\textit{a third of what's left to Zack}}{\cfrac{~~ \frac{x}{4}~~}{3}\implies \cfrac{x}{12}}\)

\(\stackrel{\textit{what was left minus Zack's}}{\cfrac{x}{4}-\cfrac{x}{12}\implies \stackrel{\textit{what's left}}{\cfrac{x}{6}}}~\hfill \stackrel{\textit{her sister gets 5 balls of what's left}}{ \cfrac{x}{6}-5 }\)

and we also know that after all that has been subtracted, she's only left with 5, so we can say that

\(\stackrel{\textit{what's finally left}}{\cfrac{x}{6}-5}~~ = ~~\stackrel{\textit{what's finally left}}{5}\implies \cfrac{x}{6}=10\implies \boxed{x = 60}\)

Answer:

the answer is 12/8

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

-3/8 ÷ -1/4

Reciprocal the second fraction.

-3/8 × -4/1

Multiply the fractions.

(-3×-4)/(8×1)

12/8

The quotient of the division is 12/8, simplified to 3/2.

Answer:

The value of test statistic

   |Z| = |-2.2883| = 2.2883

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 57.7miles/gallon

The standard deviation of the Population = 1.9

The mean of sample x⁻ = 57.4

Given that the sample size 'n' =210

level of significance = 0.1

Step(ii):-

Test statistic

        \(Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

       \(Z = \frac{57.4-57.7}{\frac{1.9}{\sqrt{210} } }\)

      Z = -2.2883

  |Z| = |-2.2883| = 2.2883

Final answer:-

The value of test statistic

   |Z|  = 2.2883

Answer:

(See explanation below for further details)

Step-by-step explanation:

Any point in rectangular form can be described in terms of radius and angle of the circle. That is:

\(P = (r\cdot \cos \theta, r\cdot \sin \theta)\)

Since circunference is divided into 8 equal parts, the point can be modelled as:

\(P = (r\cdot \cos \frac{2\pi\cdot n}{8}, r \cdot \sin \frac{2\pi\cdot n}{8} )\)

The approximate radian and degree values for one circle are:

Radians

\(0 (0), \frac{\pi}{4} (0.785), \frac{\pi}{2} (1.571), \frac{3\pi}{4} (2.355), \pi (3.142), \frac{5\pi}{4} (3.925), \frac{3\pi}{2} (4.71), \frac{7\pi}{4} (5.495), 2\pi (6.280)\)

Degrees

\(0^{\circ}, 45^{\circ}, 90^{\circ}, 135^{\circ}, 180^{\circ}, 225^{\circ}, 270^{\circ}, 315^{\circ}, 360^{\circ}\)