Angela wants to learn how to rock climb. The Rocky Climbing gym has a special where 5 climbs cost $52.50.
Select the equation that represents the total cost, t, of c climbs. Assume the relationship is proportional.

The total number (n) of distinct solutions of the equation (x + y + z = 15) with the assumption that x, y and z are all nonnegative integers is 153.

The generating function for the number of solutions of the equation (x + y + z = n) is given by the binomial coefficient (n+2)C2, where C2 is the number of ways to choose 2 objects from a set of n+2 objects.

The number of solutions for the given equation (x + y + z = 15) is then given by:

(15+2)C2 = (17C2)

We can also use the formula for binomial coefficient: nCr = n! / (r! (n-r)!)

17C2 = (17!) / (2! * 15!) = 153

So the total number of distinct solutions of the equation (x + y + z = 15) with x, y, z non-negative integers is 153.

"

Complete question

what is the total number n of distinct solutions  the equation (x + y + z = 15) after we impose that x, y and z are all nonnegative integers?

"

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The given ratio of yes votes to no votes is 3:4

Then,

The ratio of yes votes: to no votes = 3:4  

Yes votes = 2721,

Now,

2721/3 = 907

907 × 4 = 3628.

Hence, there were 3628 no votes.

To calculate the ratio, use this formula:

Ratios equate two numbers, usually by dividing them. If you are comparing one data point (x) to any other data point (y), your formula would be x/y. This means you are dividing information x by information y.

For example, if A is 50 and B is 100, your ratio will be 50/100 the ratio will be 1:2.

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Answer: here

Step-by-step explanation:

Divide each term in ma=3xma=3x by aa and simplify.m=3xa

The required value of x to satisfied the given condition is 1/5.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

We have,

3x (1 + 6) = (3 x 1) + ( 6x)​

3x(7) = 3 + 6x

21x = 3 + 6x

15x = 3

x = 1/5

Thus, required value of x is 1/5.

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In order to satisfy the requirement, x must be 1/5 of the desired value.

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The value of p from the equation 17.5 - 6.3p = 25 is 1.19

Algebraic expression can be defined as a mathematical expression that are variables, terms, factors, constants and coefficients.

These expressions are also composed of mathematical or arithmetic operations, which includes;

From the information given, we have that;

17.5 - 6.3p = 25

Now, let's take the following steps

collect like terms

-6.3p = 25 - 17.5

subtract the like terms

-6.3p = 7.5

Divide both by the coefficient of p, we get;

p = 7.5/-6.3

p = 1.19

Hence, the value is 1.19

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Complete question:

Solve for P please

17.5 - 6.3p = 25

Based on the triangle sum theorem, the value of x is: 45.

The Triangle Sum Theorem states that in any triangle, the sum of the measures of the interior angles is always equal to 180 degrees. This is true for all triangles, regardless of their size or shape.

The theorem can be proven using Euclidean geometry, which states that the sum of the angles in a triangle is always 180 degrees. This theorem is also known as the "angle sum property" of a triangle.

Therefore:

2x + 10 + 30 + 50 = 180 (based on the triangle sum theorem).

Combine like terms:

2x + 90 = 180

2x = 180 - 90

2x = 90

2x/2 = 90/2

x = 45.

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Answer:

$337,807.321.

Step-by-step explanation:

every year has 4 quarters, so 19 years = 76 quarters, so it compounds 76 times = (1+5.7%)^76.  so punch into the calculator 1.057 then the "xy"button, then 76, it'll spit out 67.56146111  number. then hit times 5000.  which is $337,807.321.  power of compounding. More than a quarter million $$$.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 5.7\%\to \frac{5.7}{100}\dotfill &0.057\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &19 \end{cases} \\\\\\ A = 5000\left(1+\frac{0.057}{4}\right)^{4\cdot 19} \implies A=5000(1.01425)^{76}\implies A \approx 14655.18[/tex]

Answer: (0, -1)

Step-by-step explanation:

Hello! One method you can use to solve a system of equations is the elimination method.  Here are the steps to use the elimination method in this equation:

 -4y + x = 4               -4y - (-6y) = -4y + 6y = 2y, x -x = 0, 4 - 6 = -2
- (-6y + x = 6)
_________
2y = -2
__    __
2       2

y = -1

You now know that y = -1 for both lines to intersect.  Let's now find x using the substitution method.

Use the equation -4y + x = 4.  Substitute -1 for y in the equation.

-4(-1) + x = 4
4 + x = 4
-4      =  -4
x = 0.  

You now know that x = 0 and y = -1.  Coordinate pairs are represented as (x, y).  Substitute 0 in for x and -1 in for y.  Your answer is (0, -1).

Step-by-step explanation:

First one is good, all you have to do is combine like terms

-28x and +4x are like terms because they both have X

Combining those is -28x+4x=+24x

Making #1 7+24x

Answer:

(Their all down there)

Step-by-step explanation:

Okie dokie so! Your answer for 17 is technically correct but you need to imply it further so it would be [tex]7-24x[/tex]

18. [tex]-2(-6+5k)-1[/tex]

do distributive property

[tex]12-10k-1[/tex]   combine like terms (12 and -1)

[tex]-10k+11[/tex]

19. [tex]6(v-5)+1\\[/tex]

do distributive property

[tex]6v-30+1[/tex]    combine like terms (-30 and 1)

[tex]6v-29\\[/tex]

20. [tex]10(n+5)-5n[/tex]

do distributive property

[tex]10n+50-5n[/tex]  combine like terms (10n and -5n)

[tex]5n+50[/tex]

21. [tex]-7(8+8x)-6x[/tex]

do distributive property

-[tex]56-56x-6x[/tex]   combine like terms (-56x and -6x)

[tex]-56-62x[/tex]

22. [tex]6(x-9)+5[/tex]

do distributive property

[tex]6x-54+5[/tex]  combine like terms (-54 and 5)

[tex]6x-49[/tex]

Answer:

Step-by-step explanation:

  f f

Answer:

1) False

2)True

3)True

4)False

The measure of angle C of the given triangle is 42.8°.

To find the angle C, the law of sines formula is used, it is the ratio of the length of the side of the triangle to the sine of the angle thus formed between the other two remaining sides, given by,

sin A / a = sin B / b = sin C / c

where, a, b, and c are the lengths of the triangle and A, B, and C are the angles of the triangle.

Given ∠A = 61°, c = 35, a = 45

∴( sin A)/a = (sin C)/c

(sin 61° )/ 45 = (sin C) / 35

sin c = ((sin 61°) / 45) × 35

sin c = 0.68

c ≈ 42.8°

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Complete question:

You have given a triangle ΔABC, where ∠A = 61°, c = 35, a = 45. Solve for measurement(s) of angle c.

The angles of the triangle are ∠Q=59°, ∠R=90°,∠S=31°.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle are less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

As sum of all angles of triangles=180°

90+2x+33+5x-34=180

7x=90+1

x=13

Therefore,

                 ∠Q=59°, ∠R=90°,∠S=31°

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Answer: -25

Step-by-step explanation:

For f(x) functions, all you do is plug in whatever value that is given in the parenthesis into x.

f(5) = -4(5) - 5

= -20 -5

= -25

Price paid for car = $23622, The loss value is $3742 and total distance the car was used for is 18000 kilometres.

Distance is a measurement of how far apart two objects or points are. It is the length of the actual route taken to get from one place to another. In physics, distance is frequently used to refer to a physical length or an estimation based on other criteria, such as "a few kilometres apart" or "some miles away."

However, the distance travelled by an object to move from its initial position to its final position will be the same as the distance travelled to move from its final position to its initial position. As a result, distance is independent of a body's motion.

a. Price paid for car = $23622

Discount = 7%

Sale price = $19880

b. The loss value is $3742

c. Let total distance travelled be d

Fuel consumption=10km per litre

Cost of fuel =1.4 per litre

Cost of fuel per kilometre =1.410= 0.14

Other cost = 938

Cost of usage =0.14*d +938

Total cost including loss = 0.14*d +938+3742

The cost per kilometre has been provided as 0.4

Total cost of the vehicle's use = 0.4*d

B=A0.4*d = 0.14*d +938+37420.26*d = 4680d = 18000

Thus, Total distance the car was used for is 18000 kilometres.

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Shop ZYX represents the cheaper plan, with a cost of $2.4 per plum.

To obtain the cheaper plan, we must obtain the cost of a single plum for each shop.

The cost of a single plum for each shop is obtained using a proportion, with the division of the total cost by the number of plums.

Hence the cost per plum in each shop is given as follows:

(division of the total cost by the number of plums).

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The probability that the system gets damaged is 0.685.

Virus A damages the system with probability 0.4.

Independently of it, virus B damages the system with probability 0.5.

Independently of A and B virus C damages the system with probability 0.2.

We have to find the probability that the system gets damaged.

P(system will not be damaged by virus 1) = 1 - 0.1 = 0.9

P(system will not be damaged by virus 2) = 1 - 0.5 = 0.5

P(system will not be damaged by virus 3) = 1 - 0.3 = 0.7

P(the system will be damaged) = 1 - P(system will not be damaged)

P(the system will be damaged) = 1 - P(system will not be damaged by virus 1) x P(system will not be damaged by virus 2) x P(system will not be damaged by virus 3)

P(the system will be damaged) = 1 - 0.9x0.5x0.7

P(the system will be damaged) = 0.685

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The required number of each type of cycles are  25 bicycle and 10 tricycle.

Tricycles will offer better stability and assistance. They can also be applied in a wider variety of circumstances, such as therapy sessions for people with disabilities. The most common vehicle will be a bicycle because they are smaller, lighter, faster, more suited for off-roading, and more widely available.

The seats are counted by 1 for both tricycles and bicycles, so t + b has to equal 35. The only answer choice that has t + b = 35

t = 35 - b

And

3t + 2b = 80

3(35 - b) + 2b = 80

105 - 3b + 2b = 80

105 - b = 80

b = 25

Put value of b in t = 35 - b,we get

t = 35 - 25

= 10

Thus, There are 25 bicycle and 10 tricycle.

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The amount of money that will be needed more to buy the amount of cups and napkins by the teacher would be = $57.5

The amount of cups needed = 12 packages

The price per package of cup = $3.50

The total money needed for cup = 12× $3.50 = $42

The amount of napkins needed = 10 package

The price per package of napkins = $4.25

The total money needed for napkins = 10×4.25 = $42.5

The total amount needed = 42+42.5 = $82.5

The difference between the amount available and the total amount = the extra money needed ;

= 82.5-25 = $57.5

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The measure of angle 8 in the figure is given as follows:

m < 8 = 27º.

Alternate interior angles happen when there are two parallel lines cut by a transversal lines.

The two alternate exterior angles are positioned on the inside of the two parallel lines, and on opposite sides of the transversal line.

The alternate interior angles for this problem are given as follows:

2 and 8.

They are congruent, hence the measure of angle 8 is given as follows:

m < 8 = 27º.

The diagram is given by the image presented at the end of the answer.

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Answer:

B.   (-∞,∞)

Step-by-step explanation:

Function is
[tex]f(x) = \frac{3}{4}\cdot \left|x-3\right|\:+\:1[/tex]

There are no bounds on this function.

x values can range from -∞ to +∞  (but will never reach infinity)

Therefore domain is:
- ∞  < x < ∞

which in interval notation is Option B

So the range of probability that at least one bond will default next year is between 0% and 80%.

The probability that at least one of two events will occur is the sum of the probability of each event minus the probability that both events will occur. In this case, the probability that at least one bond will default is:

P(A or B) = P(A) + P(B) - P(A and B)

Where P(A) is the probability of bond A defaulting (50%), P(B) is the probability of bond B defaulting (30%), and P(A and B) is the probability that both bonds will default (which we don't know).

So the range of probability that at least one bond will default is:

P(A or B) = 50% + 30% - P(A and B)

The maximum possible probability of both bonds defaulting is (0.5 * 0.3) = 15% and the minimum possible probability of both bonds defaulting is 0%. Therefore, the range of probability that at least one bond will default is:

P(A or B) = 80% - 0% = 80%

So the range of probability that at least one bond will default next year is between 0% and 80%.

It's important to note that the above formula and the range of probability is based on the assumption of independence, i.e the events of Bond A defaulting and Bond B defaulting are independent and don't affect each other.

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Answer: depending on how much it cost

Step-by-step explanation:

Answer:

Depends on the pizza prices

Answer: Amber has 50 pennies and 10 dime

Step-by-step explanation:

The number of pennies is represented by x, while the number of dimes is represented by y. This means that the statement, "there are five times as many pennies as dimes" can be written as x = 5.

The sum of the coins is $1.50, which can now be written as

0.01x + 0.1y = 1.50

0.01(5y) + 0.1y = 1.50

0.05y + 0.1y = 1.50

0.15y = 1.50

y = 10

Next up:

x = 5y

x = 5(10)

x = 50

Finally, we can conclude that Amber has 50 pennies and 10 dimes

I hope this helps!

The distance-time graphs for the given scenarios have been attached below. The solution has been obtained using distance-time function.

What is distance-time function?

The distance between a person and an object through time is described by distance-time functions. Depending on the kind of movement, a distance-time function may be linear or non-linear, increasing, decreasing, or constant. We need to tell where the object starts, what direction it moves in, how quickly it moves, and whether it is speeding up, slowing down, or travelling at a constant speed in order to explain a distance-time function.

a. The distance-time graph for this scenario is the first graph wherein the line is less steeper than the other graph because the speed is constant.

b.  The distance-time graph for this scenario is the second graph wherein the line is steeper than the first one because the speed is changing from slow to fast.

Hence, the distance-time graphs for the given scenarios have been obtained.

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The estimated probability that Pedro will eat pizza for lunch every way next week is 1/2

The term called probability in math is known as branch of mathematics that measures the uncertainty of the occurrence of an event using numbers

Here we know that the cafeteria has pizza about 80% of the time.

And here we have also know that Pedro runs a simulation to model this using a random number generator.

The result of the table shows the results of the simulation.

Here we need to estimate the probability that Pedro will eat pizza for lunch every way next week and it can be calculated as,

Here we have know that in each box, here there are 5 digits to represent the 5 days in a week.

And here there’s 10 boxes to represents 10 weeks.

Then in each box there’s a chance out of 5 for Pedro to get pizza.

Then the probability is calculated as,

=> 5/10

=> 1/2

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Answer:

By definition, if two angles are complementary, they both will add up to 90 degrees. Knowing this add 18 and (6d-6) together to equal 90.

18+(6d-6)=90

Subtract 18 from both sides, then add 6. This leaves you with 6d equal to 78. Divide by 6 to get 13.

(6d-6)=72

6d=78

d=13 degrees

Make sure of your answer. You know that d is 13, so plug it back into the equation to see if it equals 90 degrees.

18+6(13)-6=90

18+78-6=90

90=90

The quantity of more flour that she needs to add would be = 3/4

A fraction is defined as the representation of the part of a whole data in a form of numerator and denominator.

The quantity of flour Ryan needs for baking = 3¼

The quantity of flour she has already added = 2½

The remaining amount that she needs to add;

= 3¼-2½

= 3/4

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Answer:

Step-by-step explanation:

78,500 x 0.02 = 1,570--year 1 raise

(78,500 + 1,570) x 0.02 = 1,601.4--year 2 raise

(78,500 + 1,570+ 1,601.4) x 0.02 = 1,633.428--year 3 raise

(78,500 + 1,570+ 1,601.4+1,633.428) x 0.02 = 1666.1--year 4 raise

(78,500 + 1,570+ 1,601.4+1,633.428+1666.1) x 0.02 = 1699.42--year 5 raise

just keep doing this till you get to year 10 and then add up the total of money gained to the initial salary

From the SSS Property of the triangle, Both triangles BSR and DUT are congruent.

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given, In the diagram, ABCD is a square, and R, S, T, and U are the midpoints of the sides of ABCD. Also, RT is perpendicular to SU and SV are equals to VU.

Since, R, S, T, and U are midpoints, and since  RT is perpendicular to SU

in triangle DUT.

UD = TD

UD is also equal to VT  since  RT is perpendicular to SU

UD = TD = VT...(1)

And, From the Pythagorean theorem

UT = √(TD² + UD²)

In TRiangle BSR

BR = BS

BS is also equal to RV  since  RT is perpendicular to SU

BR = BS = RV...(2)

And, From the Pythagorean theorem

SR = √(BR² + BS²)

Since SV is equal to VU.

Thus, RV = VT

From equation 1 and 2

BR = BS = RV = UD = TD = VT

Therefore, From the SSS Property of the triangle, Both triangles BSR and DUT are congruent.

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