Question 10:
A plumber cut a
pipe into 5
equal pieces and had 27 cm of the pipe left. For a second
pipe 15m long, he cut 11 pieces of the same length as that of each piece cut from the
first pipe and had 15 cm of the second pipe left. What was the length, in cm, of each
shorter piece of the second pipe? What was the length of the first pipe originally?

Answer:

Domain is x-value and range is y-values

Step-by-step explanation:

In all three cases, the height of the cone is proportional to the volume and inversely proportional to the square of the radius. So, if we know the volume and radius of a cone, we can use the formula for h to find its height.

[tex]\text{Height } = h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (2^2)} = \frac{3V}{4\pi}[/tex]

The volume of a cone is given by the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone.

If we rearrange this formula to solve for h, we get h = 3V / (πr²). This means that the height of a cone is directly proportional to the volume and inversely proportional to the square of the radius.

a. If the radius of a cone is 2 inches and its volume is given, we can find its height by plugging in the values of V and r into the formula for h.

[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (2^2)} = \frac{3V}{4\pi}[/tex]

b. Similarly, if the radius is 3 inches, the height would be:

[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (3^2)} = \frac{3V}{9\pi}[/tex]

c. If the radius is 6 inches, the height would be:

[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (6^2)} = \frac{3V}{36\pi}[/tex]

In all three cases, the height of the cone is proportional to the volume and inversely proportional to the square of the radius. So, if we know the volume and radius of a cone, we can use the formula for h to find its height.

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The second year's interest rate is 1.80%.

Compound interest is defined as Since compound interest accrues and is added to the accrued interest from earlier periods, borrowers are expected to pay interest on interest in addition to principal.

We are aware that the compound interest formula is,

A = P(1 + r/100)ⁿ.

Where A is the amount, P is the principle, r is the rate, and n is the number of years.

Given, Katy places $2000 over a three-year period in a savings account.

For the first year, the account offers compound interest at a 2.5% annual rate.

∴ A = 2000(1 + 2.5/100)¹.

A = 2000(1.025). (1.025).

A = 2050.

It now earns x% for the second year.

∴ 2050(1+x/100)² = 2124.46

(1+x/100)² =2124.46/2050

1+x/100 =√(2124.46/2050)

x/100 = √(2124.46/2050) -1

x = (√(2124.46/2050) -1)*100

x = 1.80%.

the interest is 1.80 percent

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The triangles are congruent by SSS and the transformation rule is (x, y) ⇒ (x - 4, y)

From the question, we have the following parameters that can be used in our computation:

Triangles EFD and GH

The triangles are congruent because they have equal corresponding side lengths

The corresponding sides of the triangles are congruent

So, the congruent statement is SSS

From the figure, we can see that:

EFD is shifted left by 4 units

So, the rule is

(x, y) ⇒ (x - 4, y)

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The total volume of the space dome theatre is 41867 m³.

In geometry, a sphere is a three-dimensional solid figure, which is round in shape.

The surface area is 4πr².

The volume is (4/3)πr³.

The diameter is 2×radius of the sphere.

A cylinder is a three-dimensional solid object having two similarly circular bases that are joined by a curving surface that is positioned a certain distance from the center.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, The space dome theatre has a base radius of 20m.

Therefore, The volume of the hemispherical dome is,

= (2/3)π(20)³.

= (2/3)π×8000.

= (16000/3)π m³.

And, As the dome base has a radius of 20 m the cylindrical shape will also have the same.

Therefore, The volume of the cylindrical shape is,

= π(20)²×20.

= 8000π m³.

And, The total volume is the sum of the volumes of two shapes,

= 8000π + (16000/3)π m³.

= [(24000 + 16000)/3]π m³.

= (40000/3)π m³.

= 41867 m³.

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Answer: B

Step-by-step explanation:

if r is close to 1 (or -1) it means the relationship is strong, -0.2041 is really close to 0 so the data is most likely scattered and the association is weak

Answer:

Strong

Step-by-step explanation:

edge 2023

Answer:139.33 or 139 ft high

Step-by-step explanation: since building A is three times as high as building B, we can use the equation 418/3=B, which results in 139.33, and if rounding it needed you could round it to 139

The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The value of the variable 'y' is given by the tangent of the angle 27°. Then we have

tan 27° = y / 350

y = 350 tan 27°

y = 178.3

The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.

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The missing diagram is given below.

Answer: A. [tex]92cm^{3}[/tex]

Step-by-step explanation:

[tex]V= \frac{4}{3} \pi r^{3}[/tex]

[tex]V=\frac{4}{3}\pi 2.8^{3}[/tex]

[tex]4/3=1.33333333333[/tex]

calculate in calculator

[tex]1.33333333333\pi 2.8^3=91.9523225755[/tex]

round to nearest ones (9 tells 1 to go to 2)

Therefore, A. 92cm^3

Answer:  -2 ±√6
                    2

Step-by-step explanation:
Use the quadratic formula - its better to separate it into two parts
Δ = b²-4ac
   = 4² -4(2*-1)
   = 16 + 8

∴ Δ = 24
Then
x = (-b ± √Δ) ÷ 2a
  = (-4 ± √24) ÷ 4
  = (-4 ± 2√6) ÷ 4 (simplify the surd form)
∴ x = -2 ±√6   (simplify by crossing out the 2's)
             2

The inequality showing the maximum number of days he can rent a car is 10d ≤ 75.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that Passion has a budget of $75 and wants to rent a car for a trip. A fixed daily fee of 10 is charged.

The product of the number of days and the rent per day should be less than the amount he has.

The inequality mathematically can be written as:-

10t ≤ $75

Therefore, the inequality 10d ≤75 shows how many days he can rent an automobile for the most.

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Answer:

Step-by-step explanation:

Using compounding we know that after 30 years, the account balance has changed by $345.31.

Theoretically, continually compounded interest indicates that interest is continuously earned on an account balance as well as reinvested into the balance so that additional interest is generated.

So, a business owner put $7,000 into a Treasury bond paying a semiannual compound interest rate of 4.3%.

The bond's value after 30 years is $25,084.20.

Instead of compounding twice a year, the investment made by the business owner was made continuously.

After 30 years, we must determine the difference in the account balance.

Think of the continuously compounding recipe:

A = Pe∧rt

We have, p = 7000.

r = 4.3% = 0.043

t = 30

Then,

A = 7000e∧(0.043*30) = 25429..51

A = $25429.51

Therefore, using compounding we know that after 30 years, the account balance has changed by $345.31.

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Correct question:

A business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually. After 30 years, the value of the bond will be $25,084.20. If the business owner's investment was compounded continuously instead of twice per year, what would be the difference in the account balance after 30 years?

Ahlam needs to give the shopkeeper $15 more to get a balance of $25.

Word problems in Mathematics are mathematical approaches we make use of in our ongoing day to day activities. Algebra leading to word problems usually consist of numbers, variables, and its arithmetic operations.

Ahlam bought goods worth = $90, If she gave the shopkeeper $100, then she will collect $100 - $90 = $10 back.

But if the shopkeeper did not have an exact balance and Ahlam decided to give the shopkeeper $x to get a balance of $25.

Then we can write the expression as:

10 + x = 25

x = 25 - 10

x = 15

Therefore, we can conclude that Ahlam needs to give the shopkeeper $15 more to get a balance of $25.

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how will his speed compare?  or namely, will he be within speed limits or should we give him a big fat ticket for speeding?

well, the 25 mi/hr limit is expecting anyone on that road to only do 40,234 meters per hour, so since an hour is 60 minutes and a minute is 60 seconds, that means an hour is really (60)(60) seconds, or 3600 seconds, so the limit is expecting anyone on that road to do no more than 40,234 meters per 3600 seconds, let's see how Usain fares

[tex]\begin{array}{ccll} meters&seconds\\ \cline{1-2} 100 & 9.63\\ 40234& x \end{array} \implies \cfrac{100}{40234}~~=~~\cfrac{9.63}{x} \implies 100x=(40234)(9.63) \\\\\\ x=\cfrac{(40234)(9.63)}{100}\implies x\approx 3874.53[/tex]

so Usain will covering those 40,234 meters in about 3875 seconds, that's longer than 3600 seconds, meaning Usain will need more than 3600 seconds to cover those meters so he's really going slower 40,234 meters per 3600 seconds, so he's golden,  he's within speed limits, because the limit is expecting noone to do them in less than 3600 seconds.

Answer:

Step-by-step explanation:

You want to know the meaning of D(2.60) = 159 if D(p) tells you the number of toys demanded at price p in hundreds.

Compare D(p) to D(2.60) and you see that p=2.60. The problem statement tells you p is the price. This means ...

The problem statement tells you that D(p) is the number of toys in hundreds. When D(p) is 159, the demand is 159 hundred toys.

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The linear inequality that is graphed with y > –x – 2 to create the given solution set is D. y < x + 1

One of the line is having the y intercept -2 and slope -1 having the equation y=-x-2. The shaded region is having the inequality y>-x-2.

The other line is having the y intercept 1 and slope of 1. Hence equation of line is y=x+1.

The shaded part is above the line .The inequality region is represented by the inequality y <x+1.

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Which linear inequality is graphed with y > –x – 2 to create the given solution set?

A=y > x + 1

B=y < x – 1

C=y > x – 1

D=y < x + 1

The mean of the given data is 22.39.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Let us form a table by give data

Score          Frequency        Midpoint(x)          fx

1-7                    13                       4                      52

8-10                  1                        9                       9

11-15                 19                      13                     247

16-20               20                      18                    360

21-35               19                       28                   532

36-50               20                     43                  860

Mean=∑fx/N

=52+9+247+360+532+860/13+1+19+20+19+20

=2060/92

Mean=22.39

Hence, the mean of the given data is 22.39.

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Answer:

12.2 pints

Step-by-step explanation:

In all means add.  Add the two decimals together.

4.8 + 7.4

12.2 pints

The inequality is c ≤ 187, where c is the number of 130-kg crates that can be added to the shipping container

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the number of 130-kg crates that can be added to the shipping container be c

The greatest weight the shipping container can hold = 27,500 kg

The weight that is already loaded = 3,100 kg

So , the total number of 130kg weights = 130c

Substituting the values in the equation , we get

27500 - 3100 ≥ 130c

130c ≤ 24,400

Divide by 130 on both sides of the equation , we get

c ≤ 187.69

So , the value of c is 187 crates

Hence , the inequality is c ≤ 187

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Answer:

Step-by-step explanation:

You want the lateral area, base area, and total area of a square pyramid with a base 3 ft on a side and a slant height of 4 ft.

The area of one triangle is ...

  A = 1/2bh

  A = 1/2(3 ft)(4 ft) = 6 ft²

Then the area of the four triangular faces is ...

  area of triangles = 4×6 ft² = 24 ft²

The area of the square base is ...

  A = s²

  A = (3 ft)² = 9 ft²

The area of the square base is 9 ft².

The total surface area is the sum of the lateral area and the base area:

  total surface area = area of triangles + area of square = 24 ft² +9 ft²

  total surface area = 33 ft²

<95141404393>

Explanatory variable: Cooling time in seconds

Response variable: Impact strength in kj/m2

To find the equation of the linear model that describes the relationship between the predicted value of the response and the explanatory variable, we can use linear regression analysis. Using a statistical software or a calculator, we can find the slope and intercept of the line that best fits the data.

The equation of the linear model is:

Impact strength = -1.23 * Cooling time + 62.61

R-squared (R2) is a statistical measure that represents the proportion of the variance in the dependent variable (impact strength) that is explained by the independent variable (cooling time). It ranges from 0 to 1, with higher values indicating a better fit of the model.

Based on the value of R2, we can say how much of the variation in impact strength can be explained by cooling time. The closer R2 is to 1, the better the model fits the data, and the more likely it is that the impact strength is affected by cooling time. A value of 1 would indicate that all the variation in impact strength is explained by cooling time, while a value of 0 would indicate that cooling time has no effect on impact strength.

          Without knowing the actual value of R2, we cannot say for sure what the relationship is between the explanatory and response variables. However, if the value of R2 is high (close to 1), we can conclude that cooling time has a significant effect on impact strength. If the value of R2 is low (close to 0), we cannot conclude that cooling time has a significant effect on impact strength.

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The solution to the inequality are the region in the shaded area and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

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Answer:

Solution and calculation given below.

The solution is, the distance of the towns is 11.88 km

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

here, we have,

So this can be solve by solving the distance of the plane and the town to the west and also the distance of the plane to the town to the east.  

So the town with an angle of depression of 34 degrees

Let x be the distance of the plane and town  

Cos 34 = x / 8

x = 8 cos 34

x = 6.63 km  

So the town with an angle of depression of 49 degrees

Let y be the distance of the plane and town  

Cos 49 = y / 8

y = 8 cos 49

y = 5.25 km  

so the distance of the towns is 5.25 + 6.63 = 11.88 km

Hence, The solution is, the distance of the towns is 11.88 km.

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complete question:

An airplane is flying between two towns at an altitude of 8km. One town is to the west of the plane and the other is to the east. The angle of depression to one town in de34grees and to the other town is 49degrees. What is the distance between the two towns

The integer 8 represents the amount lost each time the pass was used.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that, every time Ezequiel rides the bus, money is deducted from the value of the pass.

He rode 9 times and $72 was deducted from the value of the pass.

Let x be the integer that represents the amount deducted each time.

The amount deducted after 9 times is 9x.

9x = 72

We have to divide 72 into 9 parts to know the value of x.

x = 72 / 9 = 8

Hence Ezequiel lost $8 each time the pass was used.

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If the slope of a staircase is 0. 95 and rises with 210, then the run is:

221.05 units.

In this problem, we can use the formula for the slope of a staircase, which is given by:

where "rise" is the vertical height of the staircase and "run" is the horizontal distance of the staircase.

We are given the slope of the staircase as 0.95 and the rise as 210. We can substitute these values in the formula and solve for the run:

Multiplying both sides by run, we get:

Dividing both sides by 0.95, we get:

Simplifying the expression, we get:

Therefore, the run of the staircase is approximately 221.05 units.

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The standard form of the quadratic function that represents the area of the garden is: G(x) = - 2x² + 20x

Mrs Miller has 20 ft of fencing to put around three sides of the garden.

Let us assume that l represents the length of the garden.

Here x represents the width of the rectangular garden.

So, l = 20 - 2x

We know that the formula for the area of rectangle is:

A = length × width

Let G(x) be a function that represents the area of the garden.

Using above formula,

G(x) = x × l

G(x) = x(20 - 2x)

G(x) = 20x - 2x²

G(x) = - 2x² + 20x

Therefore, the required quadratic function is: G(x) = - 2x² + 20x

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Find dthe complete question below.

The parcel is 30 acres in size, calculated as 10 acres for the NW 1/4 of the SE 1/4 and 20 acres for the S 1/2 of the SW 1/4 of the NE 1/4.

To solve the problem, we need to know the size of the quarter sections that are being referred to. In the United States, a quarter section is 160 acres.

Using this information, we can break down the given parcel as follows:

NW 1/4 of the SE 1/4: This represents 1/16 of a section, or 10 acres (160 acres / 16 * 1 = 10).

S 1/2 of the SW 1/4 of the NE 1/4: This represents 1/8 of a section, or 20 acres (160 acres / 8 * 1/2 = 20).

To find the total size of the parcel, we simply add these two areas together:

(10 + 20 )acres = 30 acres

Therefore, the parcel is 30 acres in size.

In the United States, a section of land is a unit of area measurement used in land surveys, and it is equal to 640 acres. A quarter section is, therefore, one-fourth of a section, or 160 acres.

The given parcel is described as two parts. The first part is the northwest quarter of the southeast quarter, which is equivalent to one-sixteenth of a section or 10 acres (1/4 x 1/4 x 160 acres = 10 acres).

The second part is the south half of the southwest quarter of the northeast quarter, which is equivalent to one-eighth of a section or 20 acres (1/4 x 1/4 x 1/2 x 160 acres = 20 acres).

To find the total size of the parcel, we add the area of the two parts: 10 acres + 20 acres = 30 acres. Therefore, the parcel is 30 acres in size.

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