⚠️URGENT⚠️


What is the relationship between Za and Zb?
A vertical angle
B complementary angle
C supplementary angle
D none of the above

Therefore, the ratio of the volumes of the two similar triangular prisms is approximately 1.25.

To find the ratio of the corresponding side lengths of the perimeters of the corresponding faces, we can take the square root of the ratio of the areas of the faces.

Given:

Area of first face = 49 cm²

Area of second face = 25 cm²

The ratio of the areas is:

49 cm² / 25 cm² = 1.96

Taking the square root of this ratio gives us the ratio of the corresponding side lengths:

√1.96 ≈ 1.4

Therefore, the ratio of the corresponding side lengths of the perimeters of the corresponding faces is approximately 1.4.

Now, let's find the ratio of the volumes of the two similar triangular prisms. Since the volumes of similar objects are proportional to the cubes of their corresponding side lengths, we can take the cube root of the ratio of the areas to find the ratio of the volumes.

The ratio of the volumes is:

∛(49 cm² / 25 cm²) = ∛1.96

≈ 1.25

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Answer:

Find the Central Angle from the Arc Length and Radius

You can also use the radius of the circle and the arc length to find the central angle. Call the measure of the central angle θ. Then: θ = s ÷ r, where s is the arc length and r is the radius.

Step-by-step explanation:

Answer:

47%

Step-by-step explanation:

47/100= 0.47

Answer:

2x - 7y > 10

8 + x > 5

3 < 5

Step-by-step explanation:

The equations are

Ax + By + C < 0 or Ax + By + C > 0

There is no equal in a linear inequality

The first option 2x + 8 = 10y is an equation, so it is wrong. The other 3 are correct!

To find (the derivative of \( y \) with respect to \( x \)) from the given function \( y = \ln(x^2) + \ln(x+3) - \ln(2x+1) \), we can apply the rules of logarithmic differentiation.

First, we can rewrite the function using logarithmic properties:

\(\( y = \ln(x^2) + \ln(x+3) - \ln(2x+1) = \ln(x^2(x+3)) - \ln(2x+1) \).\)

Now, using the rules of logarithmic differentiation, we can differentiate \( y \) with respect to \( x \) as follows:

\( \frac{dy}{dx} = \frac{1}{x^2(x+3)} \cdot (2x(x+3)) - \frac{1}{2x+1} \).

Simplifying further:

\(\( \frac{dy}{dx} = \frac{2x(x+3)}{x^2(x+3)} - \frac{1}{2x+1} \).\( \frac{dy}{dx} = \frac{2x^2 + 6x}{x^2(x+3)} - \frac{1}{2x+1} \).Thus, \( \frac{dy}{dx} = \frac{2x^2 + 6x}{x^2(x+3)} - \frac{1}{2x+1} \) is the derivative of \( y \) with respect to \( x \)\) for the given function.

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we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

Out of a whole population, a sample is a small part which is considered for any survey.  

The population in this case would be all the one-bedroom apartments available for rent near the college.

The sample would be the listings that Greg is looking at in the local newspaper and on the internet site.

Sample: listings in a local newspaper and on an Internet site              

Population: all available apartments near the college          

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The exponential function for the graph is obtained as y = 3^x.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

Assume that the plot of a function is in the form -

y =ab^x

where the horizontal asymptote is the x-axis.

To find a, look for the coordinate where the curve crosses the y-axis.

In the plot, it is seen that this happens at (0,1).

So, the value of a = 1.

To find b, look for the coordinate where the curve crosses the vertical line at x = 1.

In the plot, it is seen that this happens at (1,3).

Then, b is the number divided by a -

b = 3/1 = 3.

This plot is the curve -

y = 3^x

Therefore, the exponential function is y = 3^x.

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We can conclude that the special tutoring session seems to have had a positive impact on the students' performance, as their mean score increased from below 60% to 70%.

We can conclude that the special tutoring session has been effective since the students' mean score increased from 60 percent to 70 percent on the second test.

The students who scored less than 60 percent on the first test were given a special tutoring session, which resulted in their mean score increasing to 70 percent on the second test.

Therefore, we can conclude that the special tutoring session has been effective in improving the students' performance on the second test.

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If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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The solution to the system of equations is x = −2, y = ±√23.

Equation is a math statement that expresses two expressions with an equal sign. It is used to find the value of an unknown variable or unknowns. Equations are used in many branches of mathematics and science. For example, equations are used to calculate the force of gravity, the speed of light, the temperature of a gas, and the area of a triangle. Equations are also used to solve problems in physics, chemistry, engineering, and other disciplines. Equations are written in symbols and often involve multiple equations.

This system can be solved by solving the two equations separately.

For the first equation, xe^y+2e^y= 0, we can rearrange it to get xe^y = −2e^y. We can then divide both sides by e^y to get x = −2.

For the second equation, x² − 3x + y² = 19, we can plug in the value of x that we found previously, x = −2, and rearrange the equation to get y² = 23, and then solve for y by taking the square root of both sides, giving y = ±√23.

Therefore, the solution to the system of equations is x = −2, y = ±√23.

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Answer:

Step-by-step explanation:

Abc

The required coordinate of the fourth vertex is (c, c).

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

here,
A rectangle has vertices (a,b), (c,b), and (a,c)
let the vertex of the first coordinate be [x, y],
Now,
for side a Corrdiante A (a, b) and B (c , b)
Now, coordinate the opposite side C(a, c) and D(x , y)

The coordinates of D must be equal to x coordinate of B and y ordinate of C so,
D(x, y) = D(c, c)

Thus, the required coordinate of the fourth vertex is (c, c).

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Answer:

8*8 is the multiplication relatioship to that

Step-by-step explanation:

Answer:

8x8=64 which is the same to 8 +8 +8 +8 +8 +8 +8 +8

Step-by-step explanation:

Answer:

The numbers are 36 and 68.

Step-by-step explanation:

Let the smaller number be x.

"The larger number is four less than two times the smaller

number."

The larger number is

2x - 4

The sum of the numbers is x + 2x - 4, or 3x - 4.

"The sum of the numbers is 104."

3x - 4 = 104

3x = 108

x = 36

The smaller number is 36.

The larger number is 2x - 4, or

2x - 4 = 2(36) - 4 = 72 - 4 = 68

The larger number is 68.

Answer: The numbers are 36 and 68.

Answer:

∠FQD is 146°

Step-by-step explanation:

Because ∠P is on the same line as angle ∠Q, they are both corresponding angles meaning that they are equal so:

2x = 5x  - 51

Add 51 to both sides of the equation:

2x + 51 = 5x - 51 + 51

2x + 51 = 5x

Subtract 2x from both sides:

2x - 2x + 51 = 5x - 2x

51 = 3x

Divide both sides by 3:

\(\frac{3x}{3} = \frac{51}{3}\)

x = 17

Now we can calculate ∠FQE by substituting the known x into the equation:

5x-51

5(17) - 51 = 34

Now subtract this from 180 as all angles must add up to 180 on a straight line:

180 - 34 = 146

That means ∠FQD is 146°

Hope this helps!

In the following question, among the conditions given, {q1, q2} is a basis for the vector space of polynomials p(t) of degree at most two that satisfy the constraint p(2) = 0. In this particular case, we must enter our basis as [[1,0,-4],[0,1,-2]], since q1(t) = t^2 - 4 and q2(t) = t - 2.

To find a basis for the vector space of polynomials p(t) of degree at most two which satisfy the constraint p(2)=0, we can take the following steps:
1. Rewrite the polynomials as linear combinations of the form a + bt + ct^2
2. Use the constraint p(2) = 0 to eliminate one of the coefficients a, b, or c
3. Normalize the polynomials so that they are unit vectors
For example, if your basis is 1 + 2t + 3t^2, 4 + 5t + 6t2 then you can enter it as [[1,2,3],[4,5,6]].

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We are given a regression model: test score = 800 - 8(student-teacher ratio)

If the student-teacher ratio drops by 2, then the new ratio is (old ratio - 2).

So, the new predicted test score is:

test score = 800 - 8(new ratio)

          = 800 - 8(old ratio + (-2))

          = 800 - 8(old ratio) - 8(-2)

          = 800 - 8(old ratio) + 16

Therefore, the predicted effect on the test score is an increase of 16 points.

So, the answer is (d) the test score will increase by 16 points.

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Answer:

(3,4) (-3,-6)

Step-by-step explanation:

1--2 -3--7

-1-4 2-8

Answer:

I am going to say that it is option A.

Step-by-step explanation:

I hope this helped out a lot!

The simple interest that Su Young paid for borrowing $2,900 for 15 months at 5.5% per year is $199.375.

Simple interest is interest that is not compounded.

Compounding involves adding earned interests to the principal when computing the next period's interest.

Principal = $2,900

Period = 15 months or 1.25 years

Interest Rate = 5.5%

Simple interest amount = Principal x Period x Rate

= $199.375 ($2,900 x 1.25 x 5.5%)

Thus, based on simple interest, Su Young paid $199.375.

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No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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Answer:

¾x + 7

Step-by-step explanation:

"The sum of": Addition expression

"¾ of a number": ¾x

"and 7": + 7

Combine them all and you get ¾x + 7

The recursive formula for the problem remaining after each monthly payment can be found using the formula:

B(n) = (1 + r/12) * B(n-1) - p

where B(n) represents the balance remaining after the nth payment, r is the annual interest rate (6.5%), p is the monthly payment ($758.48), and n is the number of payments made.

After the first payment, the balance remaining can be calculated using the formula:

B(1) = (1 + 0.065/12) * 120000 - 758.48 = 119241.21

Using a spreadsheet or graphing utility, a table can be constructed to show the balance after each monthly payment. The table will start with B(0) = 120000 and will have a column for the payment number, the balance remaining after each payment, and the interest paid each month. The table will continue until the balance is paid off.

To determine when the balance will be below $75,000, we can look at the table and find the payment number where the balance first drops below $75,000. This occurs at payment number 248.

To

determine

when the balance will be paid off, we can continue

looking

at the table until the balance reaches zero. This occurs at payment number 360.

The interest

expense

when the loan is paid can be found by adding up the total amount of payments made and subtracting the original loan amount. The total payments made will be $758.48 * 360 = $273,052.80. The interest expense will be $273,052.80 - $120,000 = $153,052.80.

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Answer: 4.15

Step-by-step explanation:

a. The equilibrium price and quantity are 0.42 million litres and  136 cents per litre respectively. The monthly revenue for milk producers without government intervention is $5.712 million.

b. The quantity supplied and the quantity demanded at the guaranteed price are  0 million litres and 1.0897 million litres respectively.

a. To find the equilibrium price and quantity in the market for milk in Saskatchewan, we need to equate the demand and supply equations:

Demand: p = 220 - 200q

Supply: p* = 10 + 300q

Setting p equal to p*, we have:

220 - 200q = 10 + 300q

Combining like terms:

500q = 210

Dividing both sides by 500:

q = 0.42 (rounded to two decimal places)

So the equilibrium quantity is 0.42 million litres.

Substituting this value back into either the demand or supply equation, we can find the equilibrium price:

p = 220 - 200(0.42)

p = 136 (rounded to the nearest cent)

Therefore, the equilibrium price is 136 cents per litre.

To calculate the monthly revenue for milk producers without government intervention, we multiply the equilibrium quantity by the equilibrium price:

Revenue = 0.42 million litres * 136 cents per litre

Revenue = $5.712 million (rounded to one decimal place)

So the monthly revenue for milk producers without government intervention is $5.712 million.

b. If the government guarantees a price of $2.06 per litre, we can set this price equal to the supply equation and solve for the quantity supplied:

2.06 = 10 + 300q

Subtracting 10 from both sides:

300q = 2.06 - 10

300q = -7.94

Dividing both sides by 300:

q = -0.0265 (rounded to four decimal places)

Since quantity cannot be negative, the quantity supplied at the guaranteed price is 0 million litres.

To find the quantity demanded, we can substitute the guaranteed price into the demand equation:

p = 220 - 200q

2.06 = 220 - 200q

Subtracting 220 from both sides:

-217.94 = -200q

Dividing both sides by -200:

q = 1.0897 (rounded to four decimal places)

So the quantity demanded at the guaranteed price is 1.0897 million litres.

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Answer: X = -12

Step-by-step explanation:

-4x-16=32

We move all terms to the left:

-4x-16-(32)=0

We add all the numbers together, and all the variables

-4x-48=0

We move all terms containing x to the left, all other terms to the right

-4x=48

x=48/-4

x=-12

Answer:

x=12

Step-by-step explanation:

Given,

4x-16=32

4x=32+16(We transpose LHS to RHS)

4x=48

x=48/4

x=12

Hence, the answer is 12

Answer:

let

s = the number of stools bought, s is integer

c = the number of chairs bought, c is integer

they need to buy 25 more chairs than stools

c = s + 25 => s = c - 25

the chairs cost $32 each and the stools cast $28 each and the budget is $2,620

32c + 28s <= 2620

if i plug s = c - 25 in the above inequality i get

32c + 28(c - 25) <= 2620

by solving the inequality we find

c <= 55.33

since c is integer we can write c<=55

they can buy 55 chairs the most.