Triangular prism B is the image of triangular prism A after dilation by a scale factor of 1/5
. If the surface area of triangular prism B is 3 m^2 2, find the surface area of triangular prism A, the preimage.

Answer:

Step-by-step explanation:The given equations are :

y=-x+2  ....(1)

y = -4x +7 ....(2)

From equation (1) and (2)

-x+2 = -4x +7

Taking like terms together

-x+4x=7-2

3x = 5

x = 1.667

Put the value of x in equation (1)

y=-(1.667)+2

y = 0.333

The solution of the equations are (1.667,0.333). The attached figure shows the graph for the equations.

Step-by-step explanation: The given equations are : y=-x+2 ....(1) y - 1

Answer:

10

Step-by-step explanation:

85+15 is 100

the square root of 100 is 10

Answer

Tha answer is 10 type xhii

Step-by-step explanation:

hope this helps and hope you pass

have a great day/night

Solution of the given equation is r = 2

Equations are mathematical statements that shows equality, containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Given equation,

8π = 1/3πr²×6

⇒ 2r² = 8

⇒ r² = 8/2

⇒ r = √4

⇒ r = 2

Hence, r = 2 is solution for the given equation.

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The correlation coefficient with the correct association is listed as:

-0.86  = 1

-0.66 = 1

-0.01 = 2

0.52 = 3

0.93 = 1

Correlation is a statistical measure that describes the extent to which two variables are linearly related to each other.

A negative correlation is when two variables move opposite each other i.e. when one variable increases, the other decreases

For  absolute values of the correlation coefficient:

0-0.19 => very weak

0.2-0.39 => weak

0.40-0.59 => moderate

0.6-0.79 => strong

0.8-1 => very strong

Thus, the matching is listed below:

-0.86  = strong

-0.66 = strong

-0.01 = weak

0.52 = moderate

0.93 = strong

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Answer:

4 tons

Step-by-step explanation:

A ton weights 2000 pounds.

The number of tons of cargo the truck carry is 36300 tons.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

Weight= 8000 pounds

Now,

We can do:

20008000​=4

The truck carries 4 US tons of cargo.

Similarly, if we want to use the imperial ton or the metric ton, we can do:

22408000​≈3.57

2204.62268000​≈3.63

Therefore, by unitary method the answer will be 36300 tons.

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Answer:

None of these since it is not a polynomial expression

Answer:

112 in

Step-by-step explanation:

Before starting, it is important to know that lateral surface area is the sum of the area of all sides of a figure, not including the bases. Now that that is established, attached is an image with how to find the lateral surface area:

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The amount in the account after 18 years will be about $24,459.2.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Final amount in a compound interest can be calculated as,

A = P (1 + [tex]\frac{r}{n}[/tex] ) ^ (n t)

Here, A is the final amount, P is the principal amount, n is the number times interest is compounded in a year, r is the rate of interest and t is the time in years.

Here, P = $10,000

r = 5% = 0.05

n = 4, since the compounding is quarterly

t = 18 years

Substituting,

A = 10,000 (1 + [tex]\frac{0.05}{4}[/tex])^ (4 × 18)

  = 10,000 (1.0125)⁷²

  = 24,459.2

Hence there will be an amount of $24,459.2 in the account after 18 years.

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Answer:

C

Step-by-step explanation:

It's the only graph that doesn't constantly have its y value increasing the same value each time.

(2 to 6 is +4, 6 to 10 is +4, but 10 to 16 is not +4)

Answer:

C

Step-by-step explanation:

Because you see from Point (-4, 2) to (0,6), the y increases by 4, and the x increase by 4. Same thing from (0,6) to (4,10). But from (4,10) to (8,16) the y increase by 6 so it is the wrong slope.

Answer: D. 121.5

Step-by-step explanation: Use the formula [tex]\frac{4}{3}[/tex]×[tex]r^{3}[/tex], (where r is the radius, as in this case the diameter is 9 so divide that by 2 and you get the radius) and the "unit" is π. Search math w ay on the internet for any further math questions. :)

1) The new coordinate of the triangle is gotten by the transformation rule; 180° counterclockwise

2) The coordinates of the point T' are; T'(2, 8)

1) The coordinates of the triangle XYZ are;

X(1, 2), Y(3, 5), Z(-3, 4)

The coordinates of the transformed triangle X'Y'Z' are;

X'(-1, -2), Y'(-3, -5), Z'(3, -4)

The transformation rule here is; (x, y) → (-x, -y)

This is a rotation of 180 degrees counterclockwise about the origin

2) The coordinates of the line are given as;

S(6, -1) and T(2, -8)

A rotation of 210° clockwise gives the transformation rule:

(x, y) → (x, -y)

Thus, we have the new coordinate of T as; T'(2, 8)

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Answer:

[tex]y=\dfrac{1}{2}x + 1[/tex]

Step-by-step explanation:

In this question, we are asked for an equation for the graphed line, given the following information about it:

-its slope (rate of change) is 1/2

-its y-intercept (initial value) is 1

We can plug these values into the slope-intercept form equation:

[tex]y=mx+b[/tex]

where [tex]m[/tex] is the line's slope, and b is its y-intercept.

Hence,

[tex]y=\dfrac{1}{2}x + 1[/tex]

The range of the given function would be -

Range → {-2, 3, 5, 6}

An function in mathematics defines a relationship between one variable (the independent variable {x})  and another variable (the dependent variable {y}). Example → y = f{x} = ax + b.

Given is the graph of the function as shown in the image.

Range represents the set of values along the {y} - axis. So, we can write the range as -

Range → {-2, 3, 5, 6}

Therefore, the range of the given function would be -

Range → {-2, 3, 5, 6}.

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Answer:

it is b y=7 done okays hope you like it

Answer:
B, y = 7.

Step-by-step explanation:
If 6y = 42, then all we have to do is divide both sides by 6.

Therefore,
y = 42/6
y = 7.

The type of sample is a Simple Random Sample.

Hence, option (C) is correct choice.

Simple random sampling is a form of probability sampling in which a selection of participants is chosen at random from a population. Each person in the population has an equal probability of getting chosen.

Using basic random sampling allows researchers to generalise about a certain demographic while eliminating bias. Inferences and predictions about the population can be formed using statistical techniques without having to survey or gather data from every individual in that population.

A Simple Random Sample is a sort of random sample in which every member of the population has an equal probability of being chosen. In this situation, every one of the 40 students has an equal chance of being chosen, making this a simple random sample.

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The direct variation equation in the form x and y is y = 7.25x

As per the given data, the cost of renting a scooter y varies directly with the number of hours the scooter is rented x.

Suppose it costs $21.75 to rent the scooter for 3 hours.

Here we have to determine a direct variation equation in the form of y.

The renting cost (y) is directly proportional to the hours (x).

y ∝ x

y = kx.....(1)

Here k is known for the proportionality constant

From the given information we can find the value of k.

21.75 = k (3)

k = [tex]$\frac{21.75}{3}[/tex]

k = 7.25

Now we have to substitute the value of k in the equation (1)

We get:

y = 7.25x

Therefore a direct variation equation is y = 7.25x.

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The volume of the solid with the semicircular base is equal to 2250π units³

In general term integral value means the value obtained after integrating or adding the terms of a function which is divided into an infinite number of terms .

Given here: A solid with a semi circular base with radius = 15 units

We know the the equation of the circle with its center at the origin is given by

x²+y²=15²

[tex]y=\sqrt{15^2-x^2}[/tex]

Thus constructing the integral we get

 [tex]\int\limits^{15}_{-15} \ \pi .\frac{1}{2}.( {15^2-x^2}} )\, dx[/tex]

=-πx.(x²-675) /6 +C |¹⁵₋ ₁₅

=2250π

Hence, The volume of the solid with the semicircular base is equal to 2250π units³

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The slice was made perpendicular to the face BCEH.

The right rectangular prism has four rectangle-shaped lateral faces and two parallel end faces that are perpendicular to each of the bases. Parallelograms make up the faces of an oblique prism, a non-right rectangular prism. Another name for a right rectangular prism is a cuboid.

Given, The right rectangular prism in Figure has been sliced with a plane perpendicular to BCEH.

ZY = 6 inch

If we focus on ∠X of the slice, since it is a right angle, we know that WX must be perpendicular face to BCEH.  Wx lies in face of ABCD, which is perpendicular to both BCEH and ABCD, so WX is perpendicular to ABCD.

This means that WX must also be perpendicular to WZ.  A similar argument can be made for ∠Yof the slice, making all four angles of WXYZ right angles and making WXYZ a rectangle.

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Let's call the two-digit number "x" and its two digits "a" and "b".

We know that:

x = 5 * (a + b)

We also know that the reverse of x is 9 times greater than x:

x + 9 * x = 100 * a + 10 * b

Expanding x using the first equation:

10 * x = 5 * (a + b) + 9 * 5 * (a + b) = 100 * a + 10 * b

Combining like terms:

10 * x = 100 * a + 10 * b

Solving for x:

x = 10 * a + b

Since x is a two-digit number, 10 * a + b must be between 10 and 99. The only solution that meets this requirement is a = 5 and b = 6. Therefore, the number is 56.

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A “full house” (3 cards of one kind and 2 cards of another kind)

Since there are 13 sets of each type, we have to select any 2 kinds of it.

The probability becomes : 2× ¹³C2 × ⁴C3 × ⁴C2 : ^52C5

On simplification,

= 3744 / 2598960

= 0.00144

So the probability of a “full house” is 0.00144.

Probability is a measure of the probability that an event will occur in future. Probability is expressed between 0 to 1 or in percentage".

There are three important things in discussing probability, namely trials (experiment), result (outcome). and events.

For example, the activity of tossing coins will result in the appearance of images or numbers, the activity of buying and selling shares will result in buying or selling events.

So the outcome is all the possible events that will occur as a result of an experiment or activity.

Events show the results that occur from an event. In every experiment or activity there is only one possible outcome. In the activity of buying and selling shares, if you don't buy, it means selling. When prices change, inflation or deflation occurs.

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The sample of 100 students is a simple random sample (SRS) of the population of all students, and it provides evidence about the proportion of students who completed their assigned homework last week.

The sample proportion of students who completed their assigned homework is calculated as the number of students in the sample who completed their homework divided by the total number of students in the sample.

If the sample proportion is less than 60%, then this is evidence that less than 60% of all students completed their assigned homework last week. However, it is important to keep in mind that the sample proportion is just an estimate of the population proportion, and it may not be exactly equal to the population proportion. The sample proportion can vary from sample to sample due to random sampling error.

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Answer:

2

Step-by-step explanation:

The solution set of the inequality is the graph B.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

The given inequality is 3x > 12.

We have to solve the inequality.

3x > 12

Dividing both sides of the inequality by 3, we get,

3x / 3 > 12 / 3

x > 4

Solution set contains all points greater than 4, but not 4.

This solution set is shown in the graph B with the open circle at point 4.

Hence graph B shows the solution set of the inequality.

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A ratio that compares the number of loaves of rye bread to the number of loaves of wheat bread is 3:8.

A ratio is a relative size of a value compared to another.

Ratios are given as quotients from division operations between the numerators and the denominators.

Ratios can also be represented as fractional values using decimals, fractions, and percentages.

Most often, the ratio symbol (:) is used to depict the numerical relationships between values.

The number of loaves of wheat bread = 8

The number of loaves of rye bread = 3

The ratio to describe and compare the number of loaves of rye bread to the number of loaves of wheat bread is 3:8

The sum of ratios = 11 (3 + 8).

Thus, relatively, the restaurant worker used 3 loaves of rye bread and 8 loaves of wheat bread to make the sandwiches.

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This system of equations has been solved graphically and by using substitution: it has infinitely many solutions.

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x = 3y + 2     ......equation 1.

5x - 15y = 10     ......equation 2.

By substituting equation into equation 2, we have the following:

5(3y + 2) - 15y = 10

15y + 10 - 15y = 10

15y - 15y = 10 - 10 (infinitely many solutions)

Based on the graph (see attachment), we can logically deduce that the given system of equations has infinitely many solutions.

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(a) opp(A) = 17

(b) adj(A) = 8

(c) The hypotenuse can be found using the Pythagorean theorem: c^2 = a^2 + b^2.

c^2 = 8^2 + 17^2 = 64 + 289 = 353

c = √353 = 19

(d) cos(A) can be found using the formula: cos(A) = adj(A) / hypotenuse = 8 / 19 = 4 / 9

(e) tan(A) can be found using the formula: tan(A) = opp(A) / adj(A) = 17 / 8 = 9 / 4

Trigonometry is a branch of mathematics that deals with the study of triangles and their properties. It is primarily concerned with the relationships between the angles and sides of a triangle, and how these relationships can be used to solve problems. The key concepts of trigonometry include angles, degrees, radians, sine, cosine, tangent, cotangent, secant, and cosecant.

In trigonometry, the sine, cosine, and tangent functions are defined for any angle and can be used to calculate various quantities in a triangle, such as the length of a side or the size of an angle. Trigonometry has numerous applications in fields such as astronomy, physics, engineering, and computer graphics.

One of the most important uses of trigonometry is in navigation and surveying, where it is used to calculate distances, angles, and other quantities in order to determine the position of objects and landmarks. Additionally, trigonometry is used to analyze wave patterns in areas such as sound and light waves, as well as in the design of systems that require precise calculations such as radio and radar systems.

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The Speed at which Nick paddles is 13.60 miles per hour.

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here: Nick's speed= S and the current is flowing at a rate of 5 miles per hour.

Now it is given that the it takes 30 minutes longer to row upstream than down stream.

Thus we can construct the equation

8/S-5 -8/S+5 = 30 minutes or 1/2 hour

Where 8 is the distance

Thus solving for S we get

8S+40-8S+40 / S²-25 =1/2

80×2=S²-25

160=S²-25

S²=185

S=13.60 miles per hour

Hence, The Speed at which Nick paddles is 13.60 miles per hour.

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There were 34 mosquitoes on 2 June, the date when the mosquito population is 46000 is 22985 days into June and  the mosquito population on 30 June was 59.

Two or more expressions with an Equal sign is called as Equation.

For 0 ≤ t ≤ 10:

N = 2t + 30 for 0 ≤ t ≤ 10.

The table of values are:

t   0    1    2   3   4   5    

N 30 32 34 36 38 40

The graph will be a line with a positive slope, increasing from N = 30 when t = 0 to N = 50 when t = 10.

The number of mosquitoes on 2 June can be found by using t = 2 in the formula.

N = 2(2) + 30 = 34.

So there were 34 mosquitoes on 2 June.

(ii) To find the date when the mosquito population is 46 000, we can use the formula and solve for t.

N = 2t + 30

46000= 2t + 30

Subtract 30 on both sides

2t =  45970

t=22985

So the date when the mosquito population is 46000 is 22985 days into June.

iii) To find the mosquito population at the end of June, we need to find the population on 10 June and then increase it by 18%.

The population on 10 June can be found by using t = 10 in the formula:

N = 2(10) + 30 = 50

The graph will be a line with a positive slope, increasing from N = 30 when t = 0 to N = 50 when t = 10.

N = 50 (1 + 0.18)

N=59

So the mosquito population on 30 June was 59.

Hence,  there were 34 mosquitoes on 2 June, the date when the mosquito population is 46000 is 22985 days into June and  the mosquito population on 30 June was 59.

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The linear equation shows a proportional relationship is y = 2x.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the equation to find the linear equation shows a proportional relationship,

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Particularly, when the y-intercept is equal to zero:

y = a*x

We get a proportional relationship.

so the option for the proportional relationship is

y = 2x

Hence option D is correct.

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