Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle with sides of 6 cm, as shown. The sum of the perimeters of the three small triangles is equal to the perimeter of the remaining grey hexagon. What is the side length of the small triangles?

The gopher’s new elevation relative to the surface of the ground will be

13¹/₄ inches.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that a gopher is in a hole that is 6¹/₄ in. below the surface of the ground. and, Then digs 7¹/₂ in. deeper.

The gopher’s new elevation relative to the surface of the ground will be calculated as;

⇒  6¹/₄ + 7¹/₂

⇒ 25/4 + 15/2

Make denominators the same as;

⇒ 25/4 + 30/4

⇒ (25 + 30) / 4

⇒ 55 / 4

⇒ 13¹/₄ inches.

Thus, the gopher’s new elevation relative to the surface of the ground will be 13¹/₄ inches.

The complete question is given below,

A gopher is in a hole that is 6 1/4 in. below the surface of the ground. It then digs 7 1/2 in. deeper. What is the gopher’s new elevation relative to the surface of the ground? Show your work.

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The overall profit of what Stuart sold is 52 dollars.

Stuart sold 8 couches and 11 armchairs at his furniture store yesterday and he made a 10 dollars loss on each couch and a 12 dollars profit on each armchair.

Therefore, the overall profit or loss can be calculated as follows:

Total loss on the couch = 8 × 10 = 80 dollars

Total profit on the armchairs = 11 × 12 = 132 dollars

Therefore,

Overall profits = 132 - 80

Overall profits = 52 dollars

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A and B are independent events if, the probability of getting a red convertible is 0.10

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, in a video game, the probability of getting a red car is 0.25 (event A), and the probability of getting a convertible is 0.40 (event B).

We need to identify the condition for events A and event B being independent events.

We know that,

The events in probability two are independent if event one does not affect the other one.

The formula for independent events =

P(A∩B) = P(A) x P(B).

So,

P(A) = 0.25 and P(B) = 0.40

P(A∩B) = P(A)xP(B)

= 0.25 x 0.4

= 0.10

Hence, the events A and B are independent events if, the probability of getting a red convertible is 0.10

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The length of the segment AC is 40 units

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

The quadrilateral ABCD is a rhombus

The diagonals of rhombus bisect each other

Using the above as a guide, we have the following:

AC = 2 * EC

Substitute the known values in the above equation, so, we have the following representation

AC = 2 * 20

Evaluate

AC = 40

Hence, the length is 40 uints

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The vector and parametric equations are r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)] and x = t/2, y = -1 + 4t/3, z = 1 - 3t/4.

We have P(0, -1, 1), Q(1/2, 1/3, 1/4)

We have to find a vector equation and parametric equations for the line segment that joins P to Q.

Vector equation of a line segment joining the points with position vectors r0 and r1 is given by

r =(1 - t)r0 + tr1

Where, t ∈ [0, 1]

Here, r0 = (0, -1, 1) and r1 = (1/2, 1/3, 1/4)

So, r(t) = (1 - t)(0, -1, 1) + t(1/2, 1/3, 1/4)

r(t) = [((1 - t)(0) -1(1 - t) + 1(1 - t)] + [t/2, t/3, t/4]

r(t) = [0, (t - 1), (1 - t)] + [t/2, t/3, t/4]

On simplification,

r(t) = [(t/2 + 0), (t + t/3 - 1), (1 - t + t/4)]

r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)]

Where, t ∈ [0,1]

The parametric equations for the line segment are

x = t/2, y = -1 + 4t/3, z = 1 - 3t/4

Where, t ∈ [0, 1]

Therefore, the vector and parametric equations are r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)] and x = t/2, y = -1 + 4t/3, z = 1 - 3t/4.

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The given question is incomplete, complete question is:

Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, - 1, 1), Q(1/2, 1/3, 1/4).

The expression [tex](3 \times 5)^4[/tex] is equivalent to 10+5 to the fourth power.

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To find equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.

We need to find the expression into an equivalent form 10+5 to the fourth power

Therefore,

This expression 10+5 to the fourth power could also be given as;

10 + 5 = 15

That is [tex]15^4[/tex]

We can also write as;

[tex](3 \times 5)^4[/tex]

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The apartment can accommodate 24 people if each person requires 5 cubic meters of air space.

Solution:

Given,

Dimension of apartment

l = 8m

b = 5m

h = 3m

So, the volume of the apartment will be,

l*b*h = 8*5*3 = 120 cubic meters

Each person requires 5 cubic meters of air space,

Hence, the total number of persons = 120/5 = 24

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Simplified form of the polynomial -4(2a+7)+3a+18 is -5a - 10. It is a binomial.

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given expression,

-4(2a+7)+3a+18

using distributive property

-4(2a) -4(7) + 3a + 18

-8a - 28 + 3a + 18

Solving like terms

-5a - 10

The solved polynomial is a binomial, since it has two terms.

Hence, simplified form of the given polynomial is -5a - 10, it is a binomial

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Answer:10 or 25

Step-by-step explanation:

just add both  or times them

5+5 or 5x5

The distance traveled by the ping-pong ball as it rolls forward 6 meters and bounces backward 3 meters is 3 meters.

Distance is a concept that is important to understand in physics and mathematics. It refers to the amount of space between two points. In this scenario, we will be discussing the distance traveled by a ping-pong ball as it rolls forward and bounces backward.

When the ping-pong ball rolls forward, it covers a distance of 6 meters. This can be represented mathematically as d1 = 6 meters.

When the ball bounces backward, it covers a distance of 3 meters. This can be represented as d2 = -3 meters which means the negative sign indicates that it is moving in the opposite direction.

The total distance traveled by the ball can be found by adding the distance traveled in each direction. This can be represented as

=> d = d1 + d2 = 6 + (-3) = 3 meters.

In other words, the total distance traveled by the ball is 3 meters, which is the net distance covered after taking into account both the forward and backward movements.

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Answer:

The answer is: y=4+3x

Step-by-step explanation:

I know this because I believe we are solving for the system of equations or solving by the system of subtraction.

I will say I am not completely sure this is right but I hope I helped out a little :)

The relative frequency is the proportion of the total numbers in a data set corresponds to a specific class interval and hence summing over all the relative frequencies must add up to 1, or 100%.

The frequency distribution table is made by building the class intervals of the raw data set, specifically when too many values are occurring many times; we group similar values in the same category, according to a pre-determined range of values. It is a two-column table in which the first column consists of class intervals and the second consists of the frequency corresponding to each interval.

The frequency distribution is made when the raw data is large and when the same number is repeated many times, that is where the concept of frequency comes into play.

Since, the frequency is the count of specific numbers in a data set, the sum of all frequencies corresponding to every class interval has to be the total number of values in the data set.

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The given question is incomplete, complete question is:

What is the sum of all frequencies in a frequency distribution? and why is the sum of all relative frequencies equal to 1?

Answer: 125.4

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187/17 is 11, so x = 11. Substituting 11 in for x gives you 93 for the measure of angle Q and 87 for the measure of angle R.

Answer:

50%

12.5%

1%

10%

37.5%

87%

Answer:

27)50%

28)12.5%

29)1%

30)10%

31)38.4%

32)87%

Answer:

$1,489.88 (nearest cent)

Step-by-step explanation:

To calculate gross pay, multiply the number of hours worked by the pay per hour.

Warren worked 36.5 hours one week and 32 hours the week before.

Therefore, the total number of hours Warren worked was:

Multiply the total number of hours worked by Warren's rate of pay of $21.75 per hour:

Therefore, Warren's gross pay for the two weeks was $1,489.88 (nearest cent).

Answer:

$1489.875

Step-by-step explanation:

Warren's gross pay for 36.5 hours last week can be calculated as follows:

Gross pay for 36.5 hours = $21.75/hour * 36.5 hours = $793.875

Similarly, Warren's gross pay for 32 hours the week before can be calculated as follows:

Gross pay for 32 hours = $21.75/hour * 32 hours = $696

Adding the gross pay for the two weeks, we get:

Gross pay for 2 weeks = $793.875 + $696 = $1489.875

The length of the shadow of the maple tree will be 15 meters.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

A shadow 30 meters long is cast by a fir tree that is 16 meters tall. If a nearby maple tree is 8 meters tall.

Let 'S' be the shadow of the maple tree. Then the equation is given as,

16 / 30 = 8 / S

0.533 = 8 / S

S = 8 / 0.533

S = 15 meters

The length of the shadow of the maple tree will be 15 meters.

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The coordinates of P are (-0.82, 3.56).

The coordinates of M are (-2.1, -2.2).

The midpoint of a line segment is written as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) are the coordinates of the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

R = (4.3, 7.4)

T= (-8.5, -2.2)

S = (4.3, -2.2)

Segment RT is divided into 5 equal parts.

So,

TP : PR = 3 : 2 = m : n

The coordinates of P.

T= (-8.5, -2.2) = (a, b)

R = (4.3, 7.4) = (c, d)

x = [tex]\frac{mc + na}{m + n}[/tex]

x = [tex]\frac{3\times4.3 + 2\times-8.50}{5}[/tex]

x = [tex]\frac{12.9 - 17}{5}[/tex]

x = [tex]\frac{-4.1}{5}[/tex]

x = -0.82

And,

y = [tex]\frac{md + nb}{m + n}[/tex]

y = [tex]\frac{3\times7.4 + 2\times-2.2}{5}[/tex]

y = [tex]\frac{22.2 - 4.4}{5}[/tex]

y = 3.56

The coordinates of P are (-0.82, 3.56).

Now,

T= (-8.5, -2.2)

S = (4.3, -2.2)

M is the midpoint of TS.

So,

M = (x, y)

x = [tex]\frac{(4.3 - 8.5)}{2}[/tex] = [tex]\frac{x-4.2}{2}[/tex] = -2.1

y = [tex]\frac{-2.2 - 2.2}{2}[/tex] = [tex]\frac{-4.4}{2}[/tex] = -2.2

M = (x, y) = (-2.1, -2.2)

Thus,

The coordinates of P = (-0.82, 3.56).

The coordinates of M = (-2.1, -2.2).

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Answer:

The answer is (-3.38,1.64),(-0.82,-2.2)

Step-by-step explanation:

I just got it right on the test

Answer:

21

Step-by-step explanation:

21

Applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

The ratio of the corresponding sides two triangles that are similar to each other are the same/equal.

here, we have,

Given that ΔABC and ΔDEF are similar triangles, therefore:

Let, a = 6, b = 8, and c = 12 be the sides of ΔABC.

Let, x, y, and z be the sides of ΔDEF.

Let z = 18

Thus:

a/x = b/y = c/z

Substitute

6/x = 8/y = 12/18

Find x using 6/x = 12/18:

6/x = 12/18

Cross multiply

x = 18*6/ 12

x = 9

Find x using 8/y = 12/18:

8/y = 12/18

Cross multiply

x = 18*8/12

x = 12

Therefore, applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

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The option representing the solution of the inequality is given as follows:

D) There are no solutions.

The inequality for this problem is defined as follows:

-6x + 14 < -28 and 3x + 28 < 25.

The and operation means that we must solve each inequality, and then obtain the intersection of the two solutions.

The solution to the first inequality is given as follows:

-6x + 14 < -28

6x - 14 > 28

6x > 42

x > 7.

The solution to the second inequality is given as follows:

3x + 28 < 25.

3x < -3

x < -1.

There is no intersection between x > 7 and x < -1, hence the system has no solutions.

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By using the formula that connects the linear velocity to the angular velocity, we may convert metres per second (m/s) to radians per second (rad/s).

Using the formula that connects the linear velocity to the angular velocity, we may convert metres per second (m/s) to radians per second (rad/s).

The equation reads: Radius divided by linear velocity gives you the angular velocity (). (r) where R is in metres, V is in m/s, and is in rad/s.

Direct conversion from m/s to rad/s is not possible if the radius is omitted. The aforementioned formula can be used to determine the missing value and then convert m/s to rad/s if you know the radius or the angular velocity. You can use the formula to determine the angular velocity in rad/s, for instance, if you know the linear velocity v in m/s and the radius r in metres.

ω = v / r

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Since, 01 kilogram is approximately equal to 2.2046226218 lbs.

Therefore, 65 Kilogram is 143.3 lbs.

Pound:

Pound is the name of a series of units of mass ranging from 300 to 600 grams. It refers to an avoirdupois pound (454 grams), most commonly divided by 16 avoirdupois ounces.

Kilogram:

The kilogram or kilogram (symbol: kg) is the basic unit of mass in the SI system. It is defined equal to the mass of the International Prototype in kilograms. It is the only SI base unit that uses prefixes and is still defined in terms of artifacts rather than basic physical properties. A kilogram is equivalent to £2.205 in the English system used in the United States.

According to the Question:

To find how many pounds are in kilograms, you can convert kg to pounds using this formula:

X(lb) = Y(kg) / 0.45359237

Now,

Converting 65 kg to lbs:

To convert 65 kg to pounds:

⇒ X(lbs) = 65(kg) / 0.45359237

⇒ 143.3005 lbs

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In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. So , the correct option is C.

In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. The mean and median are both measures of the central tendency of a distribution and in a symmetrical distribution, they are the same value.

Option (a) is false because the range is the difference between the largest and smallest values in a distribution, whereas the interquartile range is the difference between the first quartile (25th percentile) and the third quartile (75th percentile), which are measures of variability.

Option (b) is false because the interquartile range is always smaller than the mean in any distribution, symmetrical or not.

Option (d) is false because in a symmetrical distribution, the variance and standard deviation may be equal, but this is not always the case.

So , the correct option is c.

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The area of the shape for the quilt block is 166.5 in²

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape

Given that, a quilt has blocks of design on it, we need to find the area of the block,

To find the area of the block = sum of the areas of the right triangle and the rectangle,

Area of the block = 16 × 9 + 6 × 7.5 × 1/2 = 166.5 in²

Hence, the area of the shape for the quilt block is 166.5 in²

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The figure is unavailable is the question is solved for the figure attached

True (but a parallelogram is not always a square). This is because a parallelogram is a quadrilateral with 2 pairs of parallel sides, and a square fits the requirements.

The number of mice needed is given as follows:

a) 10 snakes: 23 mice.

b) 6 snakes: 15 mice.

c) x snakes: (3 + 2x) mice.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For every feeding, she needs three mice and an additional two mice for each snake, hence the slope and the intercept of the function are given as follows:

m = 2, b = 3.

The function is then defined as follows:

y = 2x + 3.

For 10 snakes, the number of mice is given as follows:

y = 2(10) + 3

y = 23 mice.

For 6 snakes, the number of mice is given as follows:

y = 2(6) + 3

y = 15 mice.

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