Two armadillos and three aardvarks sat in a five-seat row at the Animal Auditorium. What is the probability that the two animals on the ends of the row were both armadillos or both aardvarks?

Answer:

The answer to your question is 6.- B    7.- D

Step-by-step explanation:

Data

Parallelogram ACFG

6.-

m∠GAC = 112°

m∠ACF = ?

Process

These angles are supplementary, they measure the same.

                  ∠GAC + ∠ACF = 180

-Substitution

                      112 + ∠ACF = 180°

-Solve for ∠ACF

                      ∠ACF = 180° - 112°

-Result

                      ∠ACF = 68°

7.-

m∠AGF = 2a + 10

m∠ACF = a + 20

The angles ∠GAC and ACF are equal, they measure the same.

                   ∠GAC = ∠ACF

-Substitution

                   a + 20 = 2a + 10

-Solve for a

                   a - 2a = 10 - 20

-Result

                   -a = -10

                    a = 10

-Find ∠AGF

      ∠AGF = 2(10) + 10

                 20 + 10

                = 30°

Answer:

Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let x represent the greatest number of games he can bowl.

Many goes bowling, he spends 4.25 for rent shoes and spends 2.50 for each game he bowls. It means that the amount that he would spend in bowling x games is

4.25 + 2.5x

If he has 25.00 to spend, then the inequality that Manny can use to determine the greatest number of games he can bowl is

4.25 + 2.5x ≤ 25

Answer:  7 yards will be your answer.

Step-by-step explanation:  I tried.  Sorry if the answer is wrong!

Answer:

8 yards

Step-by-step explanation:

The small triangle is inside the big triangle and shares two of it's legs which means it is similar to the big triangle.

12:15

x:10

4:5

x must be 8

In this scenario, a bungee jumper's total distance traveled can be calculated using a geometric series. The initial drop is the bridge's total height, and each following jump is 75% of the previous one. Summing this series gives the total downward and upward travel.

This problem is a classic example of a geometric series used in mathematics. The first downward travel is the entire height of the bridge, 876 feet. Each consecutive downward travel will be 75% of the previous downward travel, as the question specifies that the jumper rebounds 75% of the distance fallen.

For the downward distance after 10 jumps, you sum the geometric series with first term (a) of 876 feet, common ratio (r) of 0.75, and n terms (n) being 10. The sum S of such a series can be calculated as: S = a * (1 - r^n) / (1 - r). The upward travel distance will be 75% of the total downward distance.

To find out the total distance before the jumper comes to rest, we look at the situation when the sum of the geometric series tends to infinity (i.e., as the number of terms n approaches infinity) which can be calculated as S = a / (1 - r).

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Answer:

3 maybe

Step-by-step explanation:

 Solution shown in the picture is (x | x > 3).

Inequality given in the picture shows,

    Therefore, inequality shown in the picture will be x > 3.

Learn more about the inequalities on a number line here,

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Answer:

640

Step-by-step explanation:

the 2nd 4 rounds up making it 640 instead of 650

Answer:

$16

Step-by-step explanation:

-Given that her balance after buying one pizza is half her weekly allowance.

#We multiply her balance times 2 to determine her total weekly allowance:

[tex]Total \ Allowance=Balance \times 2\\\\=8\times 2\\\\=\$16[/tex]

Hence, her total weekly allowance is $16

Answer:

a. mean=18.6

b. standard deviation=1.0

c. The distribution is a symmetry and mound-shaped but nowhere near normal.

Step-by-step explanation:

a. let [tex]\mu_x[/tex] be the sample mean.

-For a normal distributed sample, the population mean is equal to the sample mean:

[tex]\mu_x=\mu\\\\=18.6[/tex]

Hence, the sample mean is 18.6

b. Let s denote the sample standard deviation.

-For a normally distributed population, the sample standard deviation is calculated using the formula;

[tex]s=\frac{\sigma}{\sqrt{n}}\\\\=\frac{6}{\sqrt{36}}\\\\=1.0[/tex]

Hence, the sample standard deviation is 1.0

c. The sample has a mean of 18.6 and a standard deviation of 1.0

-Since it's derived from a normally distribted population, it will be symmetrical and have an almost normal shape.

-Hence, it is a symmetry and mound-shaped, but Not Normal.

The mean of the sampling distribution is 18.6. The standard deviation of the sampling distribution is 1.0. The sampling distribution of the sample mean score for a random sample of 36 students is normally distributed with a mean of 18.6 and standard deviation of 1.0, according to the central limit theorem.

The mean and standard deviation of the population, which are given as 18.6 and 6.0 respectively, are used to calculate the mean and standard deviation of the sampling distribution.

(a) According to the central limit theorem, the mean of the sampling distribution of the sample mean score for a random sample of 36 students (µx-bar) is equal to the mean of the population (µ), so µx-bar = µ = 18.6.

(b) The standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students (σx-bar) is the standard deviation of the population (σ) divided by the square root of the sample size (n), so σx-bar = σ/√n = 6.0/√36 = 1.0.

(c) The sampling distribution of the sample mean score for a random sample of 36 students is a normal distribution with mean µx-bar = 18.6 and standard deviation σx-bar = 1.0, according to the central limit theorem, since the sample size is sufficiently large (n > 30).

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Answer:

i.)12 feet

Step-by-step explanation:

ut+1/2gt^2

7×1+1/2×10×1^2 =12

Answer:

The answer is $10.8 (1,080 cents)

Step-by-step explanation:

First of all, let us calculate the area of the frame:

Area = Length × width = 18 × 3 = 54 in²

We are told that she charges 20 cents per square inch, therefore:

1 in² = 20 cents

∴ 54 in² = 20 × 54 = 1,080 cents.

We know that 100 cents = $1

∴ 1,080 cents = 1/100 × 1,080 = $10.8

Answer:

1.24 kilograms per cubic meter.

Step-by-step explanation:

The air density is "[tex]1.24\ \frac{kg}{m^3}[/tex]"

The initial weight of 7 ball [tex]= 0.615 \ kg\\\\[/tex]

weight of 7 inflated balls[tex]= 0.624 \ kg\\\\[/tex]

Calculating the mass (weight) of 7 air:

[tex]\to 0.624-0.615\ kg\\\\ \to 0.009\ kg\\\\[/tex]

Calculating the diameter of 7 balls:

[tex]\to 0.24 \ m\\\\[/tex]

Calculating the Radius of the ball:

[tex]\to \frac{\text{diameter}}{2}\\\\ \to \frac{0.24}{2}\\\\ \to 0.12\ m\\\\[/tex]

Calculating the volume of air in the ball:

[tex]\to \frac{4}{3} \pi r^3\\\\\to \frac{4}{3} \pi (0.12)^3 \\\\ \to 1.333333 \times 3.14 \times 0.001728 \\\\ \to 0.00723456\\\\[/tex]

Calculating the density of air:

[tex]\to \text{Air density}=\frac{\text{Mass}}{\text{volume}}\\\\[/tex]

                      [tex]=\frac{ 0.009}{0.00723456}\ \frac{kg}{m^3}\\\\ =1.244\ \frac{kg}{m^3} \\\\=1.24\ \frac{kg}{m^3}[/tex]

Therefore, the air density is "[tex]1.24\ \frac{kg}{m^3}[/tex]".

Find out more information about the air density here:

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Answer:

9-8=1

Step-by-step explanation:

Substitute 8 for z and gives you 9-8 which equals 1

You know:

z = 8       so substitute/plug it into the expression

9 - z       Plug in 8 into "z" since z = 8

9 - 8

1

Answer:

C) 109.5

Step-by-step explanation:

Use cosine of 64°

cos 64° = 48/x

Put x on one side

x = 48/ cos 64°

x = 109.4962576

Answer:

The answer is C or 109.5 units

Step-by-step explanation:

We have to use the trig function cosine to find the answer.

cosine = [tex]\frac{adjacent}{hypotenuse}[/tex]

cosine of 64 = 0.438371147

the equation is:      cos 64 = [tex]\frac{48}{hypotenuse}[/tex]

So using this equation,

we must divide 48 by the cosine of 64 to get the hypotenuse

this equals 109.5

The hypotenuse is our length that we need to find so the question is solved.

Hope This helps

Branliest is appreciated!

Answer:

9

Step-by-step explanation:

3y = 27x

We want to find k  when y = kx

Divide each side by 3

3y/3 = 27x/3

y = 9x

The constant of proportionality is 9

Answer:

These equations are in slope-intercept form. I can use the y-intercept and slope to graph both lines. I plot the y-intercept and use rise over run to locate another point on the line. Then, I can draw a line through the two points.

Step-by-step explanation:

Answer:

6 x 0 = 0

Step-by-step explanation:

Answer:

A≈695.29cm²

Step-by-step explanation:

The area of a regular octagon with a perimeter of 96 cm is calculated by first finding the length of one side, then calculating the area of one of the eight isosceles triangles formed within the octagon, and finally multiplying this area by eight to get the total area, which is 384 cm².

To calculate the area of a regular octagon with a given perimeter, we first need to determine the length of one side. Since a regular octagon has equal sides, we can divide the perimeter by 8. In this case, the perimeter is 96 centimeters, so each side of the octagon is 96 cm / 8 = 12 cm.

We know that a regular octagon can be divided into eight identical isosceles triangles. The area of an isosceles triangle can be found by the formula A = (1/2)bh, where b is the base and h is the height.

To find the height of each triangle, we can draw an altitude from the center of the octagon to the base of one of the triangles, which creates two 90-degree triangles.

By using the Pythagorean theorem on one of these right-angled triangles, with the base of each being half the length of an octagon's side (6 cm), and the Pythagorean triple 6-8-10, we can determine the height to be 8 cm. Thus, the area of each triangle is (1/2) * 12 cm * 8 cm = 48 cm².

Finally, since there are eight triangles, the total area of the octagon is 8 * 48 cm² = 384 cm².

Answer:

105.88%

Step-by-step explanation:

Efficiency:

Output/input × 100

4500/4250 × 100

105.8823529%

Answer:

The area is 0.002m² to 3 dp

Step-by-step explanation:

This problem bothers on the mensuration of flat shapes(I.e cross sectional area of pipe ) , this time the a circle.

It requires us to look for the area of the shape

Given data

Diameter d = 5cm

Converting to mm = 5/100= 0.05m

Radius of circle r=d/2=0.05/2 =0.025mm

Given the area of the circle

A=πr²

A=3.14*0.025²

A=0.0019m²

To 3 dp we have area as 0.002m²

Answer:

32pi cm or 100.530964915 mm

Step-by-step explanation:

To find this answer you will need to use the equation 2*pi*r or pi*d.

Your value 32 can be plugged in as your value of d which can then be substituted to make 32 pi or if you use a calculator you get 100.530964915.

hope this helps!

Answer: 100.5 mm

Step-by-step explanation: The formula to find the circumference of a circle is 2(pi)r

Since we know the diameter is 32, divide 32 by 2 to get the radius: 16

2(pi)(16) = 100.5309

To the nearest tenth, that would be 100.5

Answer:

y = 5x - 13

Step-by-step explanation:

Use the formula  y = mx + b to solve for b. Then plug in known values.

Answer:

y=5x-13

Step-by-step explanation:

Answer:

The expression that represents the total amount of money raised from selling [tex]\(x\)[/tex]  flowerpots is [tex]\(15x\)[/tex].

Explanation:

The total amount of money raised from selling [tex]\(x\)[/tex] flowerpots can be represented by the expression:

[tex]\[ \text{Total amount of money} = \text{Price per flowerpot} \times \text{Number of flowerpots sold} \][/tex]

Given that each flowerpot sells for $15, and [tex]\(x\)[/tex] represents the number of flowerpots sold, the expression would be

[tex]\[ \text{Total amount of money} = 15x \][/tex]

So, the expression that represents the total amount of money raised from selling [tex]\(x\)[/tex] flowerpots is [tex]\(15x\)[/tex].

Answer:

42

Step-by-step explanation:

Let the number be "x"

We translate the word equation to algebraic equation.

First,

subtract 6 from me, so we have:

x - 6

Now,

Multiply by 2, so we have:

2(x-6)

Now,

Subtract 40, then divide by 4:

[tex]\frac{2(x-6)-40}{4}[/tex]

Now, you get "8", so equate this to 8, we get:

[tex]\frac{2(x-6)-40}{4}=8[/tex]

We now solve using algebra:

[tex]\frac{2(x-6)-40}{4}=8\\2(x-6)-40=4*8\\2(x-6)-40=32\\2x-12-40=32\\2x-52=32\\2x=32+52\\2x=84\\x=42[/tex]

The number is 42

Answer:its D (3,7)

Step-by-step explanation:

Answer:

Yes, acute

Step-by-step explanation:

Because 10 and 12 add up to more than 16, it is possible to construct an acute triangle with these side lengths.  Since 10^2 + 12^2 ≠ 16^2, we know that any triangle so constructed will not be a right triangle.

The measures 10, 12, and 16 can be the side lengths of a triangle because the sum of the two shorter sides must be greater than the longest side for a triangle to exist.

In this case, 10 + 12 is greater than 16, 16 + 10 is greater than 12, and 12 + 16 is greater than 10, satisfying the triangle inequality theorem. Therefore, a triangle can be formed.

Classifying the triangle: Using the Pythagorean theorem, we can determine that the triangle with side lengths 10, 12, and 16 is a scalene triangle, and since 10^2 + 12^2 is less than 16^2, it is an obtuse triangle.

Answer:

The ratio of the surface areas and volume is 8((5y+5x) /25xy)

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes.

Let us assume that the radius =x

Radius r=5x/4

And the height =y

Height h= 5y/4

We know that the total surface area of a cylinder is

A total = 2πrh+2πr²

We can factor out 2πr

A total = 2πr(h+r)

The volume of a cylinder is given as

v= πr²h

The surface area and volume ratios

Can be expressed as

2πr(h+r)/πr²h= 2(h+r)/rh

= (2h+2r)/rh= 2h/rh + 2r/rh

= 2/r + 2/h

= 2(1/r + 1/h)

Substituting our value of x and y

For radius and height we have

= 2(1/5x/4 + 1/5y/4)

=2(4/5x + 4/5y)

=2*4(1/5x + 1/5y)

= 8 (5y+5x/25xy)

Answer:

Ratio of surface area = 25/16

Ratio of volume = 125/64

Step-by-step explanation:

The surface area and volume of a cylinder are given by the formulas:

Surface area = 2*(pi*r^2 + pi*r*h)

Volume = pi*r^2*h

If we increase the radius and height by 5/4, we have that:

New surface area = 2*(pi*(5/4*r)^2 + pi*(5/4)*r*(5/4)*h) = (5/4)^2 * 2*(pi*r^2 + pi*r*h) = (5/4)^2 * Surface area

New volume = pi*(5/4*r)^2*(5/4)*h = (5/4)^3 * pi*r^2*h = (5/4)^3 * Volume

So the ratios are:

ratio of surface area = New surface area / Surface area = (5/4)^2 = 25/16

ratio of volume = New volume / Volume = (5/4)^3 = 125/64

Answer:

20π or 62.8 roughly

Step-by-step explanation:

Hello!

The formula for finding the circumference of a circle is 2rπ:

In that case, all we have to do is substitute 10m for our r.

2 × 10 = 20.

So circumference will be 20π.

Using 3.14 for π:

We get that 62.8 is a rough estimate for the circumference.

Really, it's 62.831..... going on forever since π is irrational.

Thus, the answer exactly is [tex]\boxed{20\:\pi}}[/tex].

Hope this helps!

Final answer:

The circumference of a clock with a radius of 10m is calculated using the formula C = 2πr, resulting in a circumference of 20π m or approximately 62.83185 m when using the approximate value of π (3.14159).

Explanation:

The circumference of a clock can be calculated using the formula for the circumference of a circle which is C = 2πr, where C is the circumference and r is the radius of the clock. Given that the radius of the clock is 10m, we substitute the value into the formula to get the circumference.

So, the circumference of the clock is C = 2π(10m) = 20π m.

The exact value of π (π is approximately 3.14159) would allow us to find the numerical value for the circumference, which would be approximately C ≈ 62.83185 m.

Answer:

Angle M = 120 degrees

Shortest side = MN

Middle Side = MO

Longest side = ON

Step-by-step explanation:

Answer:

MN < NO < OM

Step-by-step explanation:

∡ M = 180 -45-75=60°

45° opposite side - MN - shortest side

75° opposite side - OM - longest side

60° opposite side - NO

MN < NO < OM