Easy (7th-grade math)

Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

Answer:

  d.  6 seconds

  e.  12 seconds

Step-by-step explanation:

Given that a projectile has an altitude of 320 feet at 2 seconds and 10 seconds after launch, you want to know the time to maximum height and the time the projectile lands on the ground.

The parabolic path is symmetrical about the vertical line through its vertex. So, the time at maximum height is the average of the two times at which the height is 320 ft:

  (2 s + 10 s)/2 = (12/2) s = 6 s

The projectile is at maximum height 6 seconds after launch.

The projectile is launched from ground level at t=0, so will reach ground level again an equal time after reaching maximum height.

  2 × (6 s) = 12 s

The projectile will land after 12 seconds.

In the standard algorithm

Reminder = 2

quotient  = 13

What does quotient in mathematics mean?

The number being divided is known as the dividend, in this case, 15. The number being divided is known as the divisor (in this case, 3). The remainder following division is the quotient.

                                When we divide two integers, the result is a quantity known as the quotient. As an example, since the division resulted in the number 2, the quotient in the equation 8 4 = 2 is 2.

= 93÷7​

Reminder = 2

quotient  = 13

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6. The ratio of the birth weight to the adult weight of a male black bear is 3:1000.

7. The measure of the angles in the triangle are 36°, 15 x 36° = 540°, and 19 x 36° = 684°.

An angle is an abstract concept in geometry which is formed by two lines or rays that meet at a common point. An angle is measured in degrees and can be classified by its size as acute, right, obtuse, or reflex. An angle can also be formed by three points or two intersecting planes.

6. The average birth weight is 12 ounces. The average adult weight is 12 x 1000 = 12000 ounces. Since there are 16 ounces in 1 pound, the average adult weight of the male black bear is 12000/16 = 750 pounds.

7. The measures of the angles in a triangle are in the extended ratio 2:15:19.To find the measure of each angle, we can set up an equation using the extended ratio. Let x be the measure of the first angle, then 15x and 19x will be the measures of the other two angles. This can be written as: 2x + 15x + 19x = 360°. Solving this equation, we get x = 36°. Therefore, the measure of the angles in the triangle are 36°, 15 x 36° = 540°, and 19 x 36° = 684°.

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Jordan spend 25 minutes writing each dayNoHow much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:D + W = 75W + 25 = DSo, we haveW + W + 25 = 75EvaluateW = 25This means that Jordan spends 25 minutes on writing is it possible?Based on the answer in (a), the truth statement is No

The graph of the functions are given as attached.

Graphs are visual representations of functions that provide valuable insights into their behavior. They allow us to see the relationship between the input and output of a function, and how it changes over time or across different values.

The relationship between the two functions is that they are reciprocals of each other. Specifically, f(x) = 2sin(2x) + 1 is the reciprocal of f(x) = 2csc(2x) + 1, since csc(2x) is the reciprocal of sin(2x). Therefore, they have the same shape, but their values are inverted. See the attached graph.

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Answer:

it is not likey bc inless the class have over 2 mil ppl in it itis doouptfull

Step-by-step explanation:

Answer:

Step-by-step explanation:

The figure is a rectangular trapezoid, and this answers one question, the second question is the area, which we find by making the major base plus the minor base multiplied by the height and we divide everything by two, the two bases are the parallel ones (12 and 8) and the height is 7.

Then it is resolved with this expression

Area = [(12 + 8) ×  7] : 2

Area = (20 × 7) : 2

Area = 140 : 2

Area = 70 cm²

Step-by-step explanation:

The measure of angle p is 60°

Answer:

D) 115.2π cm².

Step-by-step explanation:

The surface area of a cylinder can be calculated using the formula:

Surface Area = 2πr² + 2πrh

where r is the radius and h is the height of the cylinder.

In this case, r = 4 cm and h = 10.4 cm. Substituting these values in the formula, we get:

Surface Area = 2π(4)² + 2π(4)(10.4)

Surface Area = 2π(16) + 2π(41.6)

Surface Area = 32π + 83.2π

Surface Area = 115.2π

Therefore, the exact surface area of the candle is 115.2π cm².

The answer is (D) 115.2π cm².

Answer: The answer is D, 115.2π cm²

Step-by-step explanation: When we use the formula of 2πrh+2πr2=2·π·4·10.4+2·π·42 to get the surface area, which equals 361.91

We can divide this by pi to get 115.2π cm²

Hope this helped!

Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.

Since "percent" is a slang term for "per hundred," when we discuss percentages, we are speaking to a fraction of a hundred. In a variety of contexts, including math, science, finance, and daily living, percentages are used. The percent sign (%) is commonly used to denote percentages. As an illustration, to determine what proportion of 50 apples are red, you would split the number of red apples by the total number of apples and multiply the result by 100.

given

If Jane had phoned 1,000 times and you had allowed 67% of those calls to go to voicemail, then 67% of those calls would have left voicemails for you.

You can multiply the overall number of calls by the proportion of calls that went to voicemail to determine how many voicemails you would have received:

1000 x 67% = 670

Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.

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The complete question is :-  

Jane called one thousand times to tell you she's sorry. If you saw she was calling and let your phone go to voicemail 67% of the time, how many voicemails would you have received if she left one each time?

Possible Answers:

3,700

57,000

67

None of the given answers

670

Answer:

Step-by-step explanation:

Let's assume that the width of the flag is "w" ft.

According to the problem, the length of the flag is 400 ft greater than the width, which means it can be expressed as:

length = w + 400

Now, we know that the perimeter of the flag is 2,120ft. The perimeter of a rectangle is given by:

perimeter = 2(length + width)

Substituting the values, we get:

2120 = 2[(w+400) + w]

2120 = 2[2w + 400]

2120 = 4w + 800

4w = 1320

w = 330

Hence, the width of the flag is 330ft.

From our equation for the length, we have:

length = w + 400

length = 330 + 400

length = 730

Therefore, the length of the flag is 730ft.

Answer:

first name is pentagon

second is decagon

third is heptagon

Step-by-step explanation:

first is irregular

second is regular

third is irregular

Answer:

8x²-30x+18

Step-by-step explanation:

8x²-24x-6x+18

8x²-30x+18

Answer:

[tex]8x^{2} -30x+18[/tex]

Step-by-step explanation:

[tex]8x^{2} -24x-6x+18[/tex]

[tex]8x^{2} -30x+18[/tex]

Answer:

26° 180 -81 - 73 = 26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

triangle= 180

81 + 73 = 154

180 - 154= 26

Answer:

4

Step-by-step explanation:

f(-1) = 2

g(2)= 4

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Based on this estimate, the insurance company's projected value of this probability insurance policy is negative, implying that the insurance company will lose money on this policy.

Probabilistic theory is a branch of mathematics that calculates the chance of an event or a claim being true. A risk is a number between 0 and 1, where 1 represents certainty and a probability of about 0 shows how likely an event appears to be to occur. Probability is a mathematical term for the likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1, or as percentages ranging from 0% to 100%. The proportion of occurrences among equally likely choices that result in a certain event in compared to all possible outcomes.

The total of the potential payouts multiplied by the odds of each payout occurring equals the anticipated value of the insurance policy. In this scenario, the possible compensation is the $1500 insurance payout, and the likelihood of the client being involved in an accident is 3.3%, or 0.033.

Expected value = (Payout if event happens) x (Probability of event happening) - (Annual premium)

($1500) x (0.033) - ($120) = expected value

Value expected = $49.50 - $120

-$70.50 is the expected value.

Based on this estimate, the insurance company's projected value of this insurance policy is negative, implying that the insurance company will lose money on this policy.

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Answer: The building is approximately 16.6 feet tall.

Step-by-step explanation:

Use Pythagorean theorem (a²+b²=c²) to solve this.

We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.

Your equation would be: 20²+x²=26²

subtract 20² from 26² --> 276=x²

then take the square root --> 16.6=x

The resultant values are as follows:

Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft

The circumference of a circle or ellipse in geometry is its perimeter.

That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.

The curve length around any closed figure is more often referred to as the perimeter.

The length of a circle's outline is referred to as its circumference, and the length of a form with straight sides is referred to as its perimeter.

So, since the fence around the circular pool is given, then it will also be the value of the circumference of the pool.

Circumference = 75 ft

Radius:

2πr = 75

r = 75/2π = 75/(2×3.14) ≈ 11.937

radius = 11.94 ft

Diameter:

2r = 2×11 ≈ 23.87 ft

Therefore, the resultant values are as follows:

Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft

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Complete question:

The fence around a circular pool is 75 ft long. Find: Radius, Diameter, and Circumference.

The     circumference   of    the circle who radius  is  14  centimeters   is approximately 87.92 centimeters.

What is circumference?

Circumference is distance around the edge of a circle. It can be thought as the perimeter of the circle. It is a measure of the total length of the circle, and is determined by the size of the circle's radius or diameter. The formula of circumference of  circle is C = 2πr

What is  radius ?

Radius is a term used in geometry to refer to the distance between the center of a circle or sphere and any point on its circumference     or surface, respectively. It is typically denoted by the letter "r"

In the given question,

The circumference of  circle is given by the formula:

C = 2πr

where r is the radius of  circle and π (pi) is  mathematical constant which is  approximately equal to 3.14.

Substituting the given value of  radius, we get:

C = 2 x 3.14 x 14

= 87.92 centimeters (rounded to two decimal places)

Therefore, the circumference of the circle is 87.92 centimeters.

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The probability of the complementary event of E occurring is 0.57.

What is probability?

Probability is a branch of mathematics that deals with the study of random events or phenomena. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to happen.

In probability theory, P(E) represents the probability of an event E occurring, while P(Ec) represents the probability of the complementary event of E occurring. The complementary event of E is the event that E does not occur. In other words, it consists of all outcomes that are not in E.

To find P(Ec), we can use the formula:

P(Ec) = 1 - P(E)

where 1 represents the total probability of all possible outcomes.

In this case, we are given that P(E) = 0.43. Substituting this value into the formula, we get:

P(Ec) = 1 - P(E)

P(Ec) = 1 - 0.43

P(Ec) = 0.57

Therefore, the probability of the complementary event of E occurring is 0.57.

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Answer:

The answer would be 14 miles!

(x-2)(x-20) is the factored form of the trinomial equation

Given the quadratic equation below

x² - 22x + 40

To factorise this expression, we need to find two factors of 40 that add up to -22.

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40.

To get a sum of -22, we can choose the factors -2 and -20.

Therefore, we can write:

x² - 22x + 40 = (x - 2)(x - 20)

Thus, the factored form of the expression 40-22x+x² is (x-2)(x-20).

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Answer:

To multiply 1 3/3 by 1 2/6, we can first convert these mixed numbers to improper fractions, then multiply them together, and finally simplify the result to its simplest form.

1 3/3 can be written as 4/3 (since 1 whole and 3/3 is equivalent to 4/3)

1 2/6 can be written as 8/6 (since 1 whole and 2/6 is equivalent to 8/6)

Now, we can multiply these two fractions together:

4/3 x 8/6 = (4 x 8) / (3 x 6) = 32/18

To simplify this fraction, we can divide the numerator and denominator by their greatest common factor, which is 2:

32/18 = (2 x 16) / (2 x 9) = 16/9

Therefore, the product of 1 3/3 and 1 2/6 is 16/9, or 1 and 7/9 in mixed number form, in its simplest form.

The given distribution is normal with mean μ = 7 and standard deviation σ = 2. So,The probability that a given garden has between 1 and 11 rows is approximately 0.9772 or 97.72%.

Probability is a mathematical concept that is used to measure the likelihood of a particular event occurring. It is a way to quantify uncertainty, and it is expressed as a number between 0 and 1.

We need to find the probability that a given garden has between 1 and 11 rows.

First, we standardize the values using the formula z = (x - μ) / σ, where x is the number of rows.

For x = 1, z = (1 - 7) / 2 = -3. For x = 11, z = (11 - 7) / 2 = 2.

Using the 68 - 95 - 99.7 rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Thus, the probability of a garden having between 1 and 11 rows can be calculated as:

P(1 ≤ x ≤ 11) = P(-3 ≤ z ≤ 2)

From the z-table, we can find that the probability of a standard normal distribution having a z-score between -3 and 2 is approximately 0.9772.

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the container needs to have a volume of  0.01514 cubic meters to hold 205 kg of mercury.

Volume is the measure of the amount of three-dimensional space enclosed by an object or space. It is typically expressed in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).

The density of mercury is approximately 13,534 kg/m³.

We can use the formula:

Volume = mass/density

To find the volume of mercury that has a mass of 205 kg:

Volume = 205 kg / 13,534 kg/m³

Volume ≈ 0.01514 m³

Therefore, the container needs to have a volume of approximately 0.01514 cubic meters to hold 205 kg of mercury.

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The complete question is:

What volume should a container have to hold 205 kg of mercury?

The volume of the solid is approximately 0.558 cubic units.

To find the volume of the solid, we need to integrate the area of the semi-circles along the a-axis.

We know that the diameter of each semi-circle is the distance between the functions f(x) and g(x), which is:

d(a) = f(a) - g(a) = ln(a) + 1 - (a-1) = ln(a) - a + 2

The radius of each semi-circle is half of the diameter, which is:

r(a) = (ln(a) - a + 2) / 2

The area of each semi-circle is π times the square of its radius, which is:

[tex]A(a) = πr(a)^2 = π/4 (ln(a) - a + 2)^2[/tex]

To find the volume of the solid, we integrate the area of each semi-circle along the a-axis, from a = e to a = 2:

V = ∫[e,2] A(a) da

V = ∫[e,2] π/4 [tex](ln(a) - a + 2)^2 da[/tex]

V ≈ 0.558 (rounded to the nearest thousandth)

Therefore, the volume of the solid is approximately 0.558 cubic units.

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The table of original value and rounded values are

x        y

0.2    0

0.5     1

0.9     1

1.08    1

1.49     1

1.72     2

2.3      2

2.94    3

The graph is attached

The graph is made in a cartesian coordinate by tracing the point of intersection of the two points

The table is represented as ordered pair as (original value, rounded value) for the given x and y values:

(0.2, 0), (0.5, 1), (0.9, 1), (1.08, 1), (1.49, 1), (1.72, 2), (2.3, 2), (2.94, 3)

The graph is a scattered plot and its attached

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