Which of the following sets of numbers could represent the three sides of a triangle?​

Answer:

60% of 80 is about 48. 70% of 60 is 42. The number of his classmates who like hip-hop is greater than the number of his relatives who like hip-hop.

Step-by-step explanation:

Answer:

60% of 80 is about 48. 70% of 60 is 42. The number of his classmates who like hip-hop is greater than the number of his relatives who like hip-hop.

Step-by-step explanation: got it on my test

when the time is between 0 and 15 minutes, the distance depends on the time on a relation: d =(1/10)t

when the time is between 15 and 40 minutes, the distance is independent of the time, it is fixed d = 1.5 miles

when the time is between 40 and 50 minutes, the distance depends on the time on the relation: d = 1.5 + (1/10)(t - 40)

Answer:

Sam has is 7/5 times the reciprocal of the total number of stamps in the new set.

Step-by-step explanation:

Let's start by finding out what fraction of the new set of stamps Sam has after adding 4/5 of the set to his collection.

Let the total number of stamps in the new set be x.

If Sam's collection initially had 3/5 of the new set, then the number of stamps in his collection before adding the new set would be:

3/5 * x = the number of stamps in Sam's collection before adding the new set

After adding 4/5 of the new set to his collection, Sam has:

3/5 * x + 4/5 * x = 7/5 * x

So Sam has 7/5 of the new set of stamps.

However, the problem asks for the fraction of the new set that Sam has, not the fraction of the total number of stamps in the new set.

To find the fraction of the new set that Sam has, we need to divide the number of stamps he has by the total number of stamps in the new set:

(7/5 * x) / x

Simplifying the expression:

(7/5) / 1

We can express this fraction in terms of x by multiplying both the numerator and denominator by 1/x:

(7/5) * (1/x)

Therefore, the fraction of the new set of stamps that Sam has is 7/5 times the reciprocal of the total number of stamps in the new set.

Step-by-step explanation:

Based on the information given in the diagram, we know that AABD and ACAD are similar triangles, which means their corresponding sides are proportional.

Let's denote the length of AD as x. According to the similarity of the triangles, we can set up the following proportion:

AB/AC = AD/AD

Since AD is common to both triangles and has a length of x, the proportion simplifies to:

AB/AC = 1

We are given that AB = 12, so we can substitute that value into the proportion:

12/AC = 1

To solve for AC, we can cross-multiply:

12 = AC

Therefore, the value of x in the figure is 12.

30° is the angle of elevation from the base to the top of the mountain.

Trigonometric ratios are the ratios of the length of sides of a triangle.

These ratios in trigonometry state the relation between the ratio of sides of a right triangle to the respective angle.

The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.

The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.

Sin θ = Perpendicular / Hypotenuse

According to the question,

Perpendicular = Vertical height of Mountain. = 1290 m

Hypotenuse    = The distance from the top of the mountain to the base                               of the Mountain. = 2580 m

⇒ Sin θ = 1290/ 2580

⇒ Sin θ = 1/2⇒ θ = Sin⁻¹(1/2)

⇒ θ = 30°

Hence, 30° is the angle of elevation from the base to the top of the mountain.

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Answer:

The simplified expression of the trigonometric identity 2sin(-20)sin160 - cos40 is -2 + 2cos²(20) + cos(140).

The given expression is 2sin(-20)sin160 - cos40.

To simplify the expression, let's first evaluate the trigonometric functions:

sin(-20) = -sin(20) [since sin(-θ) = -sin(θ)]

sin(160) = sin(180 - 20) = sin(20) [since sin(180 - θ) = sin(θ)]

cos(40) = cos(180 - 140) = -cos(140) [since cos(180 - θ) = -cos(θ)]

Substituting these values into the expression, we have:

2(-sin(20))(sin(20)) - (-cos(140))

= -2sin²(20) + cos(140)

We can further simplify the expression using a trigonometric identity:

sin²(θ) + cos²(θ) = 1

sin^2(θ) = 1 - cos^2(θ)

Substituting this identity into the expression, we get:

-2(1 - cos²(20)) + cos(140)

= -2 + 2cos²(20) + cos(140)

Now, we have simplified the given expression to -2 + 2cos²(20) + cos(140).

Complete Question:

Simply the trigonometric function: 2 sin(-20) sin 160-cos40​

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The mean median mode of the data 9,10,9,9,11,9,10,9,9,10 is

Mean =9.5

Median = 11 or 9

Mode is 9

Given that,

The data is 9,10,9,9,11,9,10,9,9,10

The data's mean, median, and mode must be determined.

We know that,

The arithmetic mean of the provided data is another name for mean. If the data are grouped and sorted in ascending order, the median is the value that falls in the middle of the set of grouped data. The value that dominates the data is known as the mode. The Mean, Median, and Mode formulas are described independently for the group of data in the sections that follow.

The data is 9,10,9,9,11,9,10,9,9,10

Mean = 9+10+9+9+11+9+10+9+9+10/10 =95/10=9.5

Median = 11 or 9

Mode is 9

Therefore, The mean median mode of the data 9,10,9,9,11,9,10,9,9,10 is

Mean =9.5

Median = 11 or 9

Mode is 9

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y=2/3x+7 is equation in slope-intercept form of the line that passes through (6, 11). and (2, 25/3). ​

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given two points are (6, 11) and (2, 25/3). ​

m=25/3-11/2-6

=-8/3/-4

=8/12=2/3

Now we have to find y intercept by considering (6,11)

y=2/3x+c

11=2/3(6)+c

11=4+c

11-4=c

7=c

The slope intercept form of line is y=2/3x+7

Hence y=2/3x+7 is equation in slope-intercept form of the line that passes through (6, 11). and (2, 25/3). ​

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Answer:

23

110

Step-by-step explanation:

We have a + 1/a = 5

(a + 1/a)² = a² + (1/a²) + 2.a.1/a =  a² + (1/a²)  + 2

But (a + 1/a)² = 5² = 25

So a² + (1/a²) = 25 - 2 = 23

(a + 1/a)³ = a³ + 3a²(1/a) + 3a(1/a)² + (1/a)2

= a³ + 1/a³ + 3a + 3/a

= a³ + 1/a³ + 3(a + 1/a)

= a³ + 1/a³ + 3(5)

=  a³ + 1/a³ + 15

But (a + 1/a)³ = 5³ = 125

So

a³ + 1/a³ + 15 = 125

a³ + 1/a³  = 110

Answer:

23 and 110

Step-by-step explanation:

using the expansion

(a + b)² = a² + 2ab + b² , then

a + \(\frac{1}{a}\) = 5 ( square both sides )

(a + \(\frac{1}{a}\) )² = 5²

a² + 2(a × \(\frac{1}{a}\) ) + \(\frac{1}{a^2}\) = 25

a² + 2(1) + \(\frac{1}{a^2}\) = 25

a² + 2 + \(\frac{1}{a^2}\) = 25 ( subtract 2 from both sides )

a² + \(\frac{1}{a^2}\) = 23

---------------------------------------------------------------------

using the expansion

(a + b)³ = a³ + b³ + 3ab(a + b) , then

a + \(\frac{1}{a}\) = 5 ( cube both sides )

(a + \(\frac{1}{a}\) )³ = 5³

a³ + \(\frac{1}{a^3}\) + 3(a × \(\frac{1}{a}\) )(a + \(\frac{1}{a}\) ) = 125

a³ + \(\frac{1}{a^3}\) + 3(1)(5) = 125

a³ + \(\frac{1}{a^3}\) + (3 × 5) = 125

a³ + \(\frac{1}{a^3}\) + 15 = 125 ( subtract 15 from both sides )

a³ + \(\frac{1}{a^3}\) = 110

Using the inscribed angle theorems, the measure of the indicated angles are:

1. m∠BOA = 26°

2. m∠BDA = 13°

3. m∠BCA = 13°

Based on the inscribed angle theorem, the following relationships are established:

Given:

Intercepted arc BA = 26°

1. ∠BOA is central angle

Thus:

m∠BOA = 26° (inscribed angle theorems)

2. ∠BDA is inscribed angle.

m∠BDA = 1/2(30) = 13° (inscribed angle theorems)

3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)

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Answer:

E) 998

Step-by-step explanation:

Members in the first year (p) is 350.

Each year members increased by (r) 14%.

We need to find the number of members after (t) 8 years.

Total members = P (1 + r)^t

= 350 ( 1 + 0.14)^8 = 998 members

So, the answer is E) 998

The basic present value equation includes the present value, future value, discount rate, and the life of the investment.

The basic present value equation is a financial concept used to determine the value of an investment or cash flow in today's dollars. It involves four key components

1. Present value, This represents the current worth of an investment or cash flow. It takes into account the time value of money, which means that a dollar received in the future is worth less than a dollar received today. The present value is calculated by discounting future cash flows using an appropriate discount rate.

2. Future value, This refers to the expected value of an investment or cash flow at a future point in time. It represents the amount of money that an investment will grow to over a specific period, taking into consideration factors such as interest or investment returns.

3. Discount rate, The discount rate is the rate of return or interest rate used to determine the present value of future cash flows. It reflects the opportunity cost of investing in a particular investment or project. The discount rate takes into account factors such as the riskiness of the investment, inflation, and alternative investment opportunities.

4. Life of the investment, This represents the duration or time period over which the investment or cash flow will occur. It is important to consider the length of time involved as it affects the magnitude and timing of cash flows, which in turn impacts the present value calculation.

By considering these four components - present value, future value, discount rate, and the life of the investment - the basic present value equation allows individuals and businesses to assess the current worth of future cash flows and make informed financial decisions.

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Answer:

y = 1/4 +3

Step-by-step explanation:

Step-by-step explanation:

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131,4..........................................

The assumption of a finite population is the answer to the question of which condition/assumption is not required for the one-sample t inference for the mean μ of a population.

The one-sample t inference for the mean μ of a population is based on several conditions and assumptions. Let's discuss each of them and identify which one is not a condition or assumption.

Random Sampling: One of the key assumptions is that the data used for the inference is obtained from a random sample. Random sampling ensures that the observations are independent and representative of the population.

Normality: The t inference assumes that the population follows a normal distribution. This assumption is necessary to apply the t-distribution for inference. However, for large sample sizes (typically above 30), the t-inference is robust to deviations from normality due to the Central Limit Theorem.

Independence: The observations in the sample should be independent of each other. This assumption ensures that each observation provides new information and is not influenced by other observations.

Finite Population: The t-inference assumes that the population from which the sample is drawn is finite. This assumption is relevant when the sample size is a large fraction of the population size. If the population is infinite or extremely large, this assumption is not necessary.

Homogeneity of Variance: The t-inference assumes that the variance of the population is the same across all levels of the independent variable. This assumption is known as homogeneity of variance. Violation of this assumption can lead to inaccurate results.

Based on these conditions and assumptions, it can be concluded that the assumption of a finite population is not a condition of the one-sample t inference for the mean μ. The assumption of a finite population is relevant only when the population size is small or the sample size is a large fraction of the population size. In most practical scenarios, where the population size is large or infinite, this assumption is not applicable.

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Answer:

Given that `x=10`, we can find the value of `a` and `b` by substituting the value of `x` into the given expressions for `a` and `b`.

For `a`, we have: `a = 5x^2/2`. Substituting `x=10`, we get: `a = 5(10)^2/2 = 250`.

For `b`, we have: `b = 2x^2(x-5)/10x`. Substituting `x=10`, we get: `b = 2(10)^2(10-5)/10(10) = 100`.

Therefore, when `x=10`, the value of `a` is 250 and the value of `b` is 100.

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Answer:

  (c)  two right triangles, each with both legs 40 inches long

Step-by-step explanation:

You want to know which pair of triangles are congruent, given their descriptions.

There are basically 4 theorems that allow you to claim congruence of triangles:

  AAS, ASA, SAS, SSS

A fifth one applies to right triangles only: HL.

These tell you that you need to have three matching parts: 3 sides, 2 sides and the angle between (except right triangle), or 1 side and 2 angles.

An isosceles triangle with only one or two sides defined is not sufficient.

A right triangle with only the hypotenuse defined is not sufficient.

A right triangle with two legs and the (right) angle between them has a sufficient number of matching parts to be able to claim congruence to another triangle similarly defined.

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line is 5000 cubic units.

The formula for calculating the volume of a solid obtained by rotating the region bounded by the given curves about the specified line is given by;

V = π ∫[a,b] (f(x))²dx

where f(x) is the function of the curve and a,b are the limits of integration of x.

Using the formula, we have;

The given curves are

4x²,

x = 5,

and

y = 0

and the specified line is the Y-axis.

The region bounded is shown below;

The graph above shows that the region is bounded between

x = 0

and

x = 5.

Therefore, we have;

∫[0,5] (4x²)²dx

= ∫[0,5] 16x^4dx

∫[0,5] 16x^4dx

= 16[ x⁵/5 ]ₓ

=0ₓ

=5

∫[0,5] 16x^4dx

= 16[(5)⁵/5] - 16[(0)⁵/5]

∫[0,5] 16x^4dx

= 16(3125/5) - 0

∫[0,5] 16x^4dx

= 5000

Therefore, the volume of the solid obtained by rotating the region bounded by the given curves about the specified line is 5000 cubic units.

The answer is 5000.

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The projection system tries to minimize the discrepancies within each zone

Zone width, specific to projection system and location, is typically around 400 miles.

The maximum allowed discrepancy between grid and geodetic distance in ratio depends on the location and the projection system being used.

In general, the discrepancy can range from a few meters to several hundred meters. As for the zone width, it also depends on the projection system and the location.

In the UTM projection, the zone width is typically 6 degrees of longitude or approximately 400 miles at the equator. However, the zone width decreases towards the poles.

It is important to note that the zone width and the discrepancy between grid and geodetic distances are related, as the projection system tries to minimize the discrepancies within each zone.

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Answer:

C -6

step by step explanation:

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

We need to find the GCF of 72 and 90 to solve this problem. We can calculate it in the following manner.

To solve this problem, we need to find the greatest number of party bags April can make with no candies left over. This means we need to find the greatest common factor (GCF) of 72 and 90.

The GCF of two numbers is the largest number that divides evenly into both of them. In this case, we need to find the largest number that can divide both 72 and 90 without any remainder.

Once we have found the GCF, we can divide both 72 and 90 by it to find the maximum number of party bags April can make with no candy left over.

Therefore, we need to find the GCF of 72 and 90 to solve this problem.

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Answer:

8 times

Step-by-step explanation:

because you do the number of times the event occurs in the sample space divided by the number of outcomes in the sample space.

The temperature dropped which means the starting temperature was higher than the final temperature.

To find the starting temperature add the amount it dropped to the final temperature:

-7 + 12 = 5

The starting temperature was 5 degrees

Answer:

  30.8 million

Step-by-step explanation:

You want the "y-intercept" of the graph of a population that is predicted to be 30.8 million in 2010 and increase at 1 per year until 2030.

The term "y-intercept" refers to the point on a graph where the curve crosses the y-axis. The x-value at that point is zero. For graphs plotted with x = time, the y-intercept is the "initial value," the value when time is considered to be zero.

In the situation described, we presume that the domain of interest is years between 2010 and 2030, and that x=0 corresponds to the year 2010. That means the "initial value", or y-intercept, will be the population in 2010.

The value of the y-intercept is 30.8 million.

__

Additional comment

We don't know the units associated with the increase of "1 per year." In this scenario, that could be 1 person, 1 million persons, or 1% of the current population. For the purpose of identifying the y-intercept, it doesn't matter. If any calculation of population is to be made, the problem statement needs further elaboration.