Five line segments are drawn in a triangle as shown. How many triangles are there?

Volume of figure A is 1375 cu ft

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Given,

Figure A ~ Figure B

In Figure A R = 5.

In Figure B R = 2.

Scale factor between Figure A and Figure B = 5/2

Volume of B = 88 cu ft

πR²h = 88

π2²h = 88

h = 88/4π

h = 22/π

Height of figure A = 5/2×height of figure B

Volume of figure A

= πR²h

= π5²×5/2×22/π

= 125 × 11

= 1375 cu ft

Hence, 1375 cu ft is volume of figure A.

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The population of bacteria in the culture after 7 hours is 4,18,607 bacteria.

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

Given:

We have the function

[tex]P_t[/tex] = [tex]P_0[/tex][tex]2^{t/d[/tex]

We have  [tex]P_0[/tex]= 37000

t= 7 hours

d= 2 hours

So, [tex]P_t[/tex] = 37000 x [tex]2^{7/2[/tex]

= 37000 x 11.313708499

= 4,18,607.21 bacteria.

Hence, the population is 4,18,607.21.

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The standard form of the monomial 2 · (1 / 3) · a² · x · (- 3 / 7) · a³ · x² is the monomial - (2 / 7) · a⁵ · x³. The coefficient es - 2 / 7.

In this problem we find the case of a monomial that must be simplified into standard form, which can be rewritten in standard form by algebra properties. First, write the complete monomial:

2 · (1 / 3) · a² · x · (- 3 / 7) · a³ · x²

Second, use commutative and associative properties between similar expressions:

[2 · (1 / 3) · (- 3 / 7)] · (a² · a³) · (x · x²)

Third, use the definition of multiplication and power properties:

- (2 / 7) · a⁵ · x³

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multiply the numbers

The area of a triangle with the given base and height is 9.5625 square inches.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

From the given triangle, height is 2.5 inches.

By using Pythagoras theorem,

3²=x²+2.5²

9=x²+6.25

x²=9-6.25

x²=2.75

x=1.65 inches

So, the base = 6+1.65=7.65 inches

Area of a triangle = 1/2 ×7.65×2.5

= 0.5×7.65×2.5

= 9.5625 square inches.

Therefore, the area is 9.5625 square inches.

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The mean is the least appropriate measure of central tendency for data sets that contain outliers.

The correct option is a.

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Given:

These numbers, which were determined from the ranking data, are not affected by outliers.

In contrast, the mean is determined by utilizing all the data.

Additionally, mean is sensitive to outliers.

Therefore, if the data set contains outliers, the mean is the least suitable measure of central tendency.

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The probability that a randomly selected tire will have a life of at least 47,500 miles is 6.68%, which corresponds to answer choice c: .0668.

Probability is a mathematical concept that measures the likelihood or chance of an event occurring.It is a number between 0 and 1, with 0 designating an impossibility and 1 indicating a certainty. The probability of an event is calculated as the number of favorable outcomes divided by the number of possible outcomes.

The probability that a randomly selected tire will have a life of at least 47,500 miles can be found using a normal distribution and the z-score formula.

The z-score is calculated as follows:

z = (47,500 - 40,000) / 5,000 = 3.5

Using a standard normal table or calculator, we can find the cumulative probability associated with a z-score of 3.5. The probability that a randomly selected tire will have a life of at least 47,500 miles is:

P(X >= 47,500) = 1 - P(X < 47,500) = 1 - .9993 = .0007

Therefore, the answer is: c. .0668

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The number 125 is a 41st term of the sequence defined by the explicit rule f(n) = 3n + 2.

A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

The sequence defined by the explicit rule,

f(n) = 3n + 2.

The number 125 is a term of the sequence.

To find the term,

125 = 3n + 2

3n = 123

n = 41

Therefore, the term is 41.

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The required standard deviation of the new data set is 9.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

When 16 is added to each number in the data set, the variance of the new data set is not affected. The variance of a data set is the average of the squared deviations of the data values from the mean, and adding a constant to each data value shifts the mean but does not affect the deviations or their squares.

However, the standard deviation, which is the square root of the variance, will change because the standard deviation is expressed in the same units as the original data, while the variance is expressed in squared units. To find the standard deviation of the new data set, we need to take the square root of the variance, which is 81, and add 16 to each data value. The standard deviation of the new data set is equal to the square root of 81 + 16 = 9.

So, the standard deviation of the new data set is 9.

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An equation describing how x and y are related should be completed as y = [1/2]x + [-5].

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (0, -5), a linear equation in slope-intercept form for this line can be calculated by using point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-4) = (-5 - (-4))/(0 - (-2))(x - (-2))

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

y = -x/2 - 1 - 5

y = -x/2 - 5

y = [1/2]x + [-5].

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Frequency distribution  is a way to organize qualitative data into categories and record the number of observations in each category.

Differentiate between frequency distribution and relative frequency ?

A frequency distribution lists how frequently each category of data occurs, but a relative frequency analysis lists how frequently each types of information occurs.

One approach to organise data is to use a "frequency distribution," which can be done by listing the data, placing it in a table, or displaying it in a graph. Then, the list's entries (distinct values) are counted in terms of how frequently they have occurred.

Define relative frequency distribution

A "relative frequency distribution," on the other hand, refers to the percentage of the total number of observations that fall into a certain group. Divide each frequency by the total amount of data in the sample to obtain this.

what is qualitative data ?

Quantitative data are counts or measures, whereas qualitative data describe categories. Examples of qualitative data include eye colours and shoe brand names in a consumer survey. Examples of quantitative data are student heights and test results.

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Answer:

I don't understand ur question.

Step-by-step explanation:

Please there is no picture or complete

The values where cos(x) is equal to 0 are excluded from the domain of the function y=sec(x)=1cos(x), or the values 2+n for all integers n. The function's range is either y<=1 or y>=1.

Its root is the Latin verb secare, which means "to cut." Any line that intersects a circle twice is referred to as a secant line, and you can conceive of this line as slicing the circle in half. The distance from the origin to the point where the tangent line intersects the x-axis is the secant function.

1/cos(x) = sec(x) Cot (x) = 1/Tan (x)

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The number of votes received by Candidate B is given as follows:

56 votes.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The input and output variables for this problem are given as follows:

Hence the constant of the relationship is given as follows:

k = 35/20

k = 1.75.

Meaning that the equation is given as follows:

y = 1.75x.

If Candidate A received 32 votes, the number of votes received by Candidate B is given as follows:

y = 1.75 x 32

y = 56 votes.

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Answer:

56

Step-by-step explanation:

took test

If 60% of household use internet service and 80% use television service , then the probability that at least one of these two services from the company is 90%  .

the percent of house hold that use internet service from company is = P(I) = 60% ;

the percent of house hold that use television service from the company is = P(T) = 80% ;

the percent of house hold that use both the services= P(I & T) = 50%  ;

So , the probability that at least one of these two services from the company is calculated as :  P(I or T) = P(I) + P(T) - P(I&T)

⇒ P(I or T)= 60 + 80 - 50 ;

⇒ P(I or T)= 90%  .

Therefore , the required probability is 90% .

The given question is incomplete , the complete question is

In a certain residential suburb, 60% of all households get internet service from the local cable company, 80% get television service from that company, and 50% get both services from that company.

What is the probability that it gets at least one of these two services from the company ?

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Answer: subtract , largest

Step-by-step explanation:

you keep the largest number, because it is the largest number there

Answer:

C

Step-by-step explanation:

test taking strategy:

1.25 is bigger than 50p

so any fractions with top smaller than bottom is wrong

so eliminate A and D

B & C remaining

B = 4

4*50p = 2 pounds, so it's wrong

C is right.

double check:

1.25 / 50 = 2.5 = 5/2 correct

The true statement about the likelihood of occurrence based on probabilities is; D: Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)

The probabilities of Players 1, 2 and 3 are;

P(player 1) = 7/11 = 0.636

P(player 2) = 6/9 = 0.667

P(player 3) = 5/7 = 0.714

The most likely batting average will be the player with the highest probability. the player with the highest probability from the above is player 3 with a probability of 0.714.

The true statement about the probability when the softball players discussed their batting averages after a game is Player 3 is more likely to hit the ball than Player 2 because P (Player 3) > P (Player 2).

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Answer:

2/3

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

y=mx+b

M=slope B=Y-intercept

The line created is a good representation of a line of best fit

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

The graph

On the graph, we can see that the line divides the points on the line evenly

A good line of best fit would have approximately equal number of points on either sides

Hence, the line is a good representation

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In order to cross the bridge, the seven cars can form groups of four to cross the bridge in 35 combinations.

The process of combination is used to calculate in how many ways seven cars can form groups of four in order to cross the bridge.

Combination formula is given by:

[tex]nCr = n!/ (n! * (n-r)!)[/tex]

The number of combinations of seven cars taken four at a time can be given by the equation:

C(7,4) = 7!/(4! * (7-4)!)

C(7.4) = 5040/(24*6) = 5040/144 = 35.

Therefore, the seven cars can cross the bridge in groups of four in 35 different combinations.

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There are 8 cans will be needed to cover 208 m² of wall space.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Five cans of paint will cover 130 m² of wall space.

Now, Number of cans to cover 208 m² of wall space is,

⇒ 5 × 208 / 130

⇒ 8

Thus, There are 8 cans will be needed to cover 208 m² of wall space.

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Theprobability of discovering one or fewer surface flaws in a randomly chosen unit is 0.35.

Let X shows the number of surface defects at a randomly selected unit. Here X has Poisson distribution with parameters [tex]\lambda[/tex] =3. So the probablity of finding one or less surface defects at a randomly selected unit is

[tex]P(X\leq 1)=\frac{e^{-3}(3)^{0}}{0!}+\frac{e^{-3}(3)^{1}}{1!}=0.199[/tex]

Hence, the required probability is 0.199.

The probability of finding more than 3 defects at a randomly selected unit is

[tex]P(X > 3)=1-P(X\leq 3)=0.35[/tex]

Therefore, the probability of discovering one or fewer surface flaws at a randomly chosen unit is 0.35.

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Answer:

[6x^2 + 7x - 20]

Step-by-step explanation:

(2x + 5)(3x - 4)

Utilize FOIL,

First

Outer

Inner

Last

2x * 3x = 6x^2

2x * -4 = -8x

5 * 3x = 15x

5 * -4 = -20

6x^2 - 8x + 15x - 20

Combine like terms:

[6x^2 + 7x - 20]

Based on the line segments, the vertical angles include the following: A. ZAFE and ZBFD.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

Since both line segment AB and line segment BE are interesting lines, we can reasonably infer and logically deduce that they are congruent and as such the magnitude of angle ZAFE is equal to angle ZBFD in accordance with the vertical angles theorem.

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The percent of sales happened on  Friday and  Saturday are respectively, 26.3% &  31.6%

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

The bar graph,

In which, Horizontal digits are representing number of shirts,

And vertical component is representing week days

The number of shirts sold  on Friday = 50

The number of shirts sold  on Saturday = 60

Percentage of sales on Friday = ?

Percentage of sales on Saturday = ?

Total sales = Monday + Tuesday + Wednesday + Thursday + Friday +            Saturday

                  = 15+ 10 + 20 + 35 + 50 + 60

                  = 190

Percentage of sales on Friday =   (50/190)x100

                                                   =   26.300 %

Percentage of sales on Saturday =   (60/190)x100

                                                       =   31.600 %

Therefore, the percentage on Friday and Saturday are respectively, 26.3% &  31.6%

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The altimeter will indicate a reading of 22,697 feet.

Standard deviation is a measure of variability in a dataset. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. This measure indicates how much variation exists in a dataset.

If you are at an altitude of Flight Level 230 (23,000 feet) and forget to set your altimeter to the local altimeter setting during descent, your altimeter will indicate different readings depending on the field elevation and the local altimeter setting.

To calculate the difference between the two, we use the standard deviation formula. Specifically, we calculate the difference between the local altimeter setting and the field elevation, and subtract that difference from the Flight Level. The standard deviation formula then looks like this:

Flight Level - (Local Altimeter Setting - Field Elevation)

In our example, the equation would look like this:

23,000 - (30.02 - 303) = 22,697

It is important to note that when making such calculations, the Flight Level should always be expressed in feet, rather than in thousands of feet.

By using the standard deviation formula and keeping track of settings like local altimeter setting and field elevation, pilots can ensure that their altimeter readings are accurate and that their aircraft will land safely

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Answer:

angle 4 is 44°

Step-by-step explanation:

180-93=87 (straight line)

180-49-84=44 (triangle)

The Data Analytics is defined below and the the techniques that university can use to recruit are Identify and target potential students , Evaluate the effectiveness of recruitment strategies .

The Data analytics is defined as the process of examining, cleaning, transforming, and modeling data to discover useful information, gain insights, and support decision-making.

A University might use data analytics techniques to recruit and attract potential students in several ways which are :

(i) Identify and target potential students :

By analyzing data from various sources, such as high school records, standardized test scores, and student behavior patterns, the university can identify students who are most likely to be interested in attending.

(ii) Evaluate the effectiveness of recruitment strategies :

By analyzing data on the response rates, conversion rates, and enrollment rates of students, the university can evaluate the effectiveness of its recruitment strategies and make decisions to improve future recruitment efforts.

(iii) Monitor student engagement:

By tracking and analyzing the student engagement data,  the university can identify which students are most likely to enroll and stay enrolled.

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