Select all conditions for which it is possible to construct a triangle. Group of answer choices A. A triangle with angle measures 30, 40, and 100 degrees. B. A triangle with side lengths 4 cm, 5 cm, and 8 cm, C. A triangle with side lengths 4 cm and 5 cm, and a 50 degree angle. D. A triangle with side lengths 4 cm, 5 cm, and 12 cm. E. A triangle with angle measures 40, 60, and 80 degrees.

Paloma's median practice time would be = 26.5

Median is defined as the middle of a set of data which will be selected after the data has been grouped in an ascending or descending order.

The list to track the number of minutes Paloma spent practicing piano in ascending order include the following:

18, 23, 24, 24, 25, |25, 28,| 28, 30, 32, 32, 35

The middle figures are 25 and 28 which should be added and divided into two.

That is;

25 + 28 = 53/2

= 26.5

Therefore, the median practice time for Paloma = 26.5

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Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Answer:

Step-by-step explanation:

Given number:

So n = -5

Correct option is:

Answer: -5

Step-by-step explanation:

Apex

To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:

w = c1V1 + c2V2 + c3V3

We can write this as a matrix equation:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

We can solve this system of equations using row reduction:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

R2 = R2 - 6R1

R3 = R3 - 2R1

R4 = R4 + 15R1

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 -23 67 -59 | | -32 |

R4 = R4 + 23R2

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 0 174 -294 | | 225 |

R3 = R3 - (12/27)R2

R4 = (1/174)R4

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 0 -1 22/3 | | c3 | | -13/3 |

| 0 0 1 -98/87 | | 25/58 |

R1 = R1 + 4R3

R2 = R2 - 59R3

R4 = R4 + (98/87)R3

| 1 0 -13 -10/3 | | c1 | | 21/29 |

| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |

| 0 0 1 -98/87 | | c3 | | 25/58 |

| 0 0 0 1390/2391 | | 1009/2391 |

R1 = R1 + (13/1390)R4

R2 = (1/27)R2

R3 = R3 + (98/1390)R4

| 1

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Answer:

75%

Step-by-step explanation:

3/4 ie 75/100. .........edge

Question:

What is the answer that you want to find? Fraction to decimal, I get it but what is the fraction? I'm sorry but I didn't get that clear.

Answer: 41/50

Step-by-step explanation:

82/100 ÷ 2/2 = 41/50

1) In this question, the best way to tackle it is to sketch out that triangle:

2) Let's use The Law of Sines and then perform some algebraic manipulation:

So let's cross multiply then:

And that's the answer.

a) The present value of $25,000 due 9 periods from now, discounted at 10%, is approximately $10,593.22.

b) The present value of $25,000 to be received at the end of each of 6 periods, discounted at 9%, is approximately $22,935.35.

(a) Present Value of $25,000 due 9 periods from now, discounted at 10%:

To calculate the present value, we need to discount the future cash flow of $25,000 back to its current value using the given discount rate of 10%. The formula to calculate the present value is:

Present Value = Future Value / (1 + Discount Rate)ⁿ

Where:

Future Value is the amount to be received in the future ($25,000).

Discount Rate is the rate at which we discount the future cash flow (10%).

'n' is the number of periods or years until the future cash flow is received (9 periods in this case).

Let's plug in the values into the formula and calculate the present value:

Present Value = $25,000 / (1 + 0.10)⁹

Calculating the denominator:

(1 + 0.10)⁹ = 1.10⁹ ≈ 2.36

Present Value = $25,000 / 2.36 ≈ $10,593.22

(b) Present Value of $25,000 to be received at the end of each of 6 periods, discounted at 9%:

In this case, we have a cash flow of $25,000 to be received at the end of each of 6 periods, discounted at 9%. Let's calculate the present value:

Present Value = $25,000 / (1 + 0.09)¹ + $25,000 / (1 + 0.09)² + ... + $25,000 / (1 + 0.09)^6

Calculating each discount factor:

(1 + 0.09)¹ ≈ 1.09

(1 + 0.09)² ≈ 1.1881

(1 + 0.09)³ ≈ 1.2950

(1 + 0.09)⁴ ≈ 1.4116

(1 + 0.09)⁵ ≈ 1.5386

(1 + 0.09)⁶ ≈ 1.6765

Plugging in the values and summing them up:

Present Value = $25,000 / 1.09 + $25,000 / 1.1881 + $25,000 / 1.2950 + $25,000 / 1.4116 + $25,000 / 1.5386 + $25,000 / 1.6765

Present Value ≈ $22,935.35

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If Leyanna choose one marble at random, the chances that it is yellow is 4/9 that is 0.44.

Total number of marbles in bag are 9

There are 5 red marbles and 4 yellow marbles

Total number of marbles = 5 + 4 = 9.

Therefore total number of cases is 9

Since there are 4 yellow marbles, the number of favorable outcomes is 4.

So P ( a yellow marble) =Number of favorable cases/ Total number of cases

= 4/9

So probability of choosing a yellow marble is 4/9.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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​

Answer:

18

Step-by-step explanation:

You can just do 6-(-12) a negative multiplied by a negative then turns into a positive which makes is 6+12=18

The first question involves finding the value and domain of f(g(x)) for specific functions f(x) and g(x).
The second question requires subtracting g(x) from f(x) to find f(x) – g(x).
The third question involves adding f(x) and g(x) to find f(x) + g(x).

To find f(g(x)), we substitute g(x) into the function f(x):

F(g(x)) = f(7)

Given that f(x) = 3x + 2, we substitute 7 into f(x):

F(g(x)) = f(7) = 3(7) + 2 = 21 + 2 = 23

Therefore, f(g(x)) = 23.

To find the domain of f(g(x)), we need to consider the domain of g(x), which is all real numbers since it is a constant function. Therefore, the domain of f(g(x)) is also all real numbers.

To find f(x) – g(x), we subtract g(x) from f(x):

F(x) – g(x) = (3x + 2) – 8 = 3x + 2 – 8 = 3x – 6

Therefore, f(x) – g(x) = 3x – 6.

To find f(x) + g(x), we add f(x) and g(x):

F(x) + g(x) = (3x + 2) + 8 = 3x + 2 + 8 = 3x + 10

Therefore, f(x) + g(x) = 3x + 10.


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The average rate of change between the given values of the variable is 21

A function can be defined as an expression or rule showing the relationship between a dependent and an independent variable.

Given the function;

h(t) = 2t^{2}\) − t

For t =2

Substitute the value of t as 2 in the function, we have;

h(2) = 2 (2)² - (2)

Find the square

h(2) = 2(4) - 2

h(2) = 8 - 2

h(2) = 6

For t = 9

Substitute the value of t as 9 in the function, we have;

h(9) = 2(9)² - 9

Find the square

h(9) = 2(81) - 9

h(9) = 153

The average change = 153 - 6 = 147/ 9 -2 = 147/ 7 = 21

Thus, the average rate of change between the given values of the variable is 21

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After answering the presented question, we can conclude that Therefore, the cubic function in standard form that has x-intercepts at (-1,0) (2,0) (4,0) and a y-intercept at (0,-24) is \(f(x) = 3x^3 - 21x^2\) \(+ 14x + 24.\)

In mathematics, a function appears to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

To find a cubic function in standard form, we can start by using the intercept form of the cubic equation:

\(f(x) = a(x-x1)(x-x2)(x-x3)\\f(x) = a(x+1)(x-2)(x-4)\\-24 = a(0+1)(0-2)(0-4)\\-24 = a(-8)\\a = 3\\\)

So the cubic function in standard form that satisfies the given conditions is:

\(f(x) = 3(x+1)(x-2)(x-4)\\f(x) = 3x^3 - 21x^2 + 14x + 24\\\)

Therefore, the cubic function in standard form that has x-intercepts at (-1,0) (2,0) (4,0) and a y-intercept at (0,-24) is \(f(x) = 3x^3 - 21x^2\) \(+ 14x + 24.\)

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Answer:

\(M=\frac{280}{140} =2\)

\(C=2+5=7\)

(2 Movies and 7 Commercials)

Step-by-step explanation:

Let's represent every time Carson's songs are played in a commercial as C and in movies as M.

Set up the following equations:

\(20C+120M=380\)  (1)

\(C=M+5\)   (2)

Substitute equation 2 for equation 1:

\(20(M+5)+120M=380\)

Distribute:

\(20M+100+120M=380\)

Simplify:

\(140M=280\)

Divide both sides by 140:

\(M=\frac{280}{140} =2\)

Substitute 2 as M back into either original equation, I will use (2):

\(C=2+5=7\)

Answer:

Step-by-step explanation:

I apologize for the confusion, but as a text-based AI model, I am unable to take pictures or upload files. However, I can assist you in solving the integrals you provided.

a) The integral of da is simply the variable "a" since the differential element "da" represents an infinitesimally small change in the area. So the integral is ∫da = a + C, where C is the constant of integration.

b) The integral of √2 (4x³ - 2x + 7) dr can be found by applying the power rule of integration and linearity of integration. Integrating each term separately, we get:

∫√2 (4x³ - 2x + 7) dr = √2 ∫(4x³ - 2x + 7) dr

= √2 ( ∫4x³ dr - ∫2x dr + ∫7 dr )

= √2 ( x⁴ - x² + 7r ) + C, where C is the constant of integration.

In the second part, we explain the step-by-step process of integrating each term in the given expression.

Starting with ∫4x³ dr, we integrate with respect to "r" while treating "x" as a constant. Using the power rule of integration, we add 1 to the exponent (3) and divide by the new exponent (4), resulting in (x³/4)r².

Next, we have ∫-2x dr. Here, the constant term "-2" can be brought outside of the integral. Integrating with respect to "r" gives us -2xr.

Lastly, we have ∫7 dr. Since "7" is a constant, integrating with respect to "r" results in 7r.

Combining the results of each term, we obtain the final integral:

∫√2 (4x³ - 2x + 7) dr = √2 ( x⁴ - x² + 7r ) + C, where C is the constant of integration.

Please note that the constant of integration (C) is added in each solution to account for the fact that the integral represents a family of functions rather than a single unique function.

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Answer:

$31.00

Step-by-step explanation:

124 x 25 = 3100, 3100 divided by 100 = 31.00

 The sample we collect plays a cruciThe sample we collect can significantly affect our understanding of a population,

especially when it comes to making generalizations or drawing conclusions about the entire population based on the sample data. The key aspect in this regard is whether the sample is representative of the population.

A representative sample is one that accurately reflects the characteristics, diversity, and distribution of the population from which it is drawn. When our sample is representative, we can have greater confidence in generalizing the findings from the sample to the larger population. However, if our sample is not representative, our understanding of the population may be biased or limited.

In the provided example, the given data represents different age groups and their reported time spent with friends per day. If we were to collect a sample from this population, it would be crucial to ensure that the sample includes individuals from each age group in proportion to their representation in the population. This would help ensure that our sample accurately reflects the age distribution of the population.

If our sample is not representative, it may lead to inaccurate conclusions. For instance, if we only surveyed individuals from the age group 55-64 and ignored the other age groups, our understanding of the population's time spent with friends would be limited to that specific age group. We wouldn't be able to generalize our findings to the entire population because we would have missed important variations in behavior across other age groups.

To improve the representativeness of our sample, we could use random sampling techniques, such as simple random sampling or stratified sampling, to ensure that individuals from all age groups are included in the sample. By doing so, we can enhance our understanding of the population as a whole and make more accurate inferences.

In conclusion, the sample we collect plays a crucial role in shaping our understanding of a population. A representative sample enables us to make valid generalizations and draw reliable conclusions about the entire population. It ensures that the characteristics and diversity of the population are properly reflected in the sample, allowing for more accurate insights and informed decision-making.al role in shaping our understanding of a population

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To determine the corresponding height of parallelogram RSTU, we need additional information or measurements related to the parallelogram. Without specific details we cannot calculate height accurately.

In a parallelogram, the height is the perpendicular distance between the base and the opposite side. However, to calculate this distance, we require either the length of the base or additional measurements, such as the length of another side or an angle.

Therefore, without more specific information, it is not possible to determine corresponding height of parallelogram RSTU. Additional measurements or details regarding parallelogram's properties would be necessary to calculate the height accurately.

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Answer:

y = 3x + 1

Step-by-step explanation:

Given the following points (0, 1) and (1, 4),

Let x1 = 0

y1 = 1

x2 = 1

y2 = 4

We can solve for the solve for the slope using the following formula:

\(m = \frac{y2 - y1}{x2 - x1} = \frac{rise}{run} = \frac{4 - 1}{1 - 0} = \frac{3}{1} = 3\)

Next, the y-intercept is the value of y, when x = 0. Looking at one of the given points, (0, 1) we can see that the value of y when x = 0 is 1.

Therefore, the y-intercept is (0, 1), or b = 1.

Given our slope, m = 3, and y-intercept, b = 1:

Our linear equation in slope-intercept form, y = mx + b is:

y = 3x + 1

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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Answer:

$8,864.73

Step-by-step explanation:

Base amount: $6,000.00

Interest Rate: 5% (yearly)

Effective Annual Rate: 5%

Calculation period: 8 years

The method of critical regions is an alternative approach to hypothesis testing, used to validate a claim. This method is based on comparing the observed sample statistic to one or more critical values, predetermined by the desired significance level, that determine the rejection or acceptance of the null hypothesis.

To use this method, the researcher first establishes the critical regions, typically denoted by critical values or cutoff points. A decision to reject or fail to reject the null hypothesis is then made by comparing the observed statistic to the critical values. If the observed value is beyond one or more of the critical values, the null hypothesis is rejected. If the observed statistic falls within the critical regions, the null hypothesis is accepted.

The critical region method is sometimes used instead of the p-value method when the probability of a Type II error is more important than the probability of a Type I error. Additionally, this method can be used to compare multiple population means, whereas the p-value method is limited to comparing one population mean. Therefore, the critical region method can be used in addition to or instead of the p-value method, depending on the researcher's desired result.

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Answer: 2.291

Step-by-step explanation:

Answer:

2.291

Step-by-step explanation:

The other guy awnser correct, checked through test

To determine the probability that Paul will not eat the pizza Chef Carl has made, we need to calculate the probability of Chef Carl selecting mushrooms as one of the toppings.

First, let's calculate the total number of possible combinations of two different toppings that Chef Carl can choose from the given options. Since order does not matter, we can use the combination formula:

C(n, r) = n! / (r! * (n-r)!),

where n is the total number of options and r is the number of choices. In this case, n = 5 (the number of toppings) and r = 2 (the number of choices).

C(5, 2) = 5! / (2! * (5-2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10.

So there are a total of 10 possible combinations of two different toppings that Chef Carl can choose.

Next, we need to calculate the number of combinations that include mushrooms. Since Paul will not eat pizza with mushrooms, we want to exclude this option.

To choose one topping from the remaining four (excluding mushrooms), there are C(4, 1) = 4 possible choices.

Therefore, the probability that Chef Carl selects a combination with mushrooms is 4/10.

Finally, the probability that Paul will not eat the pizza Chef Carl has made is the complement of this probability, which is 1 - 4/10 = 6/10 = 3/5.

So, the probability that Paul will not eat the pizza is 3/5.

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Answer:

i belive her shadow would be 11'6

Step-by-step explanation:

i think that because 54' subtract 48' is 6' so if you add 6' to 5'6 you get 11'6

The area of the given triangle is 87.55 square centimeter.

From the given triangle, base=17 cm and height=10.3 cm.

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.

Here, area of a triangle = 1/2 ×17×10.3

= 87.55 square centimeter

Therefore, area of the given triangle is 87.55 square centimeter.

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Answer:

7 by 11

Step-by-step explanation:

Let's assume that the length of the rectangular patio is "l" meters and the width is "w" meters.

According to the problem statement, the perimeter of the patio is 36 meters, so we can set up the equation:

2l + 2w = 36

Simplifying this equation by dividing both sides by 2, we get:

l + w = 18

We also know that the area of the patio is 77 square meters, so we can set up another equation:

lw = 77

We now have two equations in two variables, and we can use them to solve for l and w.

From the first equation, we can solve for one variable in terms of the other:

w = 18 - l

Substituting this expression for w into the second equation, we get:

l(18 - l) = 77

Expanding the left-hand side, we get a quadratic equation:

18l - l^2 = 77

Rearranging and simplifying, we get:

l^2 - 18l + 77 = 0

This quadratic equation can be factored as:

(l - 7)(l - 11) = 0

Therefore, the solutions are l = 7 or l = 11.

If l = 7, then w = 18 - l = 11, and the dimensions of the patio are 7 meters by 11 meters.

If l = 11, then w = 18 - l = 7, and the dimensions of the patio are 11 meters by 7 meters.

Therefore, the dimensions of the patio are either 7 meters by 11 meters or 11 meters by 7 meters.

Answer:

x = 5, y = 2

Step-by-step explanation:

    x - 5.2y = -5.4

+ (-x + 4.3y = 3.6)

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

         -0.9y = -1.8

                   y = 2

x - 5.2(2) = -5.4

x - 10.4 = -5.4

x = 5

The addition (elimination) method is a good choice for solving this system  because the x's are already opposites, and will cancel out when the two equations are added together. If one was to solve for x first, this method wouldn't be as good of a choice since it involves extra steps to eliminate the y's from the equation.