One angle of an isosceles triangle measures 78°. Which other angles could be in that isosceles triangle?

Answer:

1. -5

2. 0

Step-by-step explanation:

1. Distribute the Negative Sign:

=a−2a+−1(3a−(4a−5))

=a+−2a+−1(3a)+−1(−4a)+(−1)(5)

=a+−2a+−3a+4a+−5

Combine Like Terms:

=a+−2a+−3a+4a+−5

=(a+−2a+−3a+4a)+(−5)

Answer:

=−5

2. Distribute:

=(13)(5)+(13)(−t)+−5+t+(−12)(5)+(−12)(−t)

=65+−13t+−5+t+−60+12t

Combine Like Terms:

=65+−13t+−5+t+−60+12t

=(−13t+t+12t)+(65+−5+−60)

Answer:

=0

The distribution of the number of business majors you choose is not binomial. The correct option is c) not binomial.

The distribution of the number of business majors you choose is not binomial because the conditions for a binomial distribution are not met:

1. There must be a fixed number of trials: In this case, we are choosing 3 students out of 10, which means the number of trials is not fixed.

2. The trials must be independent: This assumption is reasonable, as choosing one student does not affect the probability of choosing another student.

3. The probability of success must be the same for each trial: The probability of choosing a business major is 0.4 for the first trial, but it will change for the second and third trials depending on the results of the previous trials. Therefore, the probability of success is not the same for each trial.

Therefore, the correct option is c) not binomial.

The complete question is:

In a group of 10 college students, 4 are business majors. You choose 3 of the 10 students at random and ask their major. The distribution of the number of business majors you choose is

(a) Binomial with n = 10 and p = 0.4

(b) Binomial with n = 3 and p = 0.4

(c) Not binomial

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On solving the provided question we can say that, the answer of the following number line will be  \(=|x-y| or |y-x|\)\(=|3-(-4)| or |-4-3|\)

A number line is a visual representation of real numbers in elementary mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. A number line in mathematics is a horizontal straight line with numbers uniformly spaced apart. A number line can show how all the numbers in a series are represented. Both endpoints of this line continue indefinitely.

On the number line, the two points are

\(x = -4\\ y=3\)

The distance is a quantity that is positive.

As a result, the distance between x and y may be expressed as:

\(=|x-y| or |y-x|\\ =|3-(-4)| or |-4-3|\\ =|3+4| or |-7|\\ =|7| or |-7|\)

The sentence will read:

\(=|x-y| or |y-x|\)

\(=|3-(-4)| or |-4-3|\)

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False. Cronbach's alpha is a measure of internal consistency reliability, not a measure of the correlation between scale items.

It assesses the extent to which the items in a scale or questionnaire are measuring the same underlying construct.

Cronbach's alpha is calculated based on the inter-item correlations among the items in a scale. It provides a measure of the average correlation between all possible pairs of items in the scale. The range of Cronbach's alpha is between 0 and 1, with higher values indicating greater internal consistency or reliability.

Essentially, Cronbach's alpha quantifies the extent to which the items in a scale are consistently measuring the same construct or concept. It assesses how well the items "hang together" as a reliable measurement tool.

While correlation between scale items is related to internal consistency, Cronbach's alpha specifically measures the degree to which the items are interrelated and provides a single coefficient that reflects the overall reliability of the scale. It does not directly indicate the extent of item-item correlations or the strength of individual item contributions to the scale.

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Answer:

y = 14

Step-by-step explanation:

Answer:

-1.4

Step-by-step explanation:

substitute 10 and -3y

so it should look like -3y=10-5.8

then simplify so its -3y=4.2

divide both sides by -3 and you get y = 4.2/-3

multiply both the numerator and denominator by 10 and you get                  y= 42/-30

reduce the fraction to lowest terms by extracting and canceling out 6.

you end up with - 7/5 which simplifies to -1.4 so y = -1.4

Answer:

its 1

Step-by-step explanation:

look it up big dig daddy

Answer:

18c - 30d + 36

Step-by-step explanation:

To apply the distributive property, we must "distribute" (multiply) the outer term by the terms in the parentheses. In this case, the outer term is 6, and the inner terms are 3c, 5d, and 6. Then, if there's any like terms, you must combine them.

6(3c - 5d + 6)

(6 · 3c) + (6 · -5d) + (6 · 6)

18c + -30d + 36

As you can see, there's no like terms in this expression, so the equivalent expression to 6(3c - 5d + 6) is 18c + -30d + 36.

Answer:

The number of times a variable appears in a date set is called a constant.

Answer:

Step-by-step explanation:

its (-1,-6)

this is your answer

Answer:

Where is the equation though

Step-by-step explanation:

Answer:

The square root of a negative number is an imaginary number. The square root of -100 is 10i where i is the imaginary unit. Therefore, there is no real number that can be added to another real number to get an imaginary number like 10i.

Step-by-step explanation:

Answer: The square root of a negative number is an imaginary number. The square root of -100 is 10i where i is the imaginary unit. Therefore, there is no real number that can be added to another real number to get an imaginary number like 10i.

Answer:25%

Step-by-step explanation:

25% × 240 = (25/100) × 240 = 60

Solution

The population of a city is modeled by the function

where y is the population of the city after t years starting in the year 2000

In what year will the population be 5000

Therefore in 32 years time the population will be 5000

The value of a in the equation is 32/81

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

log2 ab = 5 and log3 b = 4

Rewrite the above equations properly

So, we have the following representations

log₂ ab = 5 and log₃ b = 4

Apply the exponent law of logarithm

This gives

ab = 2⁵ and b = 3⁴

Divide both equations

So, we have the following representation

ab/b = 2⁵/3⁴

Evaluate the quotient

a = 32/81

Hence, the value of a is 32/81

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The rate at which water is being poured into the cup when the water level is 9 cm is approximately 0.42 cm/sec.


To solve this problem, we can use related rates. Let's consider the height of the water in the cup as "h" and the radius of the water surface as "r". We know that the water level is rising at a rate of 3 cm/sec, which can be represented as dh/dt = 3 cm/sec.

Now, we need to find dr/dt, the rate at which the radius is changing when the water level is 9 cm. To do this, we can use similar triangles. The cone and the water form similar triangles, so the ratio of the radius of the water surface to the height of the water in the cup is constant. This means that r/h = 11/11 = 1. Therefore, the radius of the water surface is equal to the height of the water, r = h.

Differentiating both sides of the equation r = h with respect to time, we get dr/dt = dh/dt. Since we know that dh/dt = 3 cm/sec, we can conclude that dr/dt is also equal to 3 cm/sec.

So, when the water level is 9 cm, the rate at which water is being poured into the cup is approximately 0.42 cm/sec. This is because dr/dt = 3 cm/sec and r = 9 cm.

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Answer:

3 minutes

Step-by-step explanation:

A) The total no. of students taking only maths is 220 students.

let's say the total no. of students taking only maths = M

M = 360 - (100 + 40) = 220 students.

B) The total no. of students in the survey is 960 students.

let's say the total no. of students in the survey = S

S = 360 + 280 + 300 - (100 + 120 + 110) + 40 = 960 students.

C) The total no. of students who are taking exactly two of the courses is 330 students.

let's say the total no. of students who are taking exactly two of the courses = T

T = 100 + 120 + 110 = 330 students.

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The unit vector in the direction of the given vector [3 27 -3] is [1/9, 1, -1/9].

Given vector is w= [3 -4 -6].

Compute ∥w∥: The norm or length of a vector w is denoted by ∥w∥ and it is defined as

∥w∥ = sqrt(w1^2 + w2^2 + w3^2 +....+ wn^2)

where w1, w2, w3, ...., wn are the components of the vector.

Using the given formula, we get:

∥w∥ = sqrt(3^2 + (-4)^2 + (-6)^2)

= sqrt(9 + 16 + 36)

= sqrt(61)

Thus, the magnitude of the given vector w= [3 -4 -6] is sqrt(61).

Therefore, ∥w∥ = sqrt(61).

A unit vector in the direction of the given vector [3 27 -3].

The unit vector of a vector u is defined as u/∥u∥ .We have to find the unit vector in the direction of the given vector

[3 27 -3].

To find the unit vector of the given vector, we need to find its magnitude.

∥u∥ = sqrt(3^2 + 27^2 + (-3)^2)

= sqrt(729)

= 27

Therefore, the unit vector in the direction of the given vector is:

u/∥u∥ = [3/27, 27/27, -3/27]

= [1/9, 1, -1/9]

Thus, the unit vector in the direction of the given vector [3 27 -3] is [1/9, 1, -1/9].

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To compute ||w|| using w = [3, -4, -6] For this, we need to apply the formula of magnitude or length of a vector which is as follows:

\($\left\| {\vec v} \right\| = \sqrt {v_1^2 + v_2^2 + v_3^2 + \cdots + v_n^2}$\)

So,\($\left\| {\vec w} \right\| = \sqrt {{w_1}^2 + {w_2}^2 + {w_3}^2}$\),  

given \($\vec w = [3,-4,-6]$\) So,\(${w_1} = 3$\), \(${w_2} = -4$\), and \(${w_3} = -6$\)

Therefore,  \($\left\| {\vec w} \right\| = \sqrt {{w_1}^2 + {w_2}^2 + {w_3}^2}= \sqrt {3^2 + (-4)^2 + (-6)^2}$\)

After calculating the above, we get

\($\left\| {\vec w} \right\| = \sqrt {9 + 16 + 36} = \sqrt {61}$\)

Thus,\($\boxed{\left\| {\vec w} \right\| = \sqrt{61}}$\)

To find a unit vector in the direction of the given vector [3, 27, -3]

We need to divide the vector by its magnitude or length.So, let \($\vec v = [3, 27, -3]$\) and \($\left\| {\vec v} \right\|$\) be the magnitude of vector \($\vec v$\).

Therefore, the unit vector in the direction of vector $\vec v$ is:

\($\frac{\vec v}{\left\| {\vec v} \right\|} = \frac{\vec v}{\sqrt {{v_1}^2 + {v_2}^2 + {v_3}^2}}$\)

Given, \($\vec v = [3, 27, -3]$\)

Thus,\(${v_1} = 3$\), \(${v_2} = 27$\), and \(${v_3} = -3$\)

Therefore, the magnitude of the given vector \($\vec v$\) is

\($\left\| {\vec v} \right\| = \sqrt {{v_1}^2 + {v_2}^2 + {v_3}^2}= \sqrt {3^2 + 27^2 + (-3)^2}$\)

After calculating the above, we get

\($\left\| {\vec v} \right\| = \sqrt {9 + 729 + 9} = \sqrt {747} = 3\sqrt{83}$\)

Thus, \($\frac{\vec v}{\left\| {\vec v} \right\|} = \frac{[3, 27, -3]}{3\sqrt{83}}$\)

This simplifies to

\($\boxed{\frac{\vec v}{\left\| {\vec v} \right\|} = \left[\frac{1}{\sqrt{83}}, \frac{9}{\sqrt{83}}, -\frac{1}{\sqrt{83}}\right]}$\)

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Therefore , the solution of the given problem of algebra comes out to be

Product means to multiply and decreased means to subtract so option C only seems valid

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

Product means to multiply and decreased means to subtract so option C only seems valid

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There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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If three different letters are to be mailed to 3 persons and the three letters are to be put at random into three envelopes, then the probability of putting all letters into the wrong envelopes is `2/3!` or `1/3`.

Three different letters are to be mailed to 3 persons. These three letters are to be put at random into three envelopes. The sample space for this problem is the number of ways to put three different letters into three envelopes. This is a permutation problem.

The total number of ways to put three different letters into three envelopes is

`3!` = `6` ways.

If you number the letters `1, 2, 3` and the envelopes `A, B, C`, the possible permutations are:

1. Letter 1 in envelope A, letter 2 in envelope B, letter 3 in envelope C

2. Letter 1 in envelope A, letter 2 in envelope C, letter

3 in envelope B3. Letter 1 in envelope B, letter 2 in envelope A, letter 3 in envelope C4. Letter 1 in envelope B, letter 2 in envelope C, letter 3 in envelope A5. Letter 1 in envelope C, letter 2 in envelope A, letter 3 in envelope B6. Letter 1 in envelope C, letter 2 in envelope B, letter 3 in envelope A The event that we're interested in is putting all letters into the wrong envelopes.

This can only happen in one of the permutations :Letter 1 in envelope B, letter 2 in envelope C, letter 3 in envelope A The probability of this event happening is `1/6`. However, there are three envelopes, so there are three equally likely ways to put the letters into the envelopes. Therefore, the probability of putting all letters into the wrong envelopes is `1/6 x 3` = `1/2` = `0.5` or `2/3!` = `1/3`.

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In a one-tail hypothesis test where you reject h0 only in the upper tail

-1.2910  is the p-value.

P value = P (z > 1.70) = 1 - P(2<1.7) = 0.0446

P value = P (z > -2.44) = 0.0073

t< n-1 = -1.2910

A p-value is a statistical measure used to test a hypothesis against observed data. The p-value measures the probability of getting the observed result given that the null hypothesis is true. The lower the p-value, the higher the statistical significance of the observed difference.

For null hypothesis significance tests, the p-value is the probability of obtaining an extreme test result that is at least as extreme as the actually observed result, given that the null hypothesis is true.

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