The four digit number abcd is a×103+b×102+c×10+d Prove that abcd is a multiple of 9 if and only if a+b+c+d is a multiple of 9 .

The mode will be = 5.2

What is mode?

A set of data values' mode is the value that appears the most frequently. The value of X at which the probability mass function reaches its highest value is known as the mode if X is a discrete random variable.

Consider the number of missed working days during a certain month of 5 employees of a company, 1,1,2,4,7

Mean age of the given data set will be its arithmetical average. Divide the sum of number of missed working days by 5. That is,

Mean number of days missed = 1+1+2+4+7/5

=15/5

=3days

hence mean = 3 days

Consider the formula for the variance for data set

σ² = ∑(X-µ)²/N

Compute the variance of given data set as follows

= 26/5

=5.2

Hence the variance is 5.2

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Answer:

I believe it is 14.

Step-by-step explanation:

Answer: The value of x is 14°

Step-by-step explanation:

Since line m is parallel to n, then then the two given angles will have the same measures. Meaning that 136 degrees has to equation (9x+10).

Set them to equal each other and solve for x.

9x + 10 = 136

    - 10      -10

  9x  = 126

x=  14

The critical points for the given expressions are needed to determine the extreme values. We are given the following expressions:

We will find the critical points for the given expressions: Taking partial derivative w.r.t x:8x - y + 3x²y + y³ = 0Partial derivative w.r.t y:-x + 8y + x³ + 3xy² = 0On solving above equations, we get two critical points:(-2, -1) and (0, 0)(ii) x³y²(12-3x - 4y) Taking partial derivative .

Partial derivative On solving above equations, we get one critical point: Taking partial derivative Partial derivative w.r.t y:1 / x = 0On solving above equations, we get one critical point:(0, 4)(v) (x² + y²) e6x+2x²Taking partial derivative Partial derivative  The above critical points are the potential candidates for the extreme values of the expressions.

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Answer:Triangle A = 7.5 Triangle B= 15 Area=22.5

Step-by-step explanation:

So first we have to get the area of Triangle A. This means we have to find the height and base of it. The base is 5 and the height is 3 as you can see in the picture. So 5x3 equals 15, but because it's a triangle we have to divide by 1/2, which makes 7.5. So the area for Triangle A is 7.5.

Now we have to find the area for Triangle B. The height is 3 and the base is 10. So like we did with Triangle A we have to multiply and then divide by 1/2. Which makes 15.

Now that you have both areas you just have to add them together. Which makes 22.5.

So 22.5 is the answer. Give brainilest if you can!

Answer:

click the points (0,4) and (1,5)

Step-by-step explanation:

y = x+4

if x  =  0 then

y = 0+4

so y = 4

0 , 4

then if x = 1

y = 1+ 4

so y = 5

1 , 5

Solving this will reveal that it will take more than 8hours for the temperature to reach this level.

Let t represent the duration in hours since the temperature began to rise. After t hours, the mercury will have risen by 2.5t degrees Celsius because the temperature is rising by 2.5°C every hour.

The inequality that indicates the number of hours needed for the average temp to rise over 20°C is as follows:2.5t + 0 > 20. When we simplify this inequality, we obtain:2.5t > 20 .

By multiplying equal parts by 2.5, we obtain:t > 8. As a result, it will take longer than eight hours for it temperature to exceed 20 °C.

We can express the hours required for the temperatures to exceed 20°C as the equation 2.5t > 20. Solving this imbalance will reveal that it will take more than 8hours for the temperature to reach this level.

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Answer:

Jessica is 60 years old.

Step-by-step explanation:

Hopes this helps.

To find the mean of the given frequency distribution of quiz completion times, we need to calculate the weighted average of the data. The mean represents the average time taken by the students to complete the quiz.

In this case, the frequency distribution provides the number of students falling within different time intervals. We can calculate the mean by multiplying each time interval midpoint by its corresponding frequency, summing up these values, and dividing by the total number of students.

Calculating the weighted average, we have:

Mean = (1 * 3 + 3 * 6 + 5 * 20 + 8 * 8) / (3 + 6 + 20 + 8) = 133 / 37 ≈ 3.59 minutes.Therefore, the mean completion time for the statistics quiz is approximately 3.59 minutes. This indicates that, on average, students took around 3.59 minutes to complete the quiz based on given frequency distribution.

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The paper clip costs $0.05 and the folder Costs $1.00 more, which is $1.05. Together, they add up to the total of $1.10.

Let's solve this problem step by step:

Let's assume the cost of the paper clip is x dollars.

According to the information given, the folder costs $1.00 more than the paper clip, so the cost of the folder would be (x + $1.00).

The total cost of the folder and the paper clip is $1.10, so we can write the equation:

x + (x + $1.00) = $1.10

Combining like terms, we have:

2x + $1.00 = $1.10

Subtracting $1.00 from both sides of the equation, we get:

2x = $0.10

Dividing both sides by 2, we find the value of x:

x = $0.10 / 2

x = $0.05

Therefore, the paper clip costs $0.05.

In summary, the paper clip costs $0.05 and the folder costs $1.00 more, which is $1.05. Together, they add up to the total of $1.10.

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The null and alternative hypotheses for this hypothesis test is H₀ : p = 0.93,  Hₐ : p > 0.93.

A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

Null and alternative hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Let 'p' be the population proportion.

Given statement : The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using.

Since null hypothesis shows that there is no significant difference between the quantities where as alternative hypothesis believes that there is some  difference,

Hence, the null and alternative hypotheses for this hypothesis test will be :-  H₀ : p = 0.93

          Hₐ : p > 0.93

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Answer:

Step-by-step explanation:

As you can observe in the image attached, the preimage RST is a tringle "pointing" to the negaitve side of the vertical axis (taking point S as reference).

The transformed triangle R'S'T' is pointing to the diagonal of the first quadrant, with a 45°, approximately.

The rotation needed in such transformation would be 90° + 45° = 135°, becasue from -y to +x there're 90°, then we rotate 45° to reach the position of R'S'T'.

Therefore, the right asnwer is a 135° rotation.

Answer:

a 135° rotation.

Step-by-step explanation:

As you can observe in the image attached, the preimage RST is a tringle "pointing" to the negaitve side of the vertical axis (taking point S as reference).

The transformed triangle R'S'T' is pointing to the diagonal of the first quadrant, with a 45°, approximately.

The rotation needed in such transformation would be 90° + 45° = 135°, becasue from -y to +x there're 90°, then we rotate 45° to reach the position of R'S'T'.

Therefore, the right asnwer is a 135° rotation.

Step-by-step explanation:

you can open the file I gave you now. the answer is there

Let x be the total amount collected at the door. Then, we can write

where the 0.02 denotes the comission of 2%. From this equation, we can find x.

Then, by moving 3000 to the right hand side, we have

which gives

Now, by moving 0.02 to the right hand side, we get

then, x is given by

Therefore, the total amount collected at the door is $ 27 000.

Answer:

3 5/9

Step-by-step explanation:

Answer: f(3) = 21

Explanation: To find f(3) or the value of the function when x = 3,

we plug in a 3 for the x in our function and we have 5(3) + 6.

Simplifying from here, we have 15 + 6 or 21.

So f(3) = 21.

The solution of the trigonometric equation is θ = π/6 radian

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

2cosθ = √3

Divide both sides by 2:

cosθ = (√3)/2

θ = cos⁻¹[(√3)/2]

θ = 30°

Convert 30° to radian by multiplying it with π/180. That is:

θ = 30 × π/180

θ = π/6 radian

Thus, the solution is θ = π/6 radian

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Answer:

let x be the number of cats and y be the number of dogs:

x + y = 40

4x + 4y = 160

If you divide both sides of the second equation by 4, you will be left with:

x + y = 40

Then, subtract both equations:

x + y =40

- (x + y = 40)

0 = 0

Since you have a number = a number, there are infinite solutions.

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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The engagement score was 3.86 three months ago.

Engagement score is a metric that measures the level of interaction and involvement that people have with a particular brand, product, or service. It is often used in marketing and advertising to assess the effectiveness of campaigns and to evaluate the success of social media strategies.

Let's call the engagement score from 3 months ago "x". If the score has been improving at a rate of 11% per month, then after 3 months, the score would be

\(x + (x \times 11) + (x \times 11 \times 11) + (x \times 11 \times 11 \times 11) = x \times 1.11^3\)

Since the score is now 4.6, we can set up an equation:

\(x \times 1.11^3 = 4.6\)

To find x, we can divide both sides by \(1.11^3\):

\(x = \frac {4.6} {1.11^3}\)

after solving, we can say that the value of  x is 3.86.

Therefore, the engagement score was 3.86 three months ago.

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1. in picture 1

2. in picture 2

Hope this helps :T

Also I am not so shure about 2, but I am 98% shure 1 is right.

Answer:

k = 3.

Step-by-step explanation:

By the Factor Theorem. if x+a is a factor of f(x)  then f(-a) = 0.

Here we use f(-1):

f(-1) = (-1)^3 + 2(-1) + k = 0

-1 - 2 + k = 0

k = 3.

Answer:

0.0576 ft2

Step-by-step explanation:

If the scale factor between a front door's blueprint and the actual front door is 0,04 The front door's actual area is 36 ft2, while its area on the blueprint will be 1.44 ft².

The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

It is given that, the scale factor of the blueprint of a front door to the actual front door is 0.04. The area of the actual front door is 36 ft².

Scale factor =Area of the new shape ÷ Area of the original shape

0.04= Area of the front door on the blueprint÷36 ft²

Area of the front door on the blueprint=0.04×36

Area of the front door on the blueprint=1.44 ft²

Thus, if the scale factor between a front door's blueprint and the actual front door is 0,04 The front door's actual area is 36 ft2, while its area on the blueprint will be 1.44 ft².

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Answer:

The term a⁴-3a²b²+b⁴ can't be factorised

The choices made by the decision-maker from each subset satisfy both Sen's properties α and β.

Based on the given payoff function, the decision-maker's preferences over the set X = {a, b, c} are as follows:

u(a) = 4

u(b) = 1

u(c) = 4

To construct the decision-maker's choices from each subset of X, we compare the payoffs associated with each alternative within the subset and select the one with the highest payoff.

Subset {a}:

The only alternative in this subset is 'a,' and its associated payoff is 4. Therefore, the decision-maker's choice from this subset is 'a.'

Subset {b}:

The only alternative in this subset is 'b,' and its associated payoff is 1. Therefore, the decision-maker's choice from this subset is 'b.'

Subset {c}:

The only alternative in this subset is 'c,' and its associated payoff is 4. Therefore, the decision-maker's choice from this subset is 'c.'

Subset {a, b}:

Comparing the payoffs of alternatives 'a' and 'b,' we have u(a) = 4 and u(b) = 1. Since 4 is greater than 1, the decision-maker's choice from this subset is 'a.'

Subset {a, c}:

Comparing the payoffs of alternatives 'a' and 'c,' we have u(a) = 4 and u(c) = 4. Both alternatives have the same payoff. In this case, the decision-maker's choice can be arbitrary, as the preferences are indifferent between 'a' and 'c.' So, the decision-maker's choice from this subset can be either 'a' or 'c.'

Subset {b, c}:

Comparing the payoffs of alternatives 'b' and 'c,' we have u(b) = 1 and u(c) = 4. Since 4 is greater than 1, the decision-maker's choice from this subset is 'c.'

Subset {a, b, c}:

Comparing the payoffs of alternatives 'a,' 'b,' and 'c,' we have u(a) = 4, u(b) = 1, and u(c) = 4. The decision-maker's choice from this subset is arbitrary, as the preferences are indifferent between 'a' and 'c.' So, the decision-maker's choice from this subset can be either 'a' or 'c.'

Now, let's check if these choices satisfy Sen's properties α and β.

Property α (Pareto efficiency):

For property α to hold, there should be no alternative in which all decision-makers prefer another alternative. In this case, as the decision-maker's choices are based on the highest payoff within each subset, there are no alternatives that are unanimously preferred over another. Therefore, property α is satisfied.

Property β (Independence of irrelevant alternatives):

For property β to hold, if two subsets have the same alternatives, the decision-maker's choice should be the same. Looking at the choices from each subset, we can see that the decision-maker's choice is consistent and does not depend on the presence or absence of irrelevant alternatives. Therefore, property β is satisfied.

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The global extreme values of the function `f(x,y) = 11x - 5y` under given conditions are:`f(x,y) = 16x + 15` (maximum)`f(x,y) = 11x - 55` (minimum).

Given function is `f(x,y)=11x−5y`We need to determine the global extreme values of the given function under the following conditions:y ≥ x - 3y ≥ -x - 3y ≤ 11Now, we need to find the critical points of the given function. For that, we'll calculate partial derivatives of the given function w.r.t x and y.`∂f/∂x = 11``∂f/∂y = -5`As we can see, the partial derivative of the function w.r.t x is positive. Therefore, the critical points of the given function would be the points where `∂f/∂y = -5 = 0`.Since there's no such point satisfying the above equation under given conditions, we can say that there's no critical point under given conditions.Now, let's evaluate the function at the boundaries given:At `y = x - 3`, `f(x,y) = 11x - 5y``= 11x - 5(x - 3)``= 6x + 15`At `y = -x - 3`, `f(x,y) = 11x - 5y``= 11x - 5(-x - 3)``= 16x + 15`At `y = 11`, `f(x,y) = 11x - 5y``= 11x - 5(11)``= 11x - 55`Now, to find the maximum value of `f(x,y)` under given conditions, we need to choose the maximum value among the above calculated values.In this case, `f(x,y)` is maximum at `y = -x - 3`, which is `16x + 15`.Therefore, the maximum value of `f(x,y)` under given conditions is `16x + 15`.Similarly, to find the minimum value of `f(x,y)` under given conditions, we need to choose the minimum value among the above calculated values.In this case, `f(x,y)` is minimum at `y = 11`, which is `11x - 55`.Therefore, the minimum value of `f(x,y)` under given conditions is `11x - 55`.Hence, the global extreme values of the function `f(x,y) = 11x - 5y` under given conditions are:`f(x,y) = 16x + 15` (maximum)`f(x,y) = 11x - 55` (minimum).

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Answer:

16

Step-by-step explanation:

336 divided by the length (21) is 16

Answer:

Step-by-step explanation:

  \(\sqrt{-90} = \sqrt{i^2\cdot 3^2\cdot 10}=3i\sqrt{10}\)

Comparing this to your form, we see that ...

  A = 3

  B = 10

Answer:

180 degrees in either direction

Step-by-step explanation:

picture it on a piece of paper, if you turn it once, the image becomes longer vertically, but if you flip it again, it looks like it does originally. If this is confusing, actually draw it and see how many times you need to rotate the page to make it look identical to the one you posted. 1 turn = 90 degrees.

- Span{v1, v2, v3, 0} is equal to the span of {v1, v2, v3}.
- Span{v1, v1-v2, v3} is equal to the span of {v1, v2, v3}.
- Span{v1, v2} is NOT equal to the span of {v1, v2, v3}.

Let's analyze each of the sets of vectors to determine if they are equal to the span of {v1, v2, v3}:
1. Span{v1, v2, v3, 0}:
This set is equal to the span of {v1, v2, v3} because adding the zero vector (0) does not affect the linear independence or the span of the other vectors.

A span is the set of all possible linear combinations of the vectors, and since the zero vector does not change the linear combinations, the span remains the same.
2. Span{v1, v1-v2, v3}:
This set is also equal to the span of {v1, v2, v3}.

The reason is that the vector (v1-v2) can be written as a linear combination of v1 and v2: (v1-v2) = 1*v1 + (-1)*v2.

Since all vectors in this set can be expressed as linear combinations of {v1, v2, v3}, the span remains the same.
3. Span{v1, v2}:
This set is NOT equal to the span of {v1, v2, v3} because it is missing the vector v3.

Since v1, v2, and v3 are linearly independent, removing one of them (v3 in this case) means that the set cannot span the same space as {v1, v2, v3}.

It has a lower dimension, and therefore, the span is different.

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Answer:

I don't know girl

Step-by-step explanation:

bc I don't know girl

Answer:ummm wht?

Step-by-step explanation: