Solve the linear congruence 2x + 6 = 4(mod 8).

Answer: Mass of a typical house cat:

Automatically eliminate B and D since they are not metric unit for mass

So, that leaves us with A and C. And since a cat is not huge nor weighs that much, the most reasonable one would be to measure it in grams.

Correct answer: C

Draw 5 new arcs from point D along DB the same distance apart as those on AC. Then the correct option is A.

A line segment in mathematics has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a path that joins two places.

Nelda is dividing AB into 6 congruent segments. She has reached the point shown.

Draw 5 new arcs from point D along DB the same distance apart as those on AC. Then connect each corresponding point on AC and BD. Then the correct option is A.

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The complete question is attached below.

Answer:

The awnser is 4.472135955

(i) The probability of the arrow pointing to 7 is 1/12.
(ii) The probability of the arrow pointing to a prime number is 5/12.
(iii) The probability of the arrow pointing to a composite number is 1/2.

The probability of an event is determined by dividing the number of favorable outcomes by the total number of possible outcomes.

(i) To find the probability of the arrow pointing to 7, we need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, there is only one favorable outcome (7) and the total number of possible outcomes is 12 (numbers 1 to 12). Therefore, the probability of the arrow pointing to 7 is 1/12.

(ii) To find the probability of the arrow pointing to a prime number, we need to determine the number of favorable outcomes (prime numbers) and the total number of possible outcomes. The prime numbers between 1 and 12 are 2, 3, 5, 7, 11, making a total of 5 favorable outcomes. The total number of possible outcomes is still 12. Therefore, the probability of the arrow pointing to a prime number is 5/12.

(iii) To find the probability of the arrow pointing to a composite number, we need to determine the number of favorable outcomes (composite numbers) and the total number of possible outcomes. The composite numbers between 1 and 12 are 4, 6, 8, 9, 10, 12, making a total of 6 favorable outcomes. The total number of possible outcomes is still 12. Therefore, the probability of the arrow pointing to a composite number is 6/12, which can be simplified to 1/2.

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Answer:

A B D

Step-by-step explanation:

those are the answers

But a closer look shows that B will be the best answer.

Answer:

Since all the rhombus is parallelogram

some are trapezoid and quadrilateral.

So

B.parallelogram is a answer:

it opposite side are equal.

diagonal bisect angle equally.

.

The probability that exactly 3 out of the first 11 customers buy a magazine is 2.23%

The proportion of customers that buy a magazine = 8.4%

If 3 out of the first 11 customers buy a magazine, then this proportion is given as; 3/11 or 27.27%

Therefore, the probability that 3 out of the first 11 customers will buy a magazine is calculated as follows;

probability = 8.4% × 27.27%

probability = (8.4/100) × (27.27/100)

probability = 0.084 × 0.2727

probability = 0.0223

Converting it into percentage as follows;

probability = 0.0223 × 100

probability = 2.23%

Therefore, the probability that 3 out of the first 11 customers buy a magazine is calculated to be 2.23%.

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Answer:

C

Step-by-step explanation:

The congruency rules, AAS and ASA do not work as these triangle do not share any congruent angles or sides.

Answer:

Step-by-step explanation:

-2x - 14 > -4 + 3x

subtract 3x from both sides

-5x - 14 > -4

add 14 to both sides

-5x > 10

divide both sides by -5

x < -2

The answer would be -5x > 10.

This is because our last inequality was -5x - 14 > -4 so we add 14 to both sides and it would look like this -5x (-14 + 14) > (-4 + 14) which would transition into our next inequality -5x > 10.

So therefore the answer would be -5x > 10.

The function describing the relationship of the given variables is a= 6r

The statement is givn as:

a varies directly with r

This means that

a= kr

Where k is the constant of variation

When r = 6 , a = 18, we have

18= 6k

Divide by 6

k = 3

Substitute k = 3 in a= kr

a= 6r

Hence, the function describing the relationship of the given variables is a= 6r

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Answer:

\(8x^{2} +14x+6\)

Step-by-step explanation:

The formula for the area of rectangle is length times width:

\((2x+2)(4x+3)\\\)

Use FOIL method:

\(8x^{2} +6x+8x+6\\8x^{2} +4x+6\)

Answer:

The answer is below

Step-by-step explanation:

Two triangles are similar if the ratio of their corresponding sides are in the same proportion.

1. ΔWXY is isosceles with legs WX and WY      (given)

2. ΔWVZ is isosceles with legs WV and WZ     (given)

3. WX =  WY, WV = WZ  (definition of an isosceles triangle)

4. \(\frac{WX}{WY}=1\\\\\)

\(\frac{WX}{WY}=\frac{WZ}{WZ} \ \ \\) (definition of ≅)

5. (WZ)(WX) = (WY)(WZ)       (multiplication property)

6. (WZ)(WX) = (WY)(WV)  (substitution property).

7. \(\frac{WY}{WZ}=\frac{WX}{WV}\)      (property of proportion)

8. ∠W = ∠W (reflexive property)

9. ΔWXY ~ ΔWVZ (side - angle - side similarity postulate)

Answer:

♣:  

✔ WX = WY; WV = WZ

♦:  

✔ substitution property

♠:  

✔ SAS similarity theorem

Step-by-step explanation:

just took it :)

Answer:

X= -7

Step-by-step explanation:

-25 + 8x +20 = -61

8x  -5 = -61

8x = -56

x = -7

The perimeter of the triangle is 170 inches.

To solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:

sin(35°) = 46/x

x = 46/sin(35°) = 65 inches

Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:

cos(35°) = 65/x

x = 65/cos(35°) = 75 inches

The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:

P = 65 + 75 + 30

= 170 inches

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Answer:

Step-by-step explanation: The slope is 10 because when x moved positive 2, y moved positive 20 so y = 10x + b and you can just pick one point that the line crosses so I will use (2, 40) so when you put that in the equation it is 40 = 20 + b so b is 20. The answer is y = 10x + 20

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

Let y represent the total monthly charges for x amount of class.

From the graph, the line passes through point (0,20) and (2, 40). Hence, the equation of the line is:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-20=\frac{40-20}{2-0} (x-0)\\\\y-20=2x\\\\y=2x+20\)

Hence the equation for the line in slope-intercept form is y = 2x + 20

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The sums of vectors are:

u + v =   <4, 1>  this is true.

v + w = <1, -3> this is false.

w + u = <-6, 1> this is true.

Remember that the sum between two vectors <a, b> and <c, d> is:

<a, b> +  <c, d> = <a + c, b + d>

The vectors in the graph are:

w = <-4, -3>

v = <6, -3>

u = <-2, 4>

Then the sums are:

u + v = <6, -3> + <-2, 4>

        = <6 - 2, -3 + 4> = <4, 1>  this is true.

v + w = <6, -3> + <-4, -3> = <6 - 4, -3 - 3> = <2, -6>  the second sum is false.

w + u = <-4, -3> + <-2, 4> = < -4 - 2, -3 + 4> = <-6, 1> so the last sum is true.,

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Answer: f(x) = -1/2(x+3)

Example: g(x) = -1/2(-x-3)

This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.

The validity of short forms may be reduced because they contain fewer items compared to the full-length version. Short forms of tests or questionnaires are often used in research and clinical settings due to their convenience and efficiency.

This means that the short form may not fully capture the construct being measured and may not accurately reflect the individual's true scores. Additionally, the items selected for the short form may not be representative of the full range of the construct, leading to bias and limited generalizability.

Therefore, researchers and clinicians should consider the trade-offs between convenience and validity when deciding to use short forms.

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The integral ∫[infinity] 4e^(-1/x) / x^2 dx is divergent.

To determine whether the integral is convergent or divergent, consider the integral: ∫[infinity] 4e^(-1/x) / x^2 dx.

Identify the limits of integration.
Since we are given an improper integral with infinity as the upper limit, we can rewrite it with a limit notation: ∫[a to ∞] 4e^(-1/x) / x^2 dx = lim (b→∞) ∫[a to b] 4e^(-1/x) / x^2 dx.

Evaluate the integral.
Now we need to evaluate the integral and see if the limit exists. To do this, let's first substitute u = -1/x, which gives us du = (1/x^2) dx. The integral now becomes:

∫[a to b] 4e^(u) du.

Calculate the antiderivative.
The antiderivative of 4e^u is 4e^u + C. Now we need to calculate the definite integral:

4e^u |[a to b] = 4(e^b - e^a).

Apply the limit and check for convergence.
Now we take the limit as b approaches infinity:

lim (b→∞) (4(e^b - e^a)).

Since e^b approaches infinity as b approaches infinity, the limit does not exist, and the integral is divergent.

The integral ∫[infinity] 4e^(-1/x) / x^2 dx is divergent.

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Answer:

$430

Step-by-step explanation:

Let the weekly income be x

Money spent on food= $86

% of weekly income spent on food = 20

20% of weekly income in terms = 20/100 * x = x/5

This, income is equal to $86 as given

thus,

x/5 = 86

x = 86*5 = 430

Thus, weekly income is $430.

We plot the means on a number line to see which means are different. Plotting the sample means on a number line serves to illustrate this when the null hypothesis that all population means are equal is rejected.

This criteria, known as (alpha) in null hypothesis testing, is typically set to.05. The null hypothesis is rejected if there is less than a 5% likelihood that a result as dramatic as the sample result would occur if the null hypothesis were true. The outcome is referred to as statistically significant when this occurs.

Plotting scientific data is used to highlight correlations between variables or to visualize variance, but not all data sets need one. If there are only one or two points, it is simple to look at the numbers directly, and adding a graph adds little to nothing.

hence we plot the means on a number line to see which means are different. Plotting the sample means on a number line serves to illustrate this when the null hypothesis that all population means are equal is rejected.

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Answer:

1 foot = 0.7 secs

Step-by-step explanation:

14 seconds divided by 20 feet = 0.7 seconds per foot descended.

Hope this helps and good luck :)

Answer:

A) \(9 *l=54\)

Step-by-step explanation:

The area of a rectangle is w*l=A, where w is the width and l is the length.

In this question, we are given 2 of the variables. We are told that the width is 9 and the area is 54. So, to find the equation that represents this situation, simply plug in the values.

Then, if needed we can find the length of the rectangle. Through the division property of equality, we know that dividing both sides of the equation maintains the equality of the equation. So, we can divide both sides by 9 to isolate the variable.

Answer:

1/3

Step-by-step explanation:

The probability that you will draw a heart is 1/3, the correct option is 3.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

Number of cards=  6 hearts, 4 clubs, and 8 spades

Now,

To find the probability of drawing a heart, we need to divide the number of hearts by the total number of cards in the pile. The number of hearts is 6 and the total number of cards is 6 + 4 + 8 = 18.

The probability of drawing a heart is 1/18=1/3

Therefore, by probability the answer will be 1/3.

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Answer: 38

Step-by-step explanation:

Subtract 1/8 from 1/2

12 - 18 is 38.

Steps for subtracting fractions

Find the least common denominator or LCM of the two denominators:

LCM of 2 and 8 is 8

Next, find the equivalent fraction of both fractional numbers with denominator 8

For the 1st fraction, since 2 × 4 = 8,

12 = 1 × 42 × 4 = 48

Likewise, for the 2nd fraction, since 8 × 1 = 8,

18 = 1 × 18 × 1 = 18

Subtract the two like fractions:

48 - 18 = 4 - 18 = 38

The rate of current in the stream on that​ day is; 2 miles per hour

When dealing with relative velocity, we can say that;

When the motorboat travels downstream, then it means the total velocity will be;

Total velocity = Velocity of the motorboat in still water + Velocity of the stream.

If the motorboat travels upstream, the total velocity will be;

Total velocity = Velocity of the motorboat in still water - Velocity of the stream.

Thus,

Upstream speed = (14 mi/h - S)

Downstream speed = (14 mi/h + S)

Where;

S is the rate of current in the stream.

We are told that going downstream, it takes 15 minutes more to travel 12 miles, then we can write the system of equations as;

(14 mi/h + S)*T = 12 mi

(14 mi/h - S)*(T - 15 min) = 12 mi

Making T the subject in the first equation gives;

T = (12 mi)/(14 mi/h + S)

Plugging in (12 mi)/(14 mi/h + S) for T in the second equation gives;

(14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi

Multiply both sides by (14 mi/h + S) to get;

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 15 min) = 12 mi*(14 mi/h + S)

Since the speeds are in miles per hours, we can rewrite as:

- 15 min = -0.25 h

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 0.25 h) = 12 mi*(14 mi/h + S)

168 mi²/h - 12mi*S  + 49mi²/h + 0.25h*S² = 168mi²/h + 12mi*S

- 12mi*S  + 49mi²/h - 0.25h*S² = 12mi*S

-24mi*S -  0.25h*S²  + 49mi²/h = 0

Solving this quadratic equation with online quadratic equation solver gives us; S = 2 mph

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Answer:

20/27

Step-by-step explanation:

To calculate the project's NPV in the best-case scenario, we need to consider the best possible values for each variable.

Here are the steps-

Step 1: Calculate the annual cash inflow.
Annual revenue = Unit price * Expected sales

= $80 * 40,600

= $3,248,000

Step 2: Calculate the annual cash outflow.

Annual variable cost = Variable cost * Expected sales

= $60 * 40,600

= $2,436,000
Annual fixed cost = Fixed cost

= $440,800
Annual depreciation = Initial investment / Project life

= $14,000,000 / 10

= $1,400,000
Annual tax = (Annual revenue - Annual variable cost - Annual fixed cost - Annual depreciation) * Tax rate

= ($3,248,000 - $2,436,000 - $440,800 - $1,400,000) * 0.21

= $208,720

Step 3: Calculate the annual net cash flow.

Annual net cash flow = Annual revenue - Annual variable cost - Annual fixed cost - Annual depreciation - Annual tax

= $3,248,000 - $2,436,000 - $440,800 - $1,400,000 - $208,720

= $162,480

Step 4: Calculate the NPV using the best-case scenario cash flows.-

\(NPV = Initial investment + (Annual net cash flow / (1 + Required rate of return)^n)\)

\(= -$14,000,000 + ($162,480 / (1 + 0.14)^1) + ($162,480 / (1 + 0.14)^2) + ... + ($162,480 / (1 + 0.14)^10)\)

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