Quadrilateral ABCD is translated 5 units right. What are the coordinates of
quadrilateral A'B'C'D?
D(1.5)
A (5,5) D
C(21) B15 1C
A
BIX
OA. A (5,0), B'(5,-4), C'(2.-4), D'(1,0)
OB. A'(10, 10), B (10, 6), C (7,6),
D'(6, 10)
OC. A'(10, 5), B' (10, 1), C'(7, 1), D'(6, 5)
OD. A'(0, 5), B'(0, 1), C'(-3, 1), D'(-4,5)

The function g in vertex form is g (x) = –5x^2 – 3.

In this case, the parent function is:

f (x) = x^2

First, after the reflection across the x-axis, we will get:

f (x) = –f (x)

And, the function will be:

g (x) = –x^2

Then, vertically stretched by a factor of 5, we will get:

g (x) = –5x^2

Last, translated 3 units down, we will get:

g (x) = –5x^2 – 3

Thus, the vertex form of the function g will be:

g (x) = –5x^2 – 3

In mathematics, a translation is a transformation which occurs when a figure is moved from one location to another location without changing its size or shape.

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36

Step-by-step explanation:

5x-6+3x+90=180

8x+84=180

8x=96

x=12

Plug it in to 3x

3x12=36

Answer:

0

Step-by-step explanation:

In the given expression, substitute -5 for x and 25 for y:

5|x|-y to the third power over x   becomes

   5|-5| - 25         25 - 25

 ------------------ = --------------   =  0

            -5                  -5

In this assignment, 1200 rolls of two balanced six-faced dice will be simulated. You will then evaluate the probabilities of obtaining each of the following three outcomes for the first 30, 90, 180, 300, and 1200 rolls.

These observed probabilities will then be compared to the actual probabilities of obtaining these outcomes.The three possible outcomes are:2: The first die will show a 1, and the second die will show a 1.7: One die will show a 1, and the other will show a 6, or one die will show a 2, and the other will show a 5, or one die will show a 3, and the other will show a 4.11: One die will show a 5, and the other will show a 6, or one die will show a 6, and the other will show a 5.There are 36 possible outcomes when two dice are rolled, with each outcome having an equal chance of 1/36. There are two dice, each with six faces, giving a total of six possible results for each die. The actual probabilities are as follows:2: 1/367: 6/3611: 2/36You will determine the observed probabilities of the three outcomes using the actual data obtained in the rolling experiment, and then compare the actual and observed probabilities.

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a) Matrix A is singular when α = 0.

b) For matrix A:

    a) It is singular when α = 0.

    b) It is invertible for any value of α that is not equal to zero.

a) To find the values of α for which matrix A is singular, we need to determine when the determinant of A is equal to zero. The determinant of A can be calculated using cofactor expansion:

|A| = 1(1(α) - 1) - 0(0(α) - 1) + (-1)(0(1) - 1(1))

= α - 1 - (-1)

= α

For matrix A to be singular, the determinant |A| must be zero. Therefore, we have:

α = 0

So, matrix A is singular when α = 0.

b) To find the values of α for which matrix A is invertible, we need to determine when the determinant of A is non-zero. From the previous calculation, we know that the determinant of A is equal to α. Therefore, matrix A will be invertible for any value of α that is not equal to zero.

In summary, for matrix A:

a) It is singular when α = 0.

b) It is invertible for any value of α that is not equal to zero.

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A two-sample t-test should be used to compare the mean waiting times of the two hospitals.

A two-sample t-test is a statistical test used to compare the means of two independent groups.

It is used to determine whether there is a significant difference between the means of the two groups, based on the assumption that the data is normally distributed and that the variances of the two groups are equal.

The test calculates a t-statistic, which is compared to a critical value based on the degrees of freedom and the desired level of significance to determine if the difference between the means is statistically significant.

Here we want to know if the eibmoz hospital or the eripmav hospital had the shortest er waiting time.

we pick 40 random days, and times each er on those days.

To compare the mean waiting times of two different hospitals, you can use a two-sample t-test.

In this case, you would collect data on the waiting times at both the Eibmoz and Eripmav hospitals on the same 40 random days and calculate the sample means and standard deviations for each hospital.

You would then use a two-sample t-test to determine if there is a statistically significant difference between the mean waiting times at the two hospitals.

Hence,

A two-sample t-test should be used to compare the mean waiting times of the two hospitals.

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After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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The total number of people who have the disease is 115.

The total number of people in the sample population is

Total = 175

The negative predictive value is

NPV= (TN / (TN + FN)) = (25 / (25 + 55) = 25 / 80 = 0.3125

The positive predictive value

PPV = (TP / (TP + FP)) = (60 / (60 + 35) = 60 / 95 = 0.6316

The sensitivity of the test

Sensitivity = (TP / (TP + FN)) = (60 / (60 + 55) = 60 / 115 = 0.5217

The total number of people who have the disease

= 60+55 = 115

The number of False Positives (FP)

= 35

The number of True Positives (TP)

= 60

The total number of people that tested negative

= 80

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Answer:

C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.

Step-by-step explanation:

An outlier is a data point that sticks out like a sore thumb. It's so different from the rest of the data that it makes you wonder if it's a mistake or a miracle. One way to spot an outlier is to use the 1.5IQR rule, where IQR stands for interquartile range. The interquartile range is the gap between the third quartile (Q3) and the first quartile (Q1) of the data. The 1.5IQR rule says that any data point that is more than 1.5*IQR above Q3 or below Q1 is an outlier.

In this case, the first quartile (Q1) is 75, the third quartile (Q3) is 85, and the interquartile range (IQR) is 10. So, any data point that is more than 1.5*10 = 15 above 85 or below 75 is an outlier. The only data point that does this is 110, which is 25 above 85. That means 110 is an outlier.

What does this outlier mean in this situation? It means that one person who came to the senior center that afternoon was way older than the rest of the folks. The average age of the visitors was not changed by this outlier, since it was just one out of 12 data points. But, the outlier does mess up the range and the standard deviation of the data, making them bigger than they would be without the outlier.

Answer:The answer is C

Step-by-step explanation:I did the test.

The improper integral ∫ 1/x dx from 0 to ∞ is divergent. The improper integral ∫ 1/x dx from 0 to ∞ represents the integral of the function 1/x with respect to x over the interval from 0 to positive infinity.

To determine whether this integral is convergent or divergent, we need to evaluate it.

Let's split the integral into two parts: from 0 to 1 and from 1 to ∞.

∫(0 to 1) 1/x dx

This part of the integral is a finite integral, and it can be evaluated as:

∫(0 to 1) 1/x dx = [ln|x|] (0 to 1) = ln(1) - ln(0)

However, ln(0) is undefined, so this part of the integral does not converge.

Now let's evaluate the second part of the integral:

∫(1 to ∞) 1/x dx

This integral represents the area under the curve of the function 1/x from 1 to ∞. This is a well-known integral and is known to diverge. As x approaches infinity, the value of 1/x approaches 0, but it never reaches 0. Therefore, the area under the curve keeps increasing indefinitely, and the integral diverges.

Since either part of the integral diverges, the overall integral ∫ 1/x dx from 0 to ∞ is divergent.

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Answer:

$22,506

hope it helped!

Based on the above, Keenan paid $9,420 in federal income tax in 2009.

Let X be the amount Keenan paid in taxes in 2009.

According to the problem, Keenan paid 70% less in 2010 than he did in 2009. This means that he paid only 30% of what he paid in 2009, since 100% - 70% = 30%.

We can express this mathematically as:

0.30X = 2,826

To solve for X, we can divide both sides of the equation by 0.30:

X = 2,826 ÷  0.30

X = 9,420

Therefore, Keenan paid $9,420 in federal income tax in 2009.

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Now we find the simplified form of algebraic expressions by algebra properties:

First part

Case A: 781 / 576

Case B: 3368 / 1125

Case C: 16

Case D: - 1077 / 200

Case E: - 145 / 144

Case F: - 41 /392

Second part

Case A: - 2 · x · a⁴

Case B: (4 · a⁵ · c³) / (- 3 · b²)

Case C: (4 · x² · w⁵) / (9 · y³)

Case D: (27 · x⁵ · y²) / (80 · z⁹)

Case E: (1600 · x¹⁷ · z⁴) / y¹⁸

Case F: 24 · a⁶ · b³

The first part of this question we find six cases of algebraic expressions involving powers, each of them can be simplified by algebra properties:

Case A:

(3 / 4)⁻² - (4 / 3)⁻³

3⁻² / 4⁻² - 4⁻³ / 3⁻³

3⁻²· 4² - 4⁻³ · 3³

4² / 3² - 3³ / 4³

(4³ · 4² - 3³ · 3²) / (3² · 4³)

(4⁵ - 3⁵) / (3² · 4³)

781 / 576

Case B:

(5 / 3)² - (- 5 / 3)⁻³

5² / 3² - (- 5)⁻³ / 3⁻³

5² / 3² - 3³ / (- 5)³

[5² · (- 5)³ - 3⁵] / [3² · (- 5)³]

3368 / 1125

Case C:

(1 / 4)⁻² - (- 3 / 2)³ - (- 2 / 3)⁻³

4² - (- 3)³ / 2³ - 3³ / (- 2)³

[4² · 2³ - (- 3)³] / 2³ - 3³ / (- 2)³

155 / 8 - 27 / 8

16

Case D:

- (- 2 / 5)⁻³ - [(- 5 / 2)⁻² ÷ 4⁻³]

- (5 / 2)³ - [(- 2 / 5)² ÷ (1 / 4)³]

- (5 / 2)³ - [(- 2)² · 4³] / 5²

- 125 / 8 - (- 256 / 25)

- 125 / 8 + 256 / 25

- 1077 / 200

Case E:

(- 1)¹⁰¹ - 12⁻²

- 1 - 1 / 12²

(- 12² - 1) / 12²

- 145 / 144

Case F:

(- 7)⁻² - 2⁻³

1 / (- 7)² - 1 / 2³

1 / 49 - 1 / 8

- 41 /392

And the second part implies other six cases:

Case A:

- 2 · x / a⁻⁴

- 2 · x · a⁴

Case B:

(4 · a · b⁻²) / (- 3 · a⁻⁴ · c⁻³)

(4 · a / b²) / [- 3 / (a⁴ · c³)]

[4 · a · (a⁴ · c³)] / (- 3 · b²)

(4 · a⁵ · c³) / (- 3 · b²)

Case C:

w · (3 · x · y)⁻² / [4 · y · (2 · x · w)⁻⁴]

[w / (3² · x² · y²)] / [(4 · y) / (2⁴ · x⁴ · w⁴)]

[w · (2⁴ · x⁴ · w⁴)] / [(3² · x² · y²) · (4 · y)]

(16 · x⁴ · w⁵) / (36 · x² · y³)

(4 · x² · w⁵) / (9 · y³)

Case D:

[(5 · x) / (3 · y² · z)]⁻³ × [(x² · y) / (2 · y · z³)]⁴

[(3 · y² · z)³ / (5 · x)³] × [(x² · y)⁴ / (2 · y · z³)⁴]

[(3 · y² · z)³ · (x² · y)⁴] / [(5 · x)³ · (2 · y · z³)⁴]

(27 · x⁸ · y⁶ · z³) / (80 · x³ · y⁴ · z¹²)

(27 · x⁵ · y²) / (80 · z⁹)

Case E:

(5 · x⁷ · y³ · z⁻¹)² × (2 · x · y⁻⁵)³ × (2 · y⁻³ · z²)³

(5² · x¹⁴ · y⁶ · z⁻²) × (2³ · x³ · y⁻¹⁵) × (2³ · y⁻⁹ · z⁶)

(1600 · x¹⁷ · z⁴) / y¹⁸

Case F:

√(2 · 6 · 8 · 3 · 2 · a¹² · b⁶)

24 · a⁶ · b³

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Answer:

we need to know something about f(x) is it an inverse function

Answer:

Their stomach is upset. they eat the grass to calm their stomach. Don't worry it is good if your dog eats grass because that helps the dog's health out. Grass gives them vitamins and nutrients that helps their bowel system. seriously let you dog eat the grass, they will be okay. my four dogs do it as well and they feel better after. hope this helps

Answer:

It's A

Step-by-step explanation:

hope the pic helps b/c you deleted my last answer so i hope this is more of use to you :)

Answer:

munanyo

Step-by-step explanation:

munanyo

Answer:1.25

Step-by-step explanation:

it just math

Therefore,Total patients with pneumonia or bronchitis = 25 + 30 - 10= 45Thus, there are a total of 45 patients diagnosed with pneumonia or bronchitis or both.

Among 50 patients admitted to a clinic, 25 are diagnosed with pneumonia, 30 with bronchitis, and 10 with both pneumonia and bronchitis. The number of patients with pneumonia or bronchitis (or both) can be determined as follows:Let A denote the number of patients diagnosed with pneumonia and B denote the number of patients diagnosed with bronchitis.

According to the inclusion-exclusion principle, the total number of patients with pneumonia or bronchitis is given by:Total patients with pneumonia or bronchitis = \(A + B - (A ∩ B)\)where A ∩ B represents the intersection of the sets A and B.In this case, A = 25, B = 30, and A ∩ B = 10.

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Answer:

48

Step-by-step explanation:

2 hours gives you 4 inches so one hour give u 2 inches 24x2 =48

Step-by-step explanation:

x = number of trucks with 16 tonnes capacity

y = number of trucks with 6 tonnes capacity

x + y = 11

16x + 6y = 126

the first equation gives us

x = -y + 11

and we use that in equation 2 :

16(-y + 11) + 6y = 126

-16y + 176 + 6y = 126

-10y = -50

10y = 50

y = 5

x = -y + 11 = -5 + 11 = 6

the number of 16 tonne trucks was 6.

Answer:gamble that,on average,will leave a person with the same amount of money.

Step-by-step explanation:

Answer:

101  

Step-by-step explanation:

100- (-1) NEGATIVE MINUS NEGATIVE CANCEL OUT ON EACH OTHER AND GIVE POSITIVE: 100 + 1 = SO THE ANSWER IS  101^F

The difference between these two extreme temperatures is of

101° F.

We have the highest temperature recorded in the town of Westgate which is equal to 100°F. Last winter, the lowest temperature recorded was -1°F.

We have to find the difference between these two extremes.

Degree of hotness or coldness measured on a definite scale is called Temperature. When the temperature of the body is high it is called hot body and when it is low it is called cold body.

According to question, we have -

Highest temperature recorded = 100°F

Lowest temperature recorded = -1°F

Let the the difference between these two extreme temperatures be x. Then -

x = Highest temperature recorded - Lowest temperature recorded

x = 100 - (- 1) = 101° F

Hence, the difference between these two extreme temperatures is of

101° F.

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To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, both to find the needed time and to find the inverse function. From this, we get that:

Number of trees infected after t years:

The number of trees infected after t years is given by:

\(f(t) = e^{0.4t}\)

Question 1:

We have to find the number of years it takes to have 21 trees infected, that is, t for which:

\(f(t) = 21\)

Thus:

\(e^{0.4t} = 21\)

To isolate t, we apply the natural logarithm to both sides of the equation, and thus:

\(\ln{e^{0.4t}} = \ln{21}\)

\(0.4t = \ln{21}\)

\(t = \frac{\ln{21}}{0.4}\)

\(t = 7.6\)

Thus, it will take 7.6 years for 21 of the trees to become infected.

Question 2:

We have to find the inverse function, that is, first we exchange y and x, then isolate x. So

\(f(x) = y = e^{0.4x}\)

\(e^{0.4y} = x\)

Again, we apply the natural logarithm to both sides of the equation, so:

\(\ln{e^{0.4y}} = \ln{x}\)

\(0.4y = \ln{x}\)

\(g(x) = \frac{\ln{x}}{0.4}\)

Thus, the logarithmic model is:

\(g(x) = \frac{\ln{x}}{0.4}\)

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If point A is the center of circle A, it means that the circle is perfectly symmetrical around point A. This means that any point on the circle will be equidistant from point A. This property of circles is fundamental to geometry and has many practical applications.

For example, it can be used in designing roundabouts or traffic circles, where cars can move around the circle while maintaining a constant distance from the center. In addition, the concept of a circle with a center point is also important in trigonometry, where it is used to calculate the angles and sides of triangles. So, understanding the relationship between a center point and a circle is crucial for many areas of mathematics and engineering.


If A is the center of circle A, it means that all points on the circle are equidistant from point A. The distance between the center A and any point on the circle is called the radius. In this context, the term "reference" could refer to a diagram or image that illustrates the circle with its center labeled as A.

When working with circle problems, it's important to identify the center and understand its relationship to other points and lines within the circle. This helps in solving problems related to angles, arc lengths, and other geometric properties of the circle.

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Equilibrium potential increases by 2.303 times when Na is increased by factor 10.

Equilibrium potential increases by 4.606 times  Na is increased by factor 100.

Equilibrium potential decreases by 4.606 times Na is decreased by factor 100.

Given,

Sodium ion

Here,

Using nernst equation,

E = RT/nF \(ln\frac{Na_{ex} }{Na^+_{in} }\)

E = 58mV

When \({Na_{ex}\) increased by a factor of 10,

E' = RT/nF ln(10 Na)/Na

E/E' = 1/ln(10)

E/E' = 1/2.303

E' = 2.303E

Thus equilibrium potential increases by 2.303 times.

Now when Na is increased by a factor of 100

E' = 4.606E

Equilibrium potential increases by 4.606 times.

Now when Na is decreased by a factor of 100

E' = 4.606E

Equilibrium potential decreases by 4.606 times.

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