Quiz 2
Below is how tall (in meters) each of the five players on Deandra's basketball team is.
17
2
1.6
Find the median height.​

\(4y ^{2} = 49 \\ = > {y}^{2} = \frac{49}{4} \\ = > {y} = \sqrt{ \frac{49}{4} } \\ = > y = \frac{ \sqrt{49} }{ \sqrt{4} } \\ = > y = \frac{7}{2} \\ = > y = 3.5\)

y = 3.5

Answer:

f(3) = 22

Step-by-step explanation:

f(x) = 2x^2 + 4

=>f(3) = 2(3)^2 + 4

         = 2(9) + 4

         = 18 + 4

         = 22

The sequence converges to ln 2.

To determine whether the sequence converges or diverges, we need to take the limit as n approaches infinity. We can simplify the sequence by using the properties of logarithms:

an = ln( 2n^2 + 1 ) - ln( n^2 +1 )

= ln[(2n^2 + 1)/(n^2 + 1)]

Now we can take the limit of this expression as n approaches infinity:

lim [ln[(2n^2 + 1)/(n^2 + 1)]]

n→∞

Using L'Hopital's Rule, we can evaluate this limit:

Lim [(4n)/(2n)]

n→∞

This limit is equal to 2. Therefore, the sequence converges to ln 2.

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The area of rectangle DEFG is 16 square units and its perimeter is 12 units.

To find the area, we can use the formula: Area = length x width We can find the length and width by calculating the distance between the coordinates of opposite sides of the rectangle.

Length = EF =

\( \sqrt{} ((2-1)^2 + (1-3)^2)\)

=

\( \sqrt{} (2 + 4) = \sqrt{} (6)\)

Width = DG =

\( \sqrt{} ((-3+2)^2 + (1+1)^2) = \sqrt{} (2 + 4) = \sqrt{} (6)\)

The area of rectangle DEFG = length x width =

\( \sqrt{} (6) x \sqrt{} (6)\)

= 6 x 2 = 16 square units.

To find the perimeter, we can add up the lengths of all four sides: Perimeter = DE + EF + FG + GD

DE =

\( \sqrt{} ((1+3)^2 + (-3+(-1))^2) = \sqrt{} (16 + 4) = \sqrt{} (20)\)

EF =

\( \sqrt{} ((2-1)^2 + (1-3)^2) = \sqrt{} (2 + 4) = \sqrt{} (6)\)

FG =

\( \sqrt{} ((2+2)^2 + (1+1)^2) = \sqrt{} (16 + 4) = \sqrt{} (20)\)

GD =

\( \sqrt{} ((-2+3)^2 + (-1-1)^2) = \sqrt{} (1 + 4) = \sqrt{} (5)\)

The perimeter of rectangle DEFG =

\( \sqrt{} (20) + \sqrt{} (6) + \sqrt{} (20) + \sqrt{} (5) \)= 12 units.

Hence, The area of the rectangle is 16 square units and the perimeter is 12 units.

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Answer:

given

definition congruent

definition bisect

Step-by-step explanation:

Answer:

Step-by-step explanation:

answer is b 9/16

area OF ABC =1/2 TIMES 9 TIMES 12 =54

area of ABD +1/2 TIMES 16 TIMES 12 =96

54=96-9:16=9/16

CALCULATE RATIO

Answer:

84 quarters

Step-by-step explanation:

Answer: 84 quarters

Step-by-step explanation: 1 dollar is 4 quarters, so if you do 4 times 21 you would get your answer. Good luck!

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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Answer:

...

Step-by-step explanation:

(x-1) will cancel each other so the answer is the last one

The domain of the composite function (f o g)(-5) for f(x) = 4x + 8 and g(x) = x² + x is equal to 88.

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domain of the function (f o g)(-5) as follows:

(f o g) = 4(x² + x) + 8

(f o g) = 4x² + 4x + 8

(f o g)(-5) = 4(-5)² + 4(-5) + 8

(f o g)(-5) = 100 - 20 + 8

(f o g)(-5) = 88

Therefore, the domain of the composite function (f o g)(-5) for f(x) = 4x + 8 and g(x) = x² + x is equal to 88.

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Answer:

14/9 inches, or an inch and 5/9 of an inch.

Step-by-step explanation:

If 2/3 inch is the same as 9 miles, then x inches represents 21 miles. We can then set up a proportion.

\(\frac{\frac{2}{3} }{9} =\frac{x}{21}\)

9 * x = (2/3) * 21

9x = 2 * 7

9x = 14

x = 14/9 inches.

Hope this helps!

Answer:

1 5/9 ich represent 21 miles

Step-by-step explanation:

Proportions:

2/3  inch  ⇔   9 miles

M  inch   ⇔    21 miles

M = 21*(2/3) / 9

M = 14/9

14/9 = 9/9 + 5/9 = 1 + 5/9 = 1 5/9 inch

Answer:

D.) 50 mi/h and 60 mi/h

Step-by-step explanation:

Answer:

50 mph and 60 mph

Step-by-step explanation:

Represent the two speeds by s and f (slower and faster).  Then f = s + 10.

We find the distance traveled by each car separately, sum up the absolute values of these distances and set this sum equal to 660:

(s + s + 10)(6 hr) = 660 mi.  Simplifying this, we get:

2s + 10 = 110, or

2s = 100.

Then s = 50 mph and f = (50 + 10) mph, or 50 and 60 mph (matches the last possible answer)

(a) The graph of the linear functions is as attached.

(b) The equation of the linear function in slope-intercept form is; y = x

(c) The equation of the transformed function in slope-intercept form is;

y = x + 2 and y = x - 3

Functions are defined as the relationship between sets of values. For example, in the function; y = f(x), for every value of x there exists a set of y values.

x is the independent variable.

y is the dependent variable.

If the linear function is; y = x,

The equation of the transformation in slope-intercept form is given as;

For translation of 2 units up, we have;

y = x + 2

For a translation of 3 units down, we have;

y = x - 3

Thus, the required graph has been attached and the solution is determined.

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Answer:

i would just do 42/12, which is 3.5 times more grams of sugar, or if you want to impress your teacher, you could also do the relative rate of change, which is (new-old)/old, or (42-12)/12= 250% increase in sugar consumption.

increase Step-by-step explanation:

Answer:

Step-by-step explanation:

This is because when you dilate a triangle it gets larger and expands. This means that it changes its position.

The edges of the triangle will get larger so the perimeter will not stay the same but it will change. But, the new perimeter is going to be rationonal to the original one.

the probability density function (PDF) of Z = X + Y is given by: fZ(z) = z, for 0 ≤ z ≤ 1 = 0, otherwise. This means that Z has a triangular distribution with a PDF that linearly increases from 0 to 1 over the range [0, 1], and then remains 0 outside that range.

What is probability density function?

A probability density function (PDF) is a mathematical function that describes the probability distribution of a continuous random variable. It is used to define the likelihood of a random variable taking on a specific value or falling within a certain range of values.

To determine the probability density function (PDF) of the random variable Z = X + Y, where X and Y are independent uniform random variables with range [0, 1], we can use the convolution of the PDFs of X and Y.

First, let's recall the PDF of a uniform random variable. A uniform random variable U with range [a, b] has a constant PDF given by:

fU(u) = 1 / (b - a), for a ≤ u ≤ b

= 0, otherwise

In this case, for X and Y with range [0, 1], the PDFs are:

fX(x) = 1, for 0 ≤ x ≤ 1

= 0, otherwise

fY(y) = 1, for 0 ≤ y ≤ 1

= 0, otherwise

Now, let's find the PDF fz of Z = X + Y by convolution:

fZ(z) = ∫ fX(x) * fY(z - x) dx

Since X and Y are independent, fY(z - x) = fY(z) since the range of Y is [0, 1].

fZ(z) = ∫ fX(x) * fY(z) dx

As the PDFs of X and Y are both 1 in the range [0, 1], the integral becomes:

fZ(z) = ∫ 1 * 1 dz

Since the integration bounds are not dependent on z, the integral evaluates to:

fZ(z) = ∫ 1 dz = z

Therefore, the probability density function (PDF) of Z = X + Y is given by:

fZ(z) = z, for 0 ≤ z ≤ 1

= 0, otherwise

This means that Z has a triangular distribution with a PDF that linearly increases from 0 to 1 over the range [0, 1], and then remains 0 outside that range.

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Answer:

Step-by-step explanation:

0.63 hope this helps

The required value of probability can be found as 0.85. The correct option is (D).

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The percentage of people having no, one, two and three or more injuries are given as 22%, 45%, 18% and 15% respectively.

Then, the probability of an event is equivalent to the percent value.

Now, the probability of skateboarders not having 3 or more injuries is given as,

⇒ 1 - P(Three or more injury)

⇒ 1 - 15/100

⇒ 0.85

Hence, the probability can be obtained for not having 3 or more injuries  as 0.85.

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Answer:

4.9,5.0

Step-by-step explanation:

Thier is two open spaces and the decimals are decreasing by 1 tenth. So if 1 tenth is being decreased the order would be 4.9, 5.0, 5.1, 5.2, 5.3, 5.4.

Answer:

4.9, 5 , 5.1 , 5.2 , 5.3 , 5.4

Step-by-step explanation:

5.4-5.3 = 0.1

5.3-5.2 = 0.1

5.2-5.1 = 0.1

then the pattern is : adding 0.1 to the number to get the next number

5.1 - 0.1 = 5

5 - 0.1 = 4.9

Step-by-step explanation:

for the given value x = -2

= 3(2x-4) + x^2 +5

= 3(-4 -4) +4+5

= -24+9

= -15

Answer:

10. 85°

11. 70°

12. 50°

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

Step-by-step explanation:

1). 3 - | x + 4 | = 10 No solutions

2). \(\frac{1}{2}\) | x | + 3 = 3 One solution x = 0

3). | x - 8 | - 4 = - 1 Two solutions x = 5 and x = 11

Answer:

the new monthly salary after both increase is 1,788.37

Step-by-step explanation:

The monthly salary is 1,622.31

There is an increase of 3.8%

So, the salary after first increase is

= 1,622.31 × (1 + 3.8%)

= 1,683.96

Now there is a second increase of 6.2%, so the salary after second increase is

= 1,683.96 × (1 + 6.2%)

= 1,788.37

Hence, the new monthly salary after both increase is 1,788.37

Answer:

parakeets

Step-by-step explanation:

Answer:

\(y=\frac{1}{8} x^{2} +1\)

Hope this helps!

There are Physical,Chemical,Biological factors that limit distribution of biota.

Physical factors such as water temperature, flow rate, and substrate type can limit the distribution of biota. For example, some species of fish can only survive in cold water, while others prefer warmer water.

Chemical factors such as pH, dissolved oxygen, and nutrient levels can also limit the distribution of biota. For example, some species of algae can only grow in water with a high pH, while others prefer water with a low pH.

Biological factors such as competition, predation, and parasitism can also limit the distribution of biota. For example, a species of fish may be limited in its distribution by competition from another species of fish that is better adapted to the same habitat.

The dissolved oxygen level in a river can also affect the distribution of biota, with some species requiring high levels of dissolved oxygen and others being able to tolerate lower levels. The nutrient levels in a river can also affect the distribution of biota, with some species requiring high levels of nutrients and others being able to tolerate lower levels.Predation can also limit the distribution of biota, with some species being more susceptible to predation than others. Parasitism can also limit the distribution of biota, with some species being more susceptible to parasites than others.

By understanding these factors, we can better understand the ecology of rivers and how they can be managed to protect biota.

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Answer:

\(15x^3-38x^2+9x+18\)

Step-by-step explanation:

\((5x-6)(3x^2-4x-3)\\(5x)(3x^2)+(5x)(-4x)+(5x)(-3)+(-6)(3x^2)+(-6)(-4x)+(-6)(-3)\\15x^3-20x^2-15x-18x^2+24x+18\\15x^3-38x^2+9x+18\)

Answer:

It's either 1:3 or 1:3

Step-by-step explanation:

A scale factor is times, calculate and, a reinduced PEMDAS

Answer:

20.84

Step-by-step explanation:

$25.36 - $4.52 = $20.84

Hope this helps

Option C is the correct choice as it accurately describes the chi-square test for independence. The chi-square test for independence is used to determine if there is a relationship between two categorical variables. It is similar to neither a single-sample t test nor a correlation because it involves categorical variables, not continuous ones.

Option C accurately describes the chi-square test for independence. It states that the test is similar to an independent-measures t test because it compares separate samples to evaluate the difference between separate populations.

The chi-square test for independence involves creating a contingency table that displays the observed frequencies of the two categorical variables. Then, it calculates the expected frequencies under the assumption of independence. The test compares the observed and expected frequencies using the chi-square statistic. If the observed frequencies significantly differ from the expected frequencies, we reject the null hypothesis and conclude that there is a relationship between the variables.

In contrast, options A, B, and D do not accurately describe the chi-square test for independence. Option A refers to a single-sample t test, which is not applicable to the chi-square test. Option B mentions a correlation, which assesses the relationship between continuous variables, not categorical ones. Option D combines elements of both a correlation and an independent-measures t test, which are not applicable to the chi-square test.

Therefore, option C is the correct choice as it accurately describes the chi-square test for independence.
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