Kaya volunteers at a local animal shelter. She made some notes about
the animal populations in the shelter this week.
doge
2/5 dogs 3/8 cats
rest are other pets,
such as birds,
hamsters, and lizards


Part A What fraction of all the animals are not dogs and cats? Explain
how you found your answers.

Answer:

The sample proportion is 0.88.

The margin of error is of 0.04.

The interval likely to contain the true population proportion is (0.84,0.92).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

Margin of error:

The margin of error is of:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

Sample of 230 teenagers, 202 would like to have smaller class sizes at their school.

This means that \(n = 230\), and that the sample proportion is:

\(\pi = \frac{202}{230} = 0.88\)

The sample proportion is 0.88.

Standard 95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a p-value of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

Margin of error:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(M = 1.96\sqrt{\frac{0.88*0.12}{230}}\)

\(M = 0.04\)

The margin of error is of 0.04.

Confidence interval:

Sample proportion plus/minus margin of error. So

0.88 - 0.04 = 0.84

0.88 + 0.04 = 0.92

The interval likely to contain the true population proportion is (0.84,0.92).

The Boolean expression A >= B is equivalent to  !(A < B) (option A)

To simplify a Boolean expression, use De Morgan's Law.

De Morgan's Law is used to simplify or find the equivalent of a negation of compound expressions.

The principle is:

NOT (A AND B) is equivalent to (NOT A) OR (NOT B)

NOT (A OR B) is equivalent to (NOT A) AND (NOT B)

When the expression involves >, <, = signs, then to simplify the expression, move the not and flip the sign.

! is the symbol of negation or NOT.

Hence,

! (>) becomes <=

! (<) becomes >=

Here are some examples:

!(A > B) is equivalent to (A <= B)

!(A <= B) is equivalent to (A > B)

!(A >= B) is equivalent to (A < B)

!(A == B) is equivalent to (A != B)

!(A != B) is equivalent to (A == B)

!(A < B) is equivalent to (A >= B)

From the above list we can conclude that A >= B is equivalent to !(A < B) (option A)

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Answer:

(x - 4)² + (y + 9)² = 25

Step-by-step explanation:

The equation of a circle is written as seen below.

(x – h)² + (y – k)² = r²

Where (h,k) represents the center of the circle and r represents the radius

We want to find the equation of a circle that has a center at (4,-9) and a radius of 5.

We know that (h,k) represents the center so h = 4 and k = -9

We also know that r represents the radius so r = 5

Now to find the equation of this specific circle we simply plug in these values into the equation of a circle formula

Equation: (x – h)² + (y – k)² = r²

h = 4, k = -9 and r = 5

Plug in values

(x - 4)² + (y - (-9))² = 5²

5² = 25

The two negative signs in front of the 9 cancel out and it changes to + 9

The equation of a circle with a center at (4,-9) and a radius of 5 is

(x - 4)² + (y + 9)² = 25

Answer:

y = 1

Step-by-step explanation:

Thus, after approximately 66 months, Darren will have saved enough money to recover his $20,000 down payment through his monthly savings. The answer is (B) 66 months.

The term "principal" has multiple meanings, depending on the context in which it is used. Here are a few possible definitions:

Principal as a noun refers to the person who holds the highest position or authority within an organization, such as a school principal or a company principal.

Principal can also refer to the original amount of money borrowed or invested, excluding any interest or other charges that may accrue over time.

In the context of finance or investments, principal can refer to the sum of money that is invested or borrowed, on which interest is calculated.

Principal can also be used as an adjective to describe something that is most important or essential, such as the principal reason for a decision or the principal goal of a project.

given by the question.

To determine the monthly mortgage payment, we first need to calculate the principal amount that Darren will be borrowing. He will be borrowing the purchase price of the house ($125,000) minus the down payment he plans to make ($20,000), which is $105,000.

We can then use the formula for calculating the monthly mortgage payment:

M = P [  I \((1 + i)^{n}\)] / [ \((1+i)^{n-1}\)]

where:

M is the monthly mortgage payment

P is the principal amount

I is the monthly interest rate (which is the annual interest rate divided by 12)

n is the total number of payments (which is the number of years multiplied by 12)

In this case, we have:

P = $105,000

I = 5.5% / 12 = 0.00458

n = 30 years x 12 = 360

Plugging in these values, we get:

M = $105,000 [ 0.00458(1 + 360] / [ (1 + 0.00458) ^360 – 1]

M ≈ $596.55

Therefore, Darren's monthly mortgage payment will be approximately $596.55.

The difference between Darren's current rent payment and his mortgage payment will be:

$900 - $596.55 = $303.45

So, Darren plans to save $303.45 per month.

To determine how long it will take for Darren to recover his down payment through his monthly savings, we can set up an equation:

$20,000 / $303.45 per month = 65.8 months

Rounding up to the nearest whole number, we get 66 months.

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The total number of yards the friends who paddle the Adventure Mid travel is 8,580 yards

Number of friends who paddle Adventure Mid Trip = 40% of 15

= 0.4 × 15

= 6 friends

Total yards the friends who paddle the Adventure Mid Trip travel = Total length of travel

= 4 7/8 miles

Recall,

1 mile = 1760 yards

Total yards the friends who paddle the Adventure = 4 7/8 × 1,760

= 39/8 × 1,760

= (39 × 1,760) / 8

= 68,640 / 8

= 8,580 yards

Consequently, the task content is solved by converting number of miles to yards.

Complete question:

Great Adventures Canoe and Kayak company offers 3 different options as shown in the table. This afternoon a group of 15 friends paddle the different options in individual kayaks and 40% of the group paddle the Adventure Mid Trip. How many total yards will the friends who paddle the Adventure Mid Trip travel? (Hint: 1 mile = 1760 yards)

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The slope of the line will be equal to -4/3.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run.

Given that the two points are (2,3) and (8,-5). The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -5 - 3 ) / (  8 - 2 )

Slope = -8 / 6

Slope = -4 / 3

Therefore, the slope of the line will be equal to -4/3.

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The number that take (a) both PE is 6 girls (b) Gymnastic but not acrobat is 7 girls (c)  At least one PE is 18 girls

How to determine the numbers?

Recall that Set theory is a branch of mathematical logic that studies sets, which can be informally described as collections of objects.

From the given parameters,

(a)  The number that play both PE is given as

13 - x + x + 17 - x + 1 = 25

Solving the equation to get the value of x

13+17-x = 25

⇒ 31 -x =25

Collecting like terms we have

-x = 25 - 31

- x = -6

Dividing by a minus we have

x = 6

This means that 5 girls play both PE

(b)  Number that play gymnastic but not acrobat is given as

Gymnastic only that is

13 - x

13 - 6 = 7 girls

(c)  Number that play at least one game is calculated thus:

n(G) ∪ n(A)

That is (13 - x )  + (17 - x)

= 13-6 + 17 -6

7 + 11 = 18 girls

Answer:

$16

Step-by-step explanation:

\(0.75x = 12\\3x = 48\\x = 16\)

(a) The probability that Shelia is diagnosed as having gestational diabetes is  0.1586.

(b) The probability that Shelia is diagnosed as needing further testing for gestational diabetes is 0.0416.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.

Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

Given:

Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy).

There is variation both in the actual glucose level and in the blood test that measures the level.

In a test to screen for gestational diabetes, a patient is classified as needing further testing for gestational diabetes if the glucose level is above 120 milligrams per deciliter (mg/dL) one hour after a sugary drink. Shelia's measured glucose level one hour after the sugary drink varies according to the Normal distribution with = 105 mg/dL and = 15 mg/dL.

(a) The sample mean \(\bar{X}\) = 120

The mean = 105

And standard deviation = 15

t = 1 - P(X ≤ 120 - 105/15)

t = 1 - P(X ≤ 15/15)

The P-Value is 0.158655.

(b) The sample mean \(\bar{X}\) = 120

The mean = 105

And standard error = 15/√3 =

t = 1 - P(X ≤ 120 - 105/8.66025403784)

t = 1 - P(X ≤ 15/8.66025403784)

The P-Value is 0.041637.

Therefore, the P-Value is 0.041637.

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Answer:

domain : - ∞ < x < 1

Step-by-step explanation:

the function is increasing on the upward part of the curve. that is

from negative infinity to the vertex at (1, 3 )

domain : - ∞ < x < 1

Answer:

x = 1

r+7 = ..

5g = 9

8r = 12

A, C, D and F

Answer:

\(h(0) = -16(0)^2 + 128\)

\(= 128\)

Therefore, the rocket goes to a maximum height of 128 feet.

4. The axis of symmetry of the parabolic path of the rocket is the vertical line that passes through the vertex of the parabola. Since the coefficient of \(t^2\) is negative, the parabola opens downwards, and the vertex represents the maximum point of the path. As we found in question 2, the time at which the maximum height occurs is t = 0, so the axis of symmetry is the vertical line passing through t = 0.

5. To find when the rocket hits the ground, we need to find the time t at which h(t) = 0. Substituting \(h(t) = -16t^2 + 128\), we get:

\(-16t^2 + 128 = 0\)

Solving for t using the quadratic formula, we get:

t = (0 ± √(0^2 - 4(-16)(128))) / (2(-16))

= (±√8192) / (-32)

= ±8

Since time cannot be negative, the rocket hits the ground after approximately 8 seconds.

6. To find how high the rocket is at t = 2 seconds, we can substitute t = 2 into the equation h(t) = -16t^2 + 128:

h(2) = -16(2)^2 + 128

= -64 + 128

= 64 feet

Therefore, the rocket is at a height of 64 feet at 2 seconds.

7. To find when the rocket is at a height of 252 feet, we need to solve the equation \(-16t^2 + 128 = 252\). Rearranging and solving for t, we get:

\(-16t^2 + 128 = 252\)

\(-16t^2 = 124\)

\(t^2 = -124/-16\)

t^2 = 7.75

t ≈ ±2.78 seconds

Since time cannot be negative, the rocket is at a height of 252 feet after approximately 2.78 seconds.

8. The graph coordinates of the rocket's path can be plotted using the function \(h(t) = -16t^2 + 128\). The x-axis represents time t in seconds and the y-axis represents the height of the rocket in feet. We can plot points on the graph by substituting different values of t into the equation and plotting the resulting height. For example, some common points to plot include the vertex at (0, 128), the point where the rocket hits the ground at approximately (8, 0), and the point where the rocket is at a height of 252 feet at approximately (2.78, 252). We can also plot other points by substituting different values of t into the equation and plotting the resulting height.

On solving the provided question, we can say that Probability(A and B) = P(A)P(B|A) and P(E or F) = P(E) + P(F) - P(E and F)

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Probability(A and B) = P(A)P(B|A).

P(A and B) = P(B and A), this may also be written as P(A and B) = P(B)P(A|B).

Using the general multiplication rule, we have

P(E and F) = P(E)P(F|E)

.392 = P(E)(.7)

P(E) = .56

   P(E and F) = P(F)P(E|F)

.392 = P(F)(.56), so

P(F) = .7

P(E or F) = P(E) + P(F) - P(E and F)

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Answer:

I need some more context

Step-by-step explanation:

Answer:

3x ( x+2)(x^2−2x+4)

Step-by-step explanation:

3x^4 + 24x.

Factor out the greatest common factor

3x*x^3 + 3x*8

3x(x^3+8)

Then factor the cubic term

The sum of cubes is a^3+b^3=(a+b)(a^2−ab+b^2)

3x ( x+2)(x^2−2x+4)

Answer:

5/2

Step-by-step explanation:

You change the signs to positive and then you put 15 as numerator and then 6 as denominator which gives you 15/6. But you can also simplify it which gives you 5/2. Hope this helps!

Answer:

0.12 ± 1.96 * √(0.12(0.88) / 100)

Step-by-step explanation:

Confidence interval :

Phat ± Zcritical * √(phat(1 -phat) / n)

Phat = 12/100 = 0.12

1 - phat = 0.88

Zcritical at 95% = 1.96

Hence, we have :

0.12 ± 1.96 * √(0.12(0.88) / 100)

0.12 ± 1.96 * 0.0324961

0.12 ± 0.0636924

Lower boundary = (0.12 - 0.0636924) = 0.0563

Upper boundary = 0.12 + 0.0636924 = 0.1837

The calculations for 95% confidence interval for this case is given as: \(CI = 0.12 \pm 1.96 \times \sqrt{\dfrac{0.12(1 - 0.12)}{100}}\)

For large enough sample( size > 30), let the population proportion of a quantity be denoted by random variable \(p\)

Then, we get:

\(p \sim N(\hat{p}, \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})\)

where

\(\hat{p}\) = estimated(mean value) proportion of that quantity

and n = size of sample drawn.

It is visible that as we increase the value of n, the standard deviation decreases, therefore, forcing the values of population proportion to be closer to the estimated proportion.

Margin of error is the distance between the mean and one of the end point of the confidence interval(assuming its equal on  both the sides of the mean). The margin of error with level of significance \(\alpha\) is calculated as:

\(MOE = Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\)

where \(Z_{\alpha/2}\) is the critical value of the test statistic for level of significance \(\alpha\)

The confidence interval is then calculated as:

\(CI = \hat{p} \pm MOE\)

For the considered case,

the confidence interval is to be found for 95% confidence, therefore,

level of significance = 100% - 95%  = 5% = 0.05

The estimated proportion of defective chips estimated from sample is:

Thus, we get the confidence interval for this case as:

\(CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\CI = 0.12 \pm 1.96 \times \sqrt{\dfrac{0.12(1 - 0.12)}{100}}\)

Thus, the calculations for 95% confidence interval for this case is given as: \(CI = 0.12 \pm 1.96 \times \sqrt{\dfrac{0.12(1 - 0.12)}{100}}\)

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The axis of symmetry is at x = 1, the domain is (-∞, +∞), the y-intercept c is at 7 and x intercept is not applying .

A parabolic function is one that satisfies the formula f(x) = ax2 + bx + c and, when represented graphically in two dimensions, has the shape of a parabola. Any quadratic equation with just a second degree in x is the equation for a parabolic function.

The following characteristics define a basic parabola:

Thus, from the given graph the value are obtained as:

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Answer:

d. 0.27

Step-by-step explanation:

Calculation to determine the probability that a corn crop has either an ear worm infestation, a corn borer infestation or both

Using this formula

P(E U B) = P(E) +P(B) -P(E n B)

Let plug in the formula

P(E U B) =0.24 + 0.16 -0.13

P(E U B)=0.27

Therefore the probability that a corn crop has either an ear worm infestation, a corn borer infestation or both will be 0.27

Answer:A.The triangles are similar but not congruent

Step-by-step explanation:

In a congruent traingle:

the both triangles are same in shape and size

There are five theorems to see if the triangles are congruent

and neither particularly applies here

sss: the sides are not equal

as none of the sides are equal, then despite the angles, congruence is not possible

However it is evident that one of the triangles is proportionally bigger than the other but similar. Hence A is correct.

Step-by-step explanation:

An inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Regan won the grand prize at a store giveaway. The grand prize winner is guaranteed to win at least $500 in cash and prizes.

Let d represent the amount of cash in dollars and p represent the amount of prizes.

Since the  grand prize winner is guaranteed to win at least $500,

So, p + d ≥ 500

Therefore, an inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.

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An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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For this problem we have the following inequality given:

If we want to solve for x the first step on this case would be add 4 in all the sides of the inequality and we got:

Now we can divide all the sides by 8 and we got:

And the solution for this case would be:

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

Step 1: Subtract 7x from both sides.

8x−8−7x=7x−7x

x−8=0

Step 2: Add 8 to both sides.

x−8+8=0+8

x=8

HGD

-ghost

Answer:0.03125

Step-by-step explanation:

GOO*OOGLE

Step-by-step explanation:

(1/2)^5   = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 =   1/32

The roots of a quadratic equation depends on the discriminant \(\Delta\).

---------------------

A quadratic equation has the following format:

\(y = ax^2 + bx + c\)

It's roots are:

\(y = 0\)

Thus

\(ax^2 + bx + c = 0\)

They are given by:

\(\Delta = b^{2} - 4ac\)

\(x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}\)

The discriminant is \(\Delta\).

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Answer:

24 ft

Step-by-step explanation:

To find the missing length, we start with the area. We know that we have an area of 96 square ft (although i dont know why someone would have such a big yard). We also know that the width of the yard is 4 ft. The next thing we do is divide. Since we multiply the length and width to find the area, we will divide the area by the width to find the missing length. 96/4= 24. Btw here is the weird yard someone has lol ( i made it to the best of my ability)

|----------------------------------------------------------|

|_______________________________|

Answer:

length=12 feet

Step-by-step explanation:

l*w=a

l*w=96

factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

12*8=96

12-8=4

12 feet=length     8 feet=width

Answer:

Step-by-step explanation:

Given the trigonometric equation;

cos x =-0.4226

To get the value of x within the range 0° < x < 360°, we need to take the arc cosine of the value as shown;

x = arccos -0.4226

x = 114.99°

x ≈ 115°

Since x is positive in the 4th quadrant, the value of x can also be 360 - \(\theta\)

where \(\theta = 115^{o}\)

x2 = 360°-115°

x2 = 245°

The value of x within the interval are 115° and 245°

Answer:

The value of x within the interval are 115° and 245°

Step-by-step explanation: