Select all pairs of vertical angles.

Angles 1 and 3, Angles 3 and 4, Angles 2 and 3, Angles 1 and 2, Angles 1 and 4, Angles 2 and 4

By solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.

A mathematical statement known as an equation is made up of two expressions joined by the equal sign.

A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the number of the variable x is 7.

So, calculate as follows:

Let g represent giraffes and o represent ostriches.

g + o = 70 ...(1)

4*g + 2*o = 200  ...(2)

g = 70 - o, according to equation 1, therefore we may enter that number in place of g in equation 2 to obtain:

4*g + 2*o = 200

4*(70-o) + 2*o = 200

280 - 4o + 2o = 200

-2o = 200 - 280

2o = 80

o = 80/2

o = 40

Ostriches are 40 then giraffes will be:

70 - 40 = 30

Therefore, by solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.

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Answer:

wot

Step-by-step explanation:

a. The margin of error for this survey is of: 4.85%.

b. The 95% confidence interval for the percentage of teenagers who occasionally smoke cigarettes is of:

(30.15%, 39.85%).

Confidence intervals for proportions are obtained using the z-distribution.

The bounds of the interval are given as follows:

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

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The sample size and the estimate in this problem are given as follows:

\(n = 371, \pi = 0.35\)

The margin of error is given as follows:

\(M = 1.96\sqrt{\frac{0.35(0.65)}{371}} = 0.0485\)

As a percentage, it is of 4.85%.

Then the bounds of the interval are given by the estimate plus/minus the margin of error, hence:

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Answer:

Lets see if the gallon fill the paint tray or not.

For that purpose we need to find out the volume of the paint tray and compare it with the volume of the gallon.

Given:

Length = 14 inches

Width = 10 inches

Depth = 4 cm = 1.57 inches

Volume = length x width x depth

Volume = 14 x 10 x 1.57

            = 220.47 inches cube

Volume of Gallon = 231 inches cube

Comparing the two volumes:

231 inches cube - 220.47 inches cube = 10.52 inches cube

Hence,

The paint will not fill the tray by 10.53 in3.

Step-by-step explanation:

Answer:

See answers and explanations

Step-by-step explanation:

A) Discriminant = b² - 4ac = (12)² - 4(9)(4) = 144 - 144 = 0

B) Since the discriminant is 0, this means the equation only has one root.

C) The root is real in this case since the discriminant is not negative. Otherwise, we would have two imaginary roots if it were (remember that complex roots come in pairs)

Answer:

C

Step-by-step explanation:

It can't be a or d because 15.75x needs to be greater than 145, so in c the how many he sells would represent the x value.

The percentage of the area of the northern hemisphere that is the land is 40%.

The ratio of the area of land to the area of water in the southern hemisphere will be 3:2.

It should be noted that in northern hemisphere, the ratio of the area of land to the area of land to the area of water is 2:3, the percentage of the area of the northern hemisphere is the land will be:

= 2 / (2+3) × 100

= 2/5 × 100

= 40%

It should be noted that the ratio of the area of land to the area of water in the southern hemisphere will be 3:2. This is the inverse of 2:3.

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Critical value is 1.96 for alpha = 0.05. Its a two tailed test,

Hence

Reject H o if Z>1.96 or Z< -1.96

a. H 0: π = 0.70

H1: π ≠ 0.70.

The critical values ​​are the thresholds (two thresholds for a two-sided test) that form the boundaries of the rejection region. That is, the critical value divides the scale of the test statistic into rejection and nonrejection regions.

Critical values ​​can refer to: In differential topology, the critical value of a differentiable function ƒ: M → N During a differentiable , the N image ƒ(x ) is.

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A procedure that is especially likely to result in strong emotional responses such as crying or other displays of distress is the administration of a painful or uncomfortable stimulus.

When individuals experience pain or discomfort, it is common for them to display strong emotional responses such as crying or distress. This is because pain is a powerful stimulus that triggers both physiological and emotional reactions.

Various procedures can elicit such emotional responses, particularly those involving painful or uncomfortable stimuli. For example, medical procedures like injections, surgeries, or dental treatments that involve physical discomfort can lead to strong emotional reactions.

Additionally, emotionally challenging situations such as receiving distressing news, experiencing traumatic events, or undergoing intense psychological interventions may also provoke strong emotional responses.

The intensity of emotional responses can vary depending on individual differences, past experiences, and the specific context in which the procedure or stimulus is encountered. It is important to provide appropriate support and care to individuals who may experience these emotional reactions to ensure their well-being and emotional comfort.

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since m▲n=m^2-2mn+n^3

3▲2=3^2-2*3*2+2^3

=9-12+8

=17-12

=15

Done!

\(\large\underline{\underline{ \sf\maltese Correct \ Question :- }}\)

If m ∆ n means m²-2mm+n², determine the value of 3∆2.

\(\large\underline{\underline{ \sf\maltese Answer :- }}\)

Here we are given that m ∆ n means m² -2mn +n². And we need to find the value of 3∆2 . So let's find out what does the " ∆ " operator does.

Here we can see that m² - 2mn - n² is the whole square of ( m - n)² . A inference can be taken out that the operator " ∆ " first subtracts the two numbers and then squares the obtained value to get the result . That is ,

\(\sf\implies m \Delta n = ( m - n )^2 \)

Now similarly let's simplify out 3 ∆ 2.

Step 1 : Subtract the two numbers :-

This means we need to subtract 2 from 3 . This will give result as ,

\(\sf\implies Result_1 = 3 - 2 =\pink{1} \)

Step 2 : Square the obtained value :-

Here , the value obtained from step 1 is 1 and the square of 1 is 1 . So our final result would be,

\(\sf\implies Result_{(final)}= 1^2 = \boxed{\pink{ 1 }} \)

Answer:

The independent variable is the variable being controlled in the problem, and the dependent variable is the variable that changes because of this control.

Step-by-step explanation:

Answer:

here it's 124°F so if we subtract 8 in 124 it will be 124-8= 114°F

now the range = height - lowest = 124°- 114°F = 8° F

The formula for the n-th term is:

aₙ = 3*(1/2)⁽ⁿ⁻¹⁾

For a geometric sequence where the first term is a₁ and the common ratio is r, the formula for the n-th term is:

aₙ = a₁*(r)⁽ⁿ⁻¹⁾

Here we know that the first term is a₁ = 3 and the common ratio is r = 1/2.

Then the formula for the n-th term of the sequence is:

aₙ = 3*(1/2)⁽ⁿ⁻¹⁾

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Answer:

i think i got

sin x =16/65 not 16/63

By definition, the absolute value of a constant is the distance from that number to zero, regardless of it's negative or positive coefficient.

The distance from -38 to 0 is 38, meaning that the absolute value is 38.

Hope this helps.

頑張って!

Answer:

38

Step-by-step explanation:

The absolute value of a number may be thought of as its distance from zero along real number line. which means - 38 is 38 times away from 0

Answer:

10 .......................

=5(10+2)/2(10)-14

=60/6

=10

mark ice bear Brainliest

Therefore, there are 86,870,400 possible anagrams that can be created from the word 'metamorphosis' where the new words do not need to be meaningful.

To determine the number of anagrams that can be created from the word 'metamorphosis', we need to calculate the permutations of its letters, accounting for repeated letters. Since 'metamorphosis' has 14 letters, including 2 'm's, 2 'o's, and 2 's's, the total number of anagrams can be calculated as:

14! / (2! * 2! * 2!)

where '!' represents the factorial function. Simplifying the expression:

14! = 14 * 13 * 12 * ... * 2 * 1

The calculation results in:

(14 * 13 * 12 * ... * 2 * 1) / (2 * 2 * 2) = 86,870,400

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In terms of the calculation, the answer is 39/4 in improper fraction.

An improper fraction has a denominator that is greater than or equal to the numerator. Based on the numerator and denominator values, proper fractions and improper fractions are the two main types of fractions in mathematics.

A mixed fraction is a fraction formed by combining a natural number and a proper fraction. It is a shortened version of an improper fraction.

The given equation is \(3\frac{1}{4}\) + \(6\frac{1}{2}\) .

Taking 4 as LCM from the above equation.

\(3\frac{1}{4}\) + \(6\frac{1}{2}\) = (13/4) + (13/2)

\(3\frac{1}{4}\) + \(6\frac{1}{2}\) = (13+26)/4

\(3\frac{1}{4}\) + \(6\frac{1}{2}\) = 39/4

Now, since the solution must be proffered in an improper fraction.

Therefore, the obtained improper fraction is 39/4.

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The equation of line is y = 2x + 8 and the slope of the line is m = 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the point be represented as P ( -2 , 4 )

y = 2x + 7   be equation (1)

On simplifying the equation , we get

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

So , the slope of the line is m = 2

Since , the lines are parallel the slopes of the lines will be equal

So , m = 2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 4 = 2 ( x - ( -2 ) )

On simplifying the equation , we get

y - 4 = 2 ( x + 2 )

y - 4 = 2x + 4

Adding 4 on both sides of the equation , we get

y = 2x + 8

Hence , the equation of line is y = 2x + 8

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Answer:

3456

Step-by-step explanation:

The value of (tanx+2cosx) = \(2\frac{7}{20}\).

Given that

sinx = \(\frac{3}{5}\)

sinx = \(\frac{opp}{hyp}\)

Using the Pythagoras' theorem

\(hyp^{2} = opp^{2} + adj^{2} \\\\adj^{2} = 5^{2}- 3^{2} \\ \\= 25-9\\\\adj^{2} = 16\\ \\adj = \sqrt{16} \\\)

adj = 4.

Now we have to find out tanx and cosx

\(tanx = \frac{opp}{adj}\)

\(= \frac{3}{4}\)

\(cosx = \frac{adj}{hyp}\\ \\= \frac{4}{5}\)

Now we have to find out the given equation (tanx+2cox)

\(= \frac{3}{4} +2(\frac{4}{5})\\ \\= \frac{15+32}{20} \\\\= \frac{47}{20} \\\\or\\\\= 2\frac{7}{20}\)

Hence the answer is the value of (tanx+2cosx) = \(2\frac{7}{20}\).

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The polynomial 7x² - 4 + 6x³ - 4x - x⁴ in standard form is - x⁴ + 6x³ + 7x² - 4x - 4  

Given that

7x² - 4 + 6x³ - 4x - x⁴

The standard form of a polynomial is when the terms are arranged in decreasing order of degree

To rewrite 7x² - 4 + 6x³ - 4x - x⁴ in standard form, we need to rearrange the terms accordingly:

- x⁴ + 6x³ + 7x² - 4x - 4  

Now the terms are in decreasing order of degree, with the highest degree term first

This is the standard form of the polynomial.

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Answer:

10200\

\\\\SHREKS GAYSDEWD

Step-by-step explanation:

the answer is 10200

The norm of f in L₁ (R₂) is not well-defined with the given information. The function f does not belong to the space L₂(R₁) because it is not square-integrable over R₁.

To compute the norm of f in L₁ (R₂), we need to find the integral of the absolute value of f over R₂ and take the infimum over all such integrals. However, the function f is only defined on the interval (0, 0), which has zero length. As a result, the integral of f over R₂ cannot be computed since R₂ does not contain any points.

Now, let's analyze whether the function f belongs to the space L₂(R₁). The space L₂(R₁) consists of functions that are square-integrable over R₁, meaning their integral squared is finite. To determine if f is square-integrable, we need to compute the integral of |f(x)|² over R₁, which is given by:

∫[0, 0] |f(x)|² dx

Since the interval [0, 0] has zero length, the integral is also zero. Therefore, the integral squared is also zero, indicating that f is square-integrable and belongs to the space L₂(R₁).

However, it is worth noting that the given function f(x) = [x + 1][x + 2] has a singularity at x = -1 and x = -2, as the brackets represent the floor function. This singularity raises concerns about the function's behavior and the applicability of standard function spaces.

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The norm of f in L₁ (R₂) is not well-defined with the given information. The function f does not belong to the space L₂(R₁) because it is not square-integrable over R₁.

To compute the norm of f in L₁ (R₂), we need to find the integral of the absolute value of f over R₂ and take the infimum over all such integrals. However, the function f is only defined on the interval (0, 0), which has zero length. As a result, the integral of f over R₂ cannot be computed since R₂ does not contain any points.

Now, let's analyze whether the function f belongs to the space L₂(R₁). The space L₂(R₁) consists of functions that are square-integrable over R₁, meaning their integral squared is finite. To determine if f is square-integrable, we need to compute the integral of |f(x)|² over R₁, which is given by: ∫[0, 0] |f(x)|² dx

Since the interval [0, 0] has zero length, the integral is also zero. Therefore, the integral squared is also zero, indicating that f is square-integrable and belongs to the space L₂(R₁). However, it is worth noting that the given function f(x) = [x + 1][x + 2] has a singularity at x = -1 and x = -2, as the brackets represent the floor function. This singularity raises concerns about the function's behavior and the applicability of standard function spaces.

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The current value of Certificate A is approximately $4322.41, and the current value of Certificate B is approximately $4319.03.

For Certificate A the first payment of $2200 is received in three months. The second payment of $2200 is received in six months.

PV = CF / (1 + r)ⁿ

PV = Present Value

CF = Cash Flow

r = Rate of return

n = Number of periods

n = 3/12

n = 0.25

PV₁ = \(\frac{2200}{(1+0.455)^{0.25}}\)

PV₁= 2200 / 1.011349

PV₁ = 2174.24

n = 6/12

n = 0.5

PV₂ =  \(\frac{2200}{(1+0.455)^{0.5}}\)

PV₂ = 2200 / 1.022595

PV₂ = 2148.17

Therefore, the current value of Certificate A is approximately $2174.24 + $2148.17 = $4322.41.

For Certificate B the first payment of $2200 is received in four months. The second payment of $2200 is received in seven months.

PV₁ =  \(\frac{2200}{(1+0.455)^{\frac{6}{12} } }\)

PV₁ = 2200 / 1.014674

PV₁ = 2161.40

PV₂ = \(\frac{2200}{(1+0.455)^{\frac{7}{12} } }\)

PV₂ = 2200 / 1.018202

PV₂ = 2158.63

Therefore, the current value of Certificate B is approximately $2161.40 + $2158.63 = $4319.03.

The current value of Certificate A is approximately $4322.41, and the current value of Certificate B is approximately $4319.03.

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Answer:

x ≥ 0

Step-by-step explanation:

The absolute value of something will always be the same number if the number is positive. Therefore, the values of x which make this true are x ≥ 0.

If lidocaine is injected intra-arterially, it can quickly lead to systemic toxicity. The first signs of toxicity may include circumoral numbness and tongue paresthesia, but these symptoms may be followed by more severe manifestations such as dizziness, seizures, and cardiac arrest.

The systemic effects of lidocaine are dose-dependent, meaning that the higher the dose, the more severe the symptoms.

Lidocaine is a local anesthetic that is commonly used for minor surgical procedures or dental work. It works by blocking the nerve signals that transmit pain to the brain. However, if it is injected into an artery, it can rapidly spread throughout the body and affect other organs, leading to potentially life-threatening complications.

If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly. The first step is to stop the injection and monitor the patient closely for signs of toxicity. If the patient is experiencing severe symptoms, such as seizures or cardiac arrest, emergency treatment should be initiated immediately. Treatment may include administering medications to counteract the effects of the lidocaine or performing cardio-pulmonary resuscitation (CPR) if necessary.

In conclusion, the first signs of lidocaine toxicity may include circumoral numbness and tongue paresthesia, but more severe symptoms may follow, such as dizziness, seizures, and cardiac arrest. If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly to prevent potentially life-threatening complications.

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Option D is not a condition to check when doing a two-sample z-test of proportions.

The correct option is D. All of the above conditions are important conditions to check when doing a two-sample z-test of proportions.

The two-sample z-test of proportions is a statistical test that is used to compare the proportion of two populations.

This statistical test helps in determining whether or not there is a significant difference between the two proportions.

The following are the conditions to check when doing a two-sample z-test of proportions:The samples are independent of each other and independent within samples.

The sample is random.

The samples are sufficiently large.

Therefore, the given statement "All of the above conditions are important conditions to check when doing a two-sample z-test of proportions" is correct.

In conclusion, option D is not a condition to check when doing a two-sample z-test of proportions.

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Answer:

c

Step-by-step explanation:

The variable y in the second equation has a coefficient of 2 so it will be easy to divide the entire equation by 2.

Answer:

Hana is wrong

Step-by-step explanation:

savings=26+34

=60

savings left after spending=60-6-3

=51