Which pair of polygons is congruent?

1 and 2


3 and 4

3 and 5


1 and 4
—Ill answer my own question since i cant find it here lol————

Correct. Polygon 3 can be mapped onto polygon 5 using a rotation and a translation.

Answer:

54.5%

Step-by-step explanation:

Given that :

Mean pulse rate (m) = 73.5

Standard deviation (σ) = 13.2

Pulse rates within 1 standard deviation of the mean :

Mean ± 1(standard deviation )

73.5 - 13.2 < X < 73.5 + 13.2

60.3 < X < 86.7

Pulse rates : 50, 51, 51, 53, 53, 53, 55, 56, 56, 57, 58, 58, 59, 59, 6060, 60, 60, 62, 62, 64, 65, 65, 65, 68, 68, 69, 71, 71, 7272, 73, 75, 76, 77, 78, 78, 81, 81, 81, 82, 82, 82, 82, 8385, 85, 85, 88, 88, 90, 90, 91, 91, 92

Total number pulse rate within 1 standard deviation of the mean = 30

Percentage of the total :

(30 / 55) * 100%

0.5454 * 100%

= 54.54%

= 54.5%

Answer:

the first one is 0.08 and the second one is 0.08x 25 then the third one is 2 then the fourth one is 10

Step-by-step explanation:

Answer:

the first one is 0.08 and the second one is 0.08x 25 then the third one is 2 then the fourth one is 10

Step-by-step explanation:

First, convert 8% to the equivalent decimal

.

Next, multiply the decimal and the number by using the expression

.

students in Leron’s class wear glasses.

Use the friendly percent

to check the answer because it is close to 8%.

Answer:

Step-by-step explanation:

Let x represent the rate at which the ticket is sold and let y represent the number of tickets sold at that rate.

When x = 4, y = 800

This means that the income from gate takings at this rate is 4 × 800 = $3200

For each 1 dollar increase in the gate fee,management expects 100 fewer customers to buy tickets. It means that the amount earned would be (x + 1)(y - 100)

For the amount to be $3500, it means that

(x + 1)(800 - 100) = 3500

700(x + 1) = 3500

x + 1 = 3500/700 = 5

Therefore, management should charge $5 per person for gate fee so that it collects 3500 dollars from gate takings.

Answer:

-5.1

Step-by-step explanation:

Since we know the starting temperature was -12.6 and the decrease was 7.5, that gives an equation.

-12.6 - 7.5.

Since we are working in temperature we need to be careful when subtracting.

-12.6 - 7.5 = -5.1

In a calculator, -12.6 - 7.5 would be 20.1 but since we are using temperature the answer is -5.1.

Hope that helps. x

Answer:

15. $8.47

16. $14.68

17. $121.04

18. $60.52

Step-by-step explanation:

15. Sale tax Round to the nearest cent=

8.65% of $97.89 = 0.0865 × $97.89 = $8.47

16. Tips Round to the nearest cent=

15% of $97.89 = 0.15 × $97.89 = $14.68

17. Total =

$97.89 + $8.47 + $14.68 = $121.04

18. Amount each person pays Round to the nearest cent =

$121.04/2 = $60.52

Answer:3 cups of Soda

UwU

Step-by-step explanation:

Step-by-step explanation:

When dividing by a negative number, you "flip" the inequalities sign so you would divide -20 by -2 which would leave you with 10. X is left where it is and you flip the inequalities sign to a ≥ sign.

final answer =

x ≥ 10

No. The reported return rate appears lower than expected.

To determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.

First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.

Then, we can use the following formula to calculate the expected rate of return:

Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1

Plugging in the given values, we get:

n = 1 (since we are only given information for a single quarter)

Initial investment = 26,245

Ending value = 26,292

Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%

Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.

Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.

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Answer:

positive 200 or +200

Step-by-step explanation:

Answer:

As a claustrophobia, I can ????

O 35°, 35°, 20°

Step-by-step explanation:

In the fourth quadrant, the equation of the unit circle is:

y = -√(1 − x²), 0 ≤ x ≤ 1

The x and y coordinates of the centroid are:

cₓ = (∫ x dA) / A = (∫ xy dx) / A

cᵧ = (∫ y dA) / A = (∫ ½ y² dx) / A

For a quarter circle in the fourth quadrant, A = -π/4.

Solving each integral:

∫₀¹ xy dx

= ∫₀¹ -x √(1 − x²) dx

= ½ ∫₀¹ -2x √(1 − x²) dx

If u = 1 − x², then du = -2x dx.

When x = 0, u = 1.  When x = 1, u = 0.

= ½ ∫₁⁰ √u du

= ½ ∫₁⁰ u^½ du

= ½ (⅔ u^³/₂) |₁⁰

= (⅓ u√u) |₁⁰

= 0 − ⅓

= -⅓

∫₀¹ ½ y² dx

= ½ ∫₀¹ (1 − x²) dx

= ½ (x − ⅓ x³) |₀¹

= ½ [(1 − ⅓) − (0 − 0)]

= ⅓

Therefore, the x and y coordinates of the centroid are:

cₓ = (-⅓) / (-π/4) = 4/(3π)

cᵧ = (⅓) / (-π/4) = -4/(3π)

Answer:

sorry

Step-by-step explanation:

What is probability? Put simply, it is the chance of an event occurring. Probability is often expressed in quantifiable terms as either a percentage or a decimal: for example, the chance of a coin landing as heads is 50% . It is impossible to be certain you can correctly predict whether the coin will land heads or tails, which makes the act of flipping the coin a random event. We can however, calculate the probability of the coin landing heads or tails.

The probability that a random selected microprocessor from Intel will not malfunction 98.8% or 0.988

Given that Intel's microprocessors have a 1.2 % chance of malfunctioning

The chance or probability of happening ant event  A is given by equation (1)

\(\rm Probability\; of \; happening \; of \; event \; A = P(A).........(1) \\The \; Probability \; of \; same \; event \; not \; happening = P(\bar A) = 100 - P(A) ........(2) \\Where \; P(A) \; is\; expressed \; in \%\)

Let one Intel microprocessor be selected at random then from equations (1) and (2) we can write that

P( Malfunctioning of Intel's microprocessor) + P( Non malfunctioning of Intel's microprocessor) = 100 %

According to the given situation  From equations (1) and (2) we can write that

\(\rm 1.2\% + P( Non\; malfunctioning\; of \; Intel's\; microprocessor) = 100\% \\ \\ P( Non \; malfunctioning\; of \; Intel's\; microprocessor) = 100\% - 1.2 \% \\P( Non \; malfunctioning\; of \; Intel's\; microprocessor) = 98.8\% = 0..988\)

So we can conclude that the probability that a random selected microprocessor from Intel will not malfunction 98.8% or 0.988

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Answer:

1119744

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out expression

\(\frac{6^{14}}{(2^5)(3^7)}\)

Step 2: Evaluate exponents

6¹⁴ = 78365164096

2⁵ = 32

3⁷ = 2187

Step 3: Replace

\(\frac{78364164096}{32(2187)}\)

Step 4: Multiply

\(\frac{78364164096}{69984}\)

Step 5: Divide

1119744

As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

For a normally distributed data set with a mean of 0 and a standard deviation of 0.5, the proportion of values between -1 and 1 is most closely related to 68%.

Approximately 68% of the data in a normal distribution lies within one standard deviation of the mean, which explains why. One standard deviation below the mean is -0.5, and one standard deviation above the mean is 0.5 since the mean is 0 and the standard deviation is 0.5. As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

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Answer:

0.005 `; 0.00499 ;

No, because np < 10 ;

2000

Step-by-step explanation:

Given that:

Number of samples , n = 100

Proportion, p = x / n

p = 1 / 200

= 0.005

p = μ

Standard deviation of sample proportion :

σp = sqrt((p(1 - p)) / n)

σp = sqrt((0.005(1 - 0.005)) / 200)

σp = sqrt((0.005(0.995)) / 200)

σp = sqrt(0.004975 / 200)

σp = sqrt(0.000024875)

σp = 0.0049874

σp = 0.00499

np = 100 * 0.005 = 0.5

n(1 - p) = 100(1-0.05) = 95

Smallest value of n for which sampling distribution is approximately normal

np ≥ 10

0.005n ≥ 10

To obtain the smallest value of n,

0.005n = 10

n = 10 / 0.005

n = 2000

Using the Central Limit Theorem, it i found that:

In this problem:

Item a:

\(\mu = p = 0.005\)

\(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.005(0.995)}{100}} = 0.0071\)

The mean is of 0.005, with a standard deviation of 0.0071.

Item b:

\(np = 100(0.005) = 0.5\)

np < 10, hence not normal, and option C is correct.

Item c:

\(np = 10\)

\(0.005n = 10\)

\(n = \frac{10}{0.005}\)

\(n = 2000\)

The smallest value of n for the sampling distribution to be approximately normal is 2000.

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Answer:

Slope of a line passing through (\(x_{1}\),\(y_{1}\)) and (\(x_{2} , y_{2}\)) is given by:

\(\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\)

Now,

Slope of line L, (m) = \(\frac{-3-(-1)}{-2-2}\) = 0.5

Slope of line M, (n) = \(\frac{-1-1}{W-1}\) = \(\frac{-2}{W-1}\)

If the lines L and M are parallel to each other,

m = n

or, 0.5 = \(\frac{-2}{W-1}\)

or, 0.5 (W - 1) = -2

or, W - 1 = -4

or, W = -3

Therefore the required value of W is -3.

The position vector of a particle that has an acceleration, a(t) = 19t i + eᵗ j + e⁻ᵗ k, is equals to the 19 (t³/6)i + (eᵗ - t )j - (e⁻ᵗ - 2t - 2)k.

We have, The acceleration vector function of a particle is defined as, a(t)

= 19t i + eᵗ j + e⁻ᵗ k and intial velocity and position is, v(0) = k, r(0) = j + k.

We have to calculate the position vector of a particle. Now, as we know, the acceleration of a particle is equals to derivative of velocity of particle with time. In other words, velocity is integration of acceleration with respect to time.

Mathematically, v(t) = ∫a(t)dt , let C be integration constant ( vector).

v(t) = ∫a(t)dt = ∫[ (19t) i + (eᵗ) j + (e⁻ᵗ) k] dt

=> v(t) = 19(t²/2) i + eᵗ j - e⁻ᵗ k + C

At t = 0 , v(0) = k

=> k = 19(0²/2) i + e⁰j - e⁻⁰ k + C

=> k = 0 + j - k + C

=> C = 2k - j

so, v(t) = 19(t²/2) i + eᵗ j - e⁻ᵗ k + 2k - j

= 19(t²/2) i + (eᵗ - 1) j - (e⁻ᵗ - 2) k

Now, Position of a particle is determined by integrating the velocity of particle with respect to time, r(t) = ∫v(t)dt , let D be integration constant ( vector). So, r(t)

= ∫[19(t²/2) i + (eᵗ - 1) j - (e⁻ᵗ - 2) k ] dt

= 19 (t³/6) i + eᵗ j - t j - e⁻ᵗ k + 2t k + D

At t = 0, r(0) = j + k

=> j + k = 19 (0³/6) i +e⁰ j - 0j - e⁻⁰ k +2× 0k +D

=> j + k = 0 + j - k + D

=> D = 2k

so, r(t) = 19 (t³/6) i + eᵗ j - t j - e⁻ᵗ k + 2t k + 2k

= 19 (t³/6)i + (eᵗ - t )j - (e⁻ᵗ - 2t - 2)k

Hence, required position vector is 19 (t³/6)i + (eᵗ - t )j - (e⁻ᵗ - 2t - 2)k.

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Answer:

a. rectangle

...........

Just factor out the 3:

3m + 3n = 3 (m + n)

The polynomial of 3rd degree whose zeros and degree are given as for zero of (-2), multiplicity 1 and for zero of (3), multiplicity 2 is \(f(x)=(x^{3}-10x^{2} -15x+18)\)

As per the question statement, a 3rd degree polynomial has a zero of (-2), multiplicity 1 and another zero of (3), multiplicity 2.

We are required to determine the polynomial.

Since, (-2) is a zero of the polynomial, then \([x-(-2)]=(x+2)\) will be a factor of the polynomial. And since for zero of (-2), multiplicity is 1, this means that the factor of (x + 2) is only multiplied once.

Similarly, as (3) is another zero of the polynomial, then \((x-3)\) will be a factor of the polynomial. And since for zero of (3), multiplicity is 2, this means that the factor of (x - 3) will be multiplied twice, i.e., \((x-3)^{2}\).

Therefore, our function, say, f(x) will be \((x+2)(x-3)^2\)

\(or, f(x) = (x+2)(x-3)^2\\or, f(x) = (x + 2)(x^{2} +9-12x)\\or,f(x) =x^{3}+9x-12x^{2} +2x^{2} +18-24x\\ or, f(x)=x^{3}+(2x^{2}-12x^{2})+(9x-24x)+18\\or, f(x)=(x^{3}-10x^{2} -15x+18)\)

Hence, our required polynomial is \(f(x)=(x^{3}-10x^{2} -15x+18)\)

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Answer:

1072.3

Step-by-step explanation:

V=(2/3)πr³ is the formula.

-hope it helps

Answer:

1072.33 cm³

Step-by-step explanation:

The volume of a hemisphere = (2/3)πr³ cubic units ...........where is is radius.

here given radius, r = 8 cm

so using the hemisphere's formula = (2/3) * π * 8³

                                                          =(2/3) * π * 8 * 8 * 8

                                                            = 1072.33 cm³

Answer:

(i) x ≤ 1

(ii) ℝ except 0, -1

(iii) x > -1

(iv) ℝ except π/2 + nπ, n ∈ ℤ

Step-by-step explanation:

(i) The number inside a square root must be positive or zero to give the expression a real value. Therefore, to solve for the domain of the function, we can set the value inside the square root greater or equal to 0, then solve for x:

\(1-x \ge 0\)

\(1 \ge x\)

\(\boxed{x \le 1}\)

(ii) The denominator of a fraction cannot be zero, or else the fraction is undefined. Therefore, we can solve for the values of x that are NOT in the domain of the function by setting the expression in the denominator to 0, then solving for x.

\(0 = x^2+x\)

\(0 = x(x + 1)\)

\(x = 0\)     OR     \(x = -1\)

So, the domain of the function is:

\(R \text{ except } 0, -1\)

(ℝ stands for "all real numbers")

(iii) We know that the value inside a logarithmic function must be positive, or else the expression is undefined. So, we can set the value inside the log greater than 0 and solve for x:

\(x+ 1 > 0\)

\(\boxed{x > -1}\)

(iv) The domain of the trigonometric function tangent is all real numbers, except multiples of π/2, when the denominator of the value it outputs is zero.

\(\boxed{R \text{ except } \frac{\pi}2 + n\pi} \ \text{where} \ \text{n} \in Z\)

(ℤ stands for "all integers")

Answer:

(i)  x ≤ 1

(ii)  All real numbers except x = 0 and x = -1.

(iii)  x > -1

(iv)  All real numbers except x = π/2 + πn, where n is an integer.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

\(\hrulefill\)

\(\textsf{(i)} \quad f(x)=\sqrt{1-x}\)

For a square root function, the expression inside the square root must be non-negative. Therefore, for function f(x), 1 - x ≥ 0.

Solve the inequality:

\(\begin{aligned}1 - x &\geq 0\\\\1 - x -1 &\geq 0-1\\\\-x &\geq -1\\\\\dfrac{-x}{-1} &\geq \dfrac{-1}{-1}\\\\x &\leq 1\end{aligned}\)

(Note that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign).

Hence, the domain of f(x) is all real numbers less than or equal to -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x \leq 1\\\textsf{Interval notation:} \quad &(-\infty, 1]\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \leq 1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(ii)} \quad g(x) = \dfrac{1}{x^2 + x}\)

To find the domain of g(x), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.

Set the denominator to zero and solve for x:

\(\begin{aligned}x^2 + x &= 0\\x(x + 1) &= 0\\\\\implies x &= 0\\\implies x &= -1\end{aligned}\)

Therefore, the domain of g(x) is all real numbers except x = 0 and x = -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x < -1 \;\;\textsf{or}\;\; -1 < x < 0 \;\;\textsf{or}\;\; x > 0\\\textsf{Interval notation:} \quad &(-\infty, -1) \cup (-1, 0) \cup (0, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq 0,x \neq -1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iii)}\quad h(x) = \log_7(x + 1)\)

For a logarithmic function, the argument (the expression inside the logarithm), must be greater than zero.

Therefore, for function h(x), x + 1 > 0.

Solve the inequality:

\(\begin{aligned}x + 1 & > 0\\x+1-1& > 0-1\\x & > -1\end{aligned}\)

Therefore, the domain of h(x) is all real numbers greater than -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x > -1\\\textsf{Interval notation:} \quad &(-1, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x > -1\right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iv)} \quad k(x) = \tan x\)

The tangent function can also be expressed as the ratio of the sine and cosine functions:

\(\tan x = \dfrac{\sin x}{\cos x}\)

Therefore, the tangent function is defined for all real numbers except the values where the cosine of the function is zero, since division by zero is undefined.

From inspection of the unit circle, cos(x) = 0 when x = π/2 and x = 3π/2.

The tangent function is periodic with a period of π. This means that the graph of the tangent function repeats itself at intervals of π units along the x-axis.

Therefore, if we combine the period and the undefined points, the domain of k(x) is all real numbers except x = π/2 + πn, where n is an integer.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &\pi n\le \:x < \dfrac{\pi }{2}+\pi n\quad \textsf{or}\quad \dfrac{\pi }{2}+\pi n < x < \pi +\pi n\\\textsf{Interval notation:} \quad &\left[\pi n ,\dfrac{\pi }{2}+\pi n\right) \cup \left(\dfrac{\pi }{2}+\pi n,\pi +\pi n\right)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq \dfrac{\pi}{2}+\pi n\;\; (n \in\mathbb{Z}) \right\}\\\textsf{(where $n$ is an integer)}\end{aligned}}\)

Answer:

to find the weight in pounds, divide the number of ounces by the unit rate, 16 ounces per pound.

Lucio is 64 meters from the starting point.

The square has four sides of equal length, so Lucio has walked half the length of one side.

To return to the starting point, he needs to walk the other half of the side, which is 64 meters.

The angle Lucio turns is irrelevant, as long as he turns 180 degrees in total.

With this in mind, it can be seen that based on the parameters and the conditions, Lucio is 64 meters from the starting point because the angle to which he turns is irrelevant.

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The question in English:

In a square Lucio walks in straight sections, starting from the flagpole, at one point he changes direction turning 150º to his left, advances 64 meters and stops. To return to the pole you have to turn 75º to the left. How far are you from the starting point?

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

Answer:

The answer is 5.4 because you'll add them up and divide by 7

Answer:

No solution

Step-by-step explanation:

Step 1: Write out equations

y = -1/4x + 2

3y = -3/4x - 6

Step 2: Substitution

3(-1/4x + 2) = -3/4x - 6

Step 3: Distribute

-3/4x + 6 = -3/4x - 6

From here, we can see that we have the same slope but different y-intercept. This means that the 2 lines are parallel and therefore never intersect.

Alternatively, you could graph the equations and see that the 2 lines are parallel and never intersect.

Answer:

No solution

Step-by-step explanation:

y = -1/4x + 2

3y = -3/4x - 6

Plug y as -1/4x + 2 in the second equation.

3(-1/4x + 2) = -3/4x - 6

-3/4x + 6 = -3/4x - 6

-3/4x + 3/4x = -6 -6

0 = -12

No solution.

Answer:28 degrees

Step-by-step explanation:

Answer:

28°

Step-by-step explanation:

Look at the angle, directly across from it and in no way touching the angle is the side with length 7. This side is OPPOSITE from the angle. The longest side, length 15, is the HYPOTENUSE. The trig function that uses Opposite and Hypotenuse is the sine function.

sin x = 7/15

Inverse sine will give you the angle given that you know the ratio (you do, its 7/15) on a calculator it will look like sin with a negative 1 exponent. It has nothing to do with exponents. Or it could be labelled arcain, sometimes abbreviated asin.

sin ^-1 (7/15)

= 27.8 approximately equal to 28°