A rectangle measures 2 1/4 Inches by 1 3/4 inches. What is its area?​

Answer:

x=20

Step-by-step explanation:

(4x-12)+(x+2)=90

5x-10=90

5x=100

x=20

Answer:

16in

Step-by-step explanation:

Plz help me too

The formula for the circumference of a circle is given by 2 * pi * r, where pi is approximately equal to 3.14 and r is the radius of the circle.

Circumference—does it indicate distance?

Definition. The circumference of a circle is the distance encircling its edge. The diameter of a circle is the distance measured through its center. The radius of a circle is the distance from the center to any point on the edge.

We can use this formula to solve for the radius by rearranging the equation:

r = C / (2 * pi)

where C is the circumference. Plugging in the given circumference of 36.91 meters:

r = 36.91 / (2 * 3.14)

r = 5.83 meters

Rounding to the nearest hundredth, the radius of the circle is approximately 5.83 meters.

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Using the hypergeometric distribution, it is found that the distribution is:

P(X = 0) = 0.0152

P(X = 1) = 0.1818

P(X = 2) = 0.4545

P(X = 3) = 0.3030

P(X = 4) = 0.0455

Hence:

A) There is a 0.0455 = 4.55% probability that all selected rats are female.

B) There is a 0.1818 = 18.18% probability that only one of the selected rats is female.

C) There is a 0.803 = 80.3% probability that at least two of the selected rats is female.

D) The mean of the probability distribution is of 2.18.

E) The standard deviation of the probability distribution is of 0.833.

The rats are chosen without replacement, hence the hypergeometric distribution is used to solve this question.

The formula is:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The distribution is the probability of each outcome, hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,11,4,6) = \frac{C_{6,0}C_{5,4}}{C_{11,4}} = 0.0152\)

\(P(X = 1) = h(1,11,4,6) = \frac{C_{6,1}C_{5,3}}{C_{11,4}} = 0.1818\)

\(P(X = 2) = h(2,11,4,6) = \frac{C_{6,2}C_{5,2}}{C_{11,4}} = 0.4545\)

\(P(X = 3) = h(3,11,4,6) = \frac{C_{6,3}C_{5,1}}{C_{11,4}} = 0.3030\)

\(P(X = 4) = h(4,11,4,6) = \frac{C_{6,4}C_{5,0}}{C_{11,4}} = 0.0455\)

Item a:

P(X = 4) = 0.0455, hence:

There is a 0.0455 = 4.55% probability that all selected rats are female.

Item b:

P(X = 1) = 0.1818, hence:

There is a 0.1818 = 18.18% probability that only one of the selected rats is female.

Item c:

\(P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.4545 + 0.3030 + 0.0455 = 0.803\)

There is a 0.803 = 80.3% probability that at least two of the selected rats is female.

Item d:

The mean of the hypergeometric distribution is:

\(\mu = \frac{nk}{N}\)

Hence:

\(\mu = \frac{4(6)}{11} = 2.18\)

The mean of the probability distribution is of 2.18.

Item e:

The standard deviation of the hypergeometric distribution is:

\(\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}\)

Hence:

\(\sigma = \sqrt{\frac{4(6)(11-6)(11-4)}{11^2(11-1)}} = 0.833\)

The standard deviation of the probability distribution is of 0.833.

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Answer:

184185

Step-by-step explanation:

W=333

L=555W

L=555(333)

L=184185

Answer:

The area is 45.

Step-by-step explanation:

Answer:

Always

sometimes

never

Step-by-step explanation:

If n < 9, the decimal equivalent is always repeating.

If n > 9, the decimal equivalent is sometimes repeating.

If n is a multiple of 9, the decimal equivalent is never repeating.

Im also on the same question!

Answer:

The order from first to last: always, sometimes, never

Step-by-step explanation:

It's going to be always because the numerator has to be less than 9 in order for it to be always.

It's going to be sometimes if n is greater than 9 it will only be sometimes.

It's going to be never because it doesn't make sense.

In the given model, the process {Yt} is a stationary process. The autocovariance function and autocorrelation function of {Yt} can be calculated.

(a) Stationarity of {Yt}:

To show that {Yt} is stationary, we need to demonstrate that its mean and autocovariance do not depend on time. Taking the expectation of Yt, we have E[Yt] = E[Xt + Zt] = E[Xt] + E[Zt] = 0 + 0 = 0, which shows that the mean of {Yt} is constant over time. For the autocovariance function, we calculate Cov(Yt, Yt+h) as Cov(Xt + Zt, Xt+h + Zh) = Cov(Xt, Xt+h) + Cov(Zt, Xt+h) + Cov(Xt, Zh) + Cov(Zt, Zh). Since {Xt} is an AR(1) process, the covariance terms involving Xt cancel out, leaving Cov(Zt, Zt+h). Since {Zt} is a white noise process, Cov(Zt, Zt+h) = 0 for h ≠ 0 and Cov(Zt, Zt) = Var(Zt) = σ². Hence, the autocovariance of {Yt} only depends on the lag h, indicating stationarity.

(b) Proving yʊ(h) = 0 for |h| > 1:

To prove that yʊ(h) = 0 for |h| > 1, we need to show that the cross-covariance between {Ut} and {Yt} is zero. By the given equation Ut = YtYt-1, we can rewrite it as Ut = (Xt + Zt)(Xt-1 + Zt-1). Expanding this expression, we get Ut = XtXt-1 + XtZt-1 + ZtXt-1 + ZtZt-1. The cross-term XtZt-1 involves Xt and Zt-1, which are not contemporaneously correlated due to the independence assumption. Therefore, E[XtZt-1] = E[Xt]E[Zt-1] = 0, and the cross-covariance yʊ(h) between {Ut} and {Yt} is zero for |h| > 1.

In conclusion, the process {Yt} is stationary, and its autocovariance function and autocorrelation function can be calculated. Additionally, it has been shown that yʊ(h) = 0 when |h| > 1 for the process {Ut}.

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Answer:

\({ \tt{distance = speed \times time}} \\ { \tt{ = 56 \times 3 \frac{1}{2} }} \\ = { \tt{196 \: miles}}\)

Answer:

The answer would be 21.25

so it would just stay the same because the number

2 is in the tens place

1 is in the ones place

.

2 is in the tenths place

5 is in the hundreths place

The correct answer is option  A: The random variable is discrete. A decibel is a unit of measure used to quantify the loudness or intensity of sound.

From 0 dB (the quietest level of sound) to 140 dB (the loudest level of sound), it is measured on a logarithmic scale (the highest level of sound).

The decibel level of a siren is normally between 110 and 120 dB, which is regarded to be within or close to the threshold of human hearing.

The decibel level of a siren is measured on a logarithmic scale, making it a discrete variable. This indicates that it is measured in whole numbers rather than fractions of a decibel.

For instance, a siren's decibel level can be 110 dB, 111 dB, 112 dB, etc., but it cannot be 110.5 dB or 111.5 dB. Therefore, the decibel level of a siren is a discrete variable.

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Given:

The regression equation for change in temperature, y, to amount of rain, r, is given by

\(\hat{y}=0.2-1.4r\)

The observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees.

To find:

The residual and interpret it.

Solution:

According to the question, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees.

So, the actual value is 2.3 degrees.

Put r=0.4 in the given equation, to find the predicted value.

\(\hat{y}=0.2-1.4(0.4)\)

\(\hat{y}=0.2-0.56\)

\(\hat{y}=-0.36\)

We know that,

Residual = Actual value - Predicted value

\(Residual=2.3-(-0.36)\)

\(Residual=2.3+0.36\)

\(Residual=2.66\)

Residual is positive because predicated value is less than the actual value.

So, the regression line underpredicts the temperature change.

Therefore, the correct option is B.

Answer:

the soda is less

Step-by-step explanation:

if you divide both the soda and the waters ounces by their price than you will get 0.15 for the soda and 0.16 for the water showing that its 1 cent more expensive than the soda

Euclidean Geometry is normally taught by starting with the statement of the theorem, then its proof (which includes the diagram, given and RTP – Required To Prove), then a few numerical examples and finally, some non-numerical examples. Have you seen the problem yet?? The PROOF is given at the beginning!

Step-by-step explanation:

hope this will help you

please mark me brainliest

Answer:

An hour is a unit of time.

Step-by-step explanation:

An hour is a period of 60 minutes.

1 hour = 60 minutes.

Answer:

an hour is the si unit of time

1 hour = 60 minutes

1 minutes = 60 seconds

pls mark as brainliest

Step-by-step explanation:

Answer: The y-intercept is 30 and the coefficient is -5

Step-by-step explanation:

In the slope-intercept form (y = mx + b) b stands for your y-intercept, in this case, 30.

The coefficient is the number being multiplied by the variable, or in this case, the slope, or -5.

Answer:

A.

Step-by-step explanation:

when you distribute it you keep the subtraction sign and have to multiply 6 by 50 and then 6 by 1

Answer:

so 30 books are mystery novels.

Step-by-step explanation:

300 / 10 = 30

Answer:

wait whats ur question

Step-by-step explanation:

If ur asking the percent then its 30

(pretty sure)

The amount of the tip that Jack gave to the waiter will be $9.42.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Jack took Diane out to supper to praise her birthday. The all out bill for the supper was $62.80. Jack needs to tip the server precisely 15%.

The amount of the tip will be given as,

⇒ 15% of $62.8

⇒ 0.15 x $62.8

⇒ $9.42

The amount of the tip that Jack gave to the waiter will be $9.42.

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Isaiah's thinking is correct. Compound interest does earn $341.95 more than simple interest in 60 months.

Let P be the principal amount of $7,000

Let r be the annual interest rate of 6%

Let n be the number of compounding periods per year.

Using formula for simple interest: I = Prt, the interest earned after 60 months is:

I = 7,000 × 0.06 × 5

I = $2,100.

Using formula for compound interest \(A = P(1 + r/n)^{nt}\). The amount after 60 months with monthly compounding is:

\(A = 7,000*(1 + 0.06/12)^{12*5}\\A = 7,000*1.34885015255\\A = 9441.95106785\\A = $9441.95\)

The interest earned is:

I = A - P

I = $9441.95 - $7,000

I = $2,441.95.

The difference in interest earned between compound and simple interest is:

= $2,441.95 - $2,100

= $341.95.

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Answer:

The answer is 4.5

Step-by-step explanation:

Part (a)

-----------

Explanation:

Draw a vertical line through -2 on the x axis. This vertical line will cross the blue parabola at some point P. From point P, draw a horizontal line to the y axis. You should arrive at y = -2. Figure 1, in the attached diagram below, shows this process.

================================================

Part (b)

-----------

Explanation:

Draw a horizontal line through y = 1 on the y axis. This is because y = f(x).

This horizontal line crosses the parabola at two places. Drop a vertical line straight down to the x axis to note the x values that make f(x) = 1 true.

You should find the solutions to be x = -3 and x = 1

See figure 2.

The value of the coefficient of the 1st harmonic of the Fourier series for the given rectangular wave can be determined using the provided information.

The coefficient represents the amplitude of the first harmonic component in the Fourier series. In this case, the rectangular wave has a peak voltage (Vp) of 4.0 and a negative peak voltage (-Vp) of -2.1, with a period (T) of 3.

To find the coefficient of the 1st harmonic, we need to consider the relationship between the harmonic amplitudes and the peak voltage of the waveform. For a rectangular wave, the amplitude of the nth harmonic is given by (4/πn) times the peak voltage. Since we are interested in the 1st harmonic, the coefficient can be calculated as (4/π) times Vp.

Using the given values, the coefficient of the 1st harmonic is determined as follows:

\(\[\text{Coefficient of 1st harmonic} = \frac{4}{\pi} \times Vp = \frac{4}{\pi} \times 4.0 \approx 5.09.\]\)

Therefore, the coefficient of the 1st harmonic of the Fourier series for the given rectangular wave is approximately 5.09. This coefficient indicates the amplitude of the fundamental frequency component in the waveform's Fourier series representation.

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Answer:

Range = 3.3

Step-by-step explanation:

Range = Max value - Min value

Max value = 100.1

Min Value = 96.8

Range = 100.1 - 96.8

Range = 3.3

The data set which has an outlier is the last set, 3, 6, 7, 7, 8, 8, 9, 9, 9, 10.

Outlier in a data set is simply the extremely low data point or an extremely high data point compared to other points in the dataset.

Given are 4 data sets.

Outlier can be found using the interquartile range.

If any data point does not contain in the interval,

[Q₁ - (1.5) IQR, Q₃ + (1.5) IQR]

then the data point is an outlier.

Consider the last data set.

3, 6, 7, 7, 8, 8, 9, 9, 9, 10

Two equal sets are (3, 6, 7, 7, 8), (8, 9, 9, 9, 10)

Mean = (8 + 8) / 2 = 8

First quartile, Q₁ = 7

Third quartile, Q₃ = 9

Interquartile range = Q₃ - Q₁ = 9 - 7 = 2

Interval = [7 - (1.5) 2, 9 + (1.5)2]

             = [4, 12]

3 is not contained in the interval. So it is an outlier.

Hence the last set is the one with the outlier.

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(a) The probability of drawing 2 Jack cards and 1 King card is approximately 0.096.

(a) To calculate the probability of drawing 2 Jack cards and 1 King card, we need to consider the number of favorable outcomes and divide it by the total number of possible outcomes. The favorable outcomes occur when we choose 2 Jacks from the 4 available and 1 King from the 4 available.

The total number of possible outcomes is the number of ways to choose 3 cards from a deck of 52. Dividing the favorable outcomes by the total outcomes gives us the probability of approximately 0.096.

(b) To calculate the probability of drawing 3 cards of the same type, we consider the four types of cards (hearts, diamonds, clubs, and spades). For each type, there are 13 cards available.

We need to choose 3 cards of the same type from each set, and then sum up the probabilities for each type. This gives us the probability of approximately 0.055.

(c) To calculate the probability of drawing at least 2 aces, we consider two cases: drawing exactly 2 aces and drawing all 3 aces. The probability of drawing exactly 2 aces is calculated by choosing 2 aces from the 4 available and choosing the third card from the remaining 49 cards.

The probability of drawing all 3 aces is calculated by choosing all 3 aces from the 4 available. Adding these two probabilities gives us the probability of approximately 0.147 for drawing at least 2 aces.

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Answer:

While some call having one to two months' wages in reserve ideal, most financial experts say that the recommended emergency fund amount should cover three to six months' worth of household expenses. That's a great idea, and a key part of any sound financial plan, but it also requires some effort to achieve

The first five terms of the given sequence, starting with \(a_1 = 42\) and following the recursive rule \(a_n = a_n - 1 - 7\), are 42, 35, 28, 21, and 14.

To find the subsequent terms of the sequence, we apply the recursive rule. Given that \(a_1 = 42\), we can calculate \(a_2\) as follows:

\(a_2 = a_1 - 7= 42 - 7= 35\)

Continuing this pattern, we can calculate the next terms:

\(a_3 = a_2 - 7= 35 - 7= 28\)

\(a_4 = a_3 - 7= 28 - 7= 21\)

\(a_5 = a_4 - 7= 21 - 7= 14\)

Hence, the first five terms of the sequence are 42, 35, 28, 21, and 14.

The sequence follows a pattern of subtracting 7 from the previous term to obtain the next term. Each term decreases by 7 compared to its preceding term.

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Answer:

C. It is used to find the sum of interior angles

Also , it can be used to find the number of triangles in the polygon,

Step-by-step explanation:

Example :

Find the sum of interior angles whose no of sides is 6 and give the name of the polygon

  Solution

S = (n-2)180°

S = (6-2)180°

S = (4)180°

S = 720°

The polygon is a Hexagon

I hope it helps  :)

S = (n – 2)180° is used to calculate the sum of interior angles of the polygon. Then the correct option is A.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The sum of the interior angle of the polygon is given as,

S = (n – 1)180°

Where, n be the number of the sides.

Then the correct option is A.

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Answer:

Top right corner

Step-by-step explanation: