24 (1 point)
ASQR is similar to ASPT. Which choice below lists two corresponding sides?
a
b
PS and RS
TP and RQ
SP and SR
QS and PT
c
d
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Answer: = 16

Step-by-step explanation: Hope this help :D

Answer:

The last option:  \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Step-by-step explanation:

Main concepts:

Concept 1. Parts of a Radical

Concept 2. Radicals as exponents

Concept 3. Exponent properties

Concept 4. How to simplify a radical

Concept 1. Parts of a Radical

Radicals have a few parts:

If the index isn't shown, it is the default index of "2".  This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.

In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.

Concept 2. Radicals as exponents

For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical.  In equation form:

\(\sqrt[n]{x} =x^{^{\frac{1}{n}}}\)

So, the original expression can be rewritten as follows:

\(\sqrt[4]{81x^{18}y^{6}}\)

\((81x^{18}y^{6})^{^{\frac{1}{4}}}\)

Concept 3. Exponent properties

There are a number of properties of exponents:

Continuing with our expression, \((81x^{18}y^{6})^{^{\frac{1}{4}}}\), we can apply the "distributive" property since all of the parts are multiplied to each other...

\((81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}\)

Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})\)

Reducing those fractions, (both the numerators and denominators have a factor of 2)...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})\)

Rewriting the exponent of the "81" back as a radical...

\(\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Concept 4. How to simplify a radical

For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.

In our case, the index is 4.  So, we're looking for a number that when multiplied together four times, gives a result of 81.

One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).

Note that 81 factors into 9*9, which further factors into 3*3*3*3

This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:

\(\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3\)

So, our original expression, simplifies finally to \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

This is the last option for the multiple choice.

Where the above conditions exist,

The random variable T = L + C represents the total time it takes Lorelei and Chance to finish a randomly selected 3-layer wedding cake. Since L and C are independent and Normally distributed, T is also Normally distributed with mean:

Mu_T = Mu_L + Mu_C = 37 + 52 = 89

and variance:

Var(T) = Var(L) + Var(C) = 12^2 + 7^2 = 193

So the standard deviation of T is:

Sigma_T = sqrt(Var(T)) = sqrt(193) = 13.89

The shape of T is also Normally distributed, since it is a sum of two independent Normally distributed variables.

To find the probability that Lorelei and Chance finish a randomly selected 3-layer wedding cake in under 90 minutes, we need to calculate the z-score for this value and then find the corresponding probability from the z-table. The z-score is:

z = (90 - 89) / 13.89

= 0.072

From the z-table, we find that the probability of a Z-score less than or equal to 0.072 is 0.5287.

Therefore, the probability that Lorelei and Chance totally finish a randomly selected 3-layer wedding cake in under 90 minutes is 0.5287 or approximately 53%.

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Answer:

ok thx

Step-by-step explanation:

Any positive integer n that meets the three requirements is a multiple of 9 and 11, as well as an odd multiple of 5. Lcm(5,9,11)=5911=495 is the smallest such n.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers.

Here,

The n subsequent integers from -(n-1)/2 to (n+1)/2 have a sum of 0 if n is an odd number. Sum n is produced by translating the interval to the right by 1. Each positive sum is therefore a positive multiple of n.

If n is even, the sum of the next n even integers from -n/2-1 to +n/2 is n/2. Sum n+n/2 is produced by moving the interval to the right by 1. As a result, every positive sum is an odd multiple of n/2.

Therefore, any positive integer n that meets the three requirements is a multiple of 9 and 11, as well as an odd multiple of 5. Lcm(5,9,11)=5911=495 is the smallest such n.

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Answer:

9 * pi inches squared

Step-by-step explanation:

Answer: The probability of getting a prime number exactly five times = 0.1908

Step-by-step explanation:

Prime numbers from 1 to 30 are 2,3,5,7,11, 13, 17, 19, 23, 29.

The probability of getting a prime number p= \(\dfrac{10}{30}=\dfrac13\)

Number of trials n = 12

Binomial probability formula:

\(P(X=x) = \ ^nC_x p^x(1-p)^{n-x}\)

, where x= number of successes

n= number of trials.

x = Number of successes

p= probability of getting one success.

The probability of getting a prime number exactly five times:

\(P(X=5)=\ ^{12}C_5(\frac13)^5(1-\frac13)^{7}\)

\(=\frac{12!}{5!7!}(\frac1{243})(\frac{128}{2187})\\\\=0.1908\)

Hence, the probability of getting a prime number exactly five times = 0.1908

If a function is not continuous, it may or may not be differentiable.

The differentiability of a function is not determined solely by its continuity.

A continuous function is a function that can be drawn without picking up a pen. In mathematical terms, a function f(x) is continuous if, as x approaches a point a, f(x) approaches f(a).

For a function to be differentiable, it must be continuous. If a function is not continuous, it is not differentiable. However, the opposite is not always true; a function may be continuous but not differentiable.

In summary, a function that is not continuous may or may not be differentiable, while a function that is differentiable must be continuous.

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Answer:

\(x = ln(2 - 1) \)

Answer: 4√2

Step-by-step explanation:

Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.

Try multiplying 4*4*2 = 32. So you would bunch up those two 4's and so it would be the front of the answer. Then you would square root 2 because it is remaining.

~I hope I helped you! :)~

Answer:

So Y, which represents height, goes down depending on how far you are in time, which is X.

The slope of the graph represents the elevator's descent speed, calculated as 12 feet per second based on the points (1, 838) and (2, 826).

The Slope of the line in the graph represents the rate of change of height with respect to time, or the speed of the elevator's descent.

In this case, the slope can be calculated using the formula: slope = (change in height) / (change in time). We know that the elevator's height changes from 838 feet at 1 second to 826 feet at 2 seconds,

So, the change in height is : 838 - 826 = 12 feet, and the change in time is 2 - 1 = 1 second.

Therefore, the slope is 12 feet/second, this indicates that the elevator is descending at a speed of 12 feet per second.

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Answer:

\((x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} = c^{2}\)

\(V(x_{1}, y_{1}) = V(4, 4)\\X(x_{2}, y_{2}) = V(5, 8)\\\)

\((5-4)^{2} + (8-4)^{2} = c^{2}\\1^{2} + 4^{2} = c^{2}\\\)

\(1+16=c^{2}\\17= c^{2}\\c = \sqrt{17}\)

Step-by-step explanation:

Start by plotting your points.

If the line is diagonal, then realize you can make a triangle with the line connecting the two points being the hypotenuse.

Use Pythagorean Theroem to solve.

The distance between V(4,4) and X(5,8) is √17 unit.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

First find the difference of between the 2 points V(4,4) and X(5,8) to find the length of the legs.

The distance between 4 and 5 = 1

The distance between 4 and 8 = 4

So,

1^2 + 4^2 = c^2

1 + 16 = c^2

17 = c^2

√17 = c

Therefore, the distance between V(4,4) and X(5,8) is √17 unit.

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The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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Answer:

resistant

because the median is not affected by the size of an outlier and does not change even if a particular outlier is replaced by an even more extreme value, we say the median is resistant to outliers.

Answer:

x = 44/7

Step-by-step explanation:

7x+3 = 47

Subtract 3 from each side

7x+3-3 = 47-3

7x = 44

Divide by 7

7x/7 = 44/7

x = 44/7

Answer:

(a) 2058 m2

Step-by-step explanation:

This track can be broken down into 4 components

A positive space rectangle and negative space rectangle in the middle.

A positive space circle, and negative space circle, due to there being 4 semicircles total at the end of each of the aforementioned rectangles.

Now we have to find the dimensions for all these shapes by simply looking at the image:

The total height is 56m (42m+7m+7m), that means Positive circle has a radius of 28m (56m diameter/2 = 28m radius).

The height for the negative space within the track is 42m, thus negative circle has a radius of 21m (42m diameter/2 = 21m radius)

Now for the rectangles:

Total length is 126m, and since we already found the diameter/radius of those semicircles, we can do simple subtraction to find the length of the rectangles: 126m-56m=70m.

Finding the height of both rectangles is easy, its the same as the circles:

Total height is 56m and negative space height is 42m.

Now we use those dimensions we found to calculate the area of all the shapes.

Positive circle area = (22/7)*(56m^2)=2464m2

Negative circle area = (22/7)*(42m^2)=1386m2

We now subtract the negative area from the positive area and we get a total circle area of 2464m2-1286m2=1078m2

Positive rectangle area = 56m*70m=3920m2

Negative rectangle area = 42m*70m=2940m2

Like we did with the circles, we subtract: 3920m2-2940m2=980m2

To finally find the total area of the tracks we add both areas we found together: (1078m2+980m2=2058m2)

So there's our answer!

P.S. This took a long time to solve so I hope it's appreciated :)

The predicted number of adults in Oak City whose main source of news is newspapers or the radio is 85

To predict the number of adults in Oak City whose main source of news is newspapers or the radio, we need to add the number of adults who answered "Newspapers" to the number of adults who answered "Radio".

According to the sample data

Number of adults who answered "Newspapers": 64

Number of adults who answered "Radio": 21

Therefore, the predicted number of adults in Oak City whose main source of news is newspapers or the radio we have to use the addition

64 + 21 = 85

Rounding this answer to the nearest whole number, we get

85 ≈ 85

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The given question is incomplete, the complete question is:

There are 44,000 adults living in Oak City. In examining attitudes toward the news, a research group asked a random sample of Oak City adults "What is your main source of news?" The results are shown below. Main Source of News Newspapers Number of Adults 64 Internet 80 Television 126 Radio 21 Other 40 Based on the sample, predict the number of adults in Oak City whose main source of news is newspapers or the radio. Round your answer to the nearest whole number.

Answer:

The average speed on the return trip is 2.44 miles/h.                  

Step-by-step explanation:

To find the average speed we need to use the following equation:

\( \overline{v} = \frac{d}{t} \)

Where:

d: is the distance

t: is the time

Since the question is to find the average speed on the return trip, we will take the data of the time and speed of only the return trip.

\(\overline{v} = \frac{d}{t} = \frac{5 + 1/2}{2 + 1/4} = 2.44 miles/h\)                

Therefore, the average speed on the return trip is 2.44 miles/h.

I hope it helps you!

Answer:

To get the Greates Common Factor (GCF) of 39375 and 779625 we need to factor each value first and then we choose all the copies of factors and multiply them:

39375:    3 3     5 5 5 5 7  

779625:    3 3 3 3 5 5 5   7 11

GCF:    3 3     5 5 5   7  

The Greates Common Factor (GCF) is:   3 x 3 x 5 x 5 x 5 x 7 = 7875

Step-by-step explanation:

The probability that both the father and mother are current smokers is 0.12.

The probability that the mother is a current smoker is, 0.3 and the father is a current smoker is, 0.4.

The events are independent, the probability that both the events will occur is the multiplication of probability of individual events.

Therefore, the required probability is product of probability that mother is a current smoker with the probability that father is a current smoker.

P(Father and Mother are current smokers) = P(Father is a current smoker) × P(Mother is a current smoker)

P(Father and Mother are current smokers) = 0.4 × 0.3

P(Father and Mother are current smokers) = 0.12

The required probability is 0.12.

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Ratio analysis can be made more meaningful in all the following ways except by focusing more on long-term solvency than on short-term solvency.

Ratio analysis is a mathematical technique for analyzing a company's financial documents, such as the balance sheet and income statement, to gather knowledge about its liquidity, operational effectiveness, and profitability. Fundamental equity research is built on ratio analysis.

In order to get insights into profitability, liquidity, operational effectiveness, and solvency, ratio analysis examines line-item data from a company's financial statements.

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The full question:

ratio analysis can be made more meaningful in all the following ways except by?

Answer:

y=6x+8 or y=6x-22

Step-by-step explanation:

use the equation y=mx+b

m is the slope and b is the y-intercept

to find the slope use the equation m = y2-y1 over x2-x1

-22 - 8 / -2 - 3 = -30 / -5 = 6

6 is your slope and for the y-intercept you can choose whichever y-intercept to put into the equation.

HOPE THIS HELPS!!

Retain the null because 1.74 is greater than 1.645.

What is z - test statistic?

Any statistical test for which the test statistic's distribution under the null hypothesis can be roughly represented by a normal distribution is known as a Z-test.

Z-tests examine a distribution's mean.

Let X be the average time that prescholars spend on tablets.

X ~ N(μ, α^2)

To test H0: μ = 3 hours Vs H1: μ ≠ 3 hours.

The z - test statistic is obtained as 1.74.

Taking level of significance α = 0.05

Zα/2 = \(Z_0_._0_2_5 = 1.96\)

Since the observed z - statistic is 1.74 which is less than Zα/2 = \(Z_0_._0_2_5 = 1.96\),

so we retain the null hypothesis.

Hence, retain the null because 1.74 is greater than 1.645.

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Complete question:

Complete question is attached below.

Answer:

  identity element property

Step-by-step explanation:

June's value did not change, so the value she added was the additive identity element: 0.

She made use of the identity element property of addition, which says that adding the identity element does not change the value.

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

Answer:

(x - 7)² + (y + 3)² = 7

Step-by-step explanation:

The equation of a circle is denoted by: \((x -x_1)^2+(y-y_1)^2=r^2\), where \((x_1,y_1)\) is the centre and r is the radius.

Here, the centre is (7, -3), which means \(x_1=7\) and \(y_1=-3\). The radius is r = √7. Plug these values into the formula:

\((x -x_1)^2+(y-y_1)^2=r^2\)

\((x -7)^2+(y-(-3))^2=(\sqrt{7}) ^2\)

\((x -7)^2+(y+3)^2=7\)

Thus, the answer is (x - 7)² + (y + 3)² = 7.

~ an aesthetics lover

In order to solve this question, we need to use the z-score z of value x, belonging to a normal distribution with mean μ and standard deviation σ.

z is defined as:

In this problem, we have, in pounds:

μ = 8.9

σ = 1.1

PART 1

So, the percentage of domestic house cats that weigh less than 7.8 pounds is:

And from a z-score table, we have:

Therefore, the percentage of domestic house cats that weigh less than 7.8 pounds is approximately 0.1587 or 15.87%.

PART 2

The percentage of domestic house cats that weigh more than 11.1 pounds is 1 minus the percentage of them that weigh less than that:

Therefore, the percentage of domestic house cats that weigh more than 11.1 pounds is approximately 0.0228 or 2.28%.

PART 3

The domestic house cat weighing 9 pounds is in percentile P(x<9):

Therefore, a domestic house cat weighing 9 pounds is in the 54th percentile.