PLEASE HELP ME!

Suppose that ∆EFG ~ ∆ABC and the ratio between corresponding sides of ∆EFG to ∆ABC is 3 : 2.




If AB = 4 cm, BC = 6 cm, AC = 8 cm, and EF = 6 cm, what is EG?



a. 8 cm

b. 9 cm

c. 10 cm

d. 12 cm

To find the exact value of the expression 2log₂⁸ - log₂⁹, we can use the properties of logarithms.

First, let's simplify each logarithm separately:

log₂⁸ can be rewritten as log₂(2³), using the property that logₐ(b^c) = clogₐ(b).

So, log₂⁸ = 3log₂(2).

Similarly, log₂⁹ can be rewritten as log₂(3²), since 9 can be expressed as 3².

So, log₂⁹ = 2log₂(3).

Now, substituting these simplified forms back into the original expression:

2log₂⁸ - log₂⁹ = 2(3log₂(2)) - (2log₂(3))

Using the property that alogₐ(b) = logₐ(b^a), we can further simplify:

= log₂(2³) - log₂(3²)

= log₂(8) - log₂(9)

Applying the property that logₐ(b) - logₐ(c) = logₐ(b/c), we have:

= log₂(8/9)

Therefore, the exact value of the expression 2log₂⁸ - log₂⁹ is log₂(8/9).

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5/x = x/ 9

Cross-multiply

x² =45

Take the square root of both-side

x = 3√5 or 6.7082039325

Answer:

9\(y^{5}\)\(w^{2}\)

Step-by-step explanation:

Find what both expressions have in common

Answer:

The perimeter is 16 units.

Step-by-step explanation:

Once you graph all the sides you can easily count and see the perimeter is 16. :)

A two-column proof is used to prove geometric statements by presenting the logical steps and corresponding justifications.

To prove that ∠G and ∠K, ∠K and ∠L, ∠L and ∠M, and ∠M and ∠G are supplementary angles based on the given information √GKLM, we can use a two-column proof.

In the left column, we list the statements or steps, while in the right column, we provide the corresponding justifications or reasons for each step. The proof will involve the properties and theorems related to angles and their measures.

Starting with the given statement that √GKLM, we can apply Theorem 6.5, which states that if two angles are vertical angles, then they are congruent. Using this theorem, we can conclude that ∠G ≅ ∠M and ∠K ≅ ∠L.

Next, we can use the definition of supplementary angles, which states that two angles are supplementary if their measures add up to 180 degrees. Since ∠G ≅ ∠M and ∠K ≅ ∠L, we can conclude that ∠G + ∠M = 180 degrees and ∠K + ∠L = 180 degrees, respectively.

Finally, since ∠G ≅ ∠M and ∠K ≅ ∠L, it follows that ∠L and ∠M are congruent, and ∠G and ∠K are congruent as well. Therefore, we can conclude that ∠L + ∠M = 180 degrees and ∠G + ∠K = 180 degrees, proving that the given angles are supplementary.

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Answer: Caiden

Step-by-step explanation:

For Caiden, at the second minute, the water is already at 7 ounces. However, Bella is still at 8 ounces. And Caiden is drinking at a speed of 2.5 ounces per minute while Bella is drinking at a speed of 2 ounces per minute.

Hope that helped!

The equation for the circle is given by:

Where (h,k) is the center and r represents the radius.

Now, if we look at the given equation:

For h:

h = 2

For k:

k=-4

for r:

r²=36

r=√36

r =6

Hence, the center is (2,-4) and the radius is 6.

The correct answer is option b.

Answer:

1.08 = m

Step-by-step explanation:

2= 2.27- m/4

Subtract 2.27 from each side

2-2.27= 2.27-2.27- m/4

-.27 = -m/4

Multiply each side by -4

-.27 * -4 = -m/4 *-4

1.08 = m

Katty rode the roller coaster four times after riding the slide eight times.

Let R be the number of times she rode the roller coaster

Let S be the number of slides

The following mathematical equation can be created using the information provided:

R + S = 12. ........(i)

25R + 10S = 180 .......(ii)

From equation i, R = 12 - S.

Therefore, 25(12 - s) + 10s = 180

300 - 25s + 10s = 180

300 - 15s = 180

15s = 300 - 180

15s = 120

S = 120/15

S = 8 ,

Therefore R = 12 - S = 12 - 8 = 4

Katty rode the roller coaster four times after riding the slide eight times.

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The first chi-square statistic of 3.86 is not statistically significant at an alpha level of .01 because it is smaller than the critical value of 6.63. However, the second chi-square statistic of 67.81 is statistically significant at an alpha level of .05 because it is greater than the critical value of 3.84.

In statistical hypothesis testing, the chi-square statistic is used to determine if there is a significant association between categorical variables. To assess the statistical significance of the results, we compare the chi-square statistic to the critical value obtained from the chi-square distribution at a specific alpha level. The alpha level represents the probability of rejecting the null hypothesis when it is true.

For the first case, where the chi-square statistic is 3.86 and the critical value is 6.63 with an alpha level of .01, we find that the chi-square statistic is smaller than the critical value. In this scenario, we fail to reject the null hypothesis and conclude that the results are not statistically significant at the specified alpha level. This means that there is insufficient evidence to suggest a significant association between the categorical variables.

In the second case, where the chi-square statistic is 67.81 and the critical value is 3.84 with an alpha level of .05, we observe that the chi-square statistic is greater than the critical value. In this situation, we reject the null hypothesis and conclude that the results are statistically significant at the specified alpha level. This indicates strong evidence to support the presence of a significant association between the categorical variables.

Finally, the first chi-square statistic of 3.86 is not statistically significant at an alpha level of .01, while the second chi-square statistic of 67.81 is statistically significant at an alpha level of .05. The decision to reject or fail to reject the null hypothesis is based on comparing the chi-square statistic to the critical value obtained from the chi-square distribution at a specific alpha level.

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Answer:

16x+6

Step-by-step explanation:

5x+2+3x+1+5x+2+3x+1 =

16x+6

Answer:

16x + 2

Step-by-step explanation:

\(\boxed{\begin{minipage}{4 cm}\underline{Perimeter of a rectangle}\\\\$P=2(w+l)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\\phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}\)

Given expressions:

To write an expression for the perimeter of the rectangle, substitute the given expressions for the width and length into the perimeter formula:

\(\begin{aligned}\implies \textsf{Perimeter} &=2\left(5x+2+3x-1 \right)\\ &= 2(5x+3x+2-1)\\&=2(8x+1)\\&=16x+2\end{aligned}\)

Answer:

S.I = (P × R × T)/100

where;

P - principal

R - rate

T - time

By using the concept of Probability, 0.771 is the probability by which worker 1 will outproduce worker 2

Let Xi be the random variable representing the number of units the first worker produces in day i.

Define X = X₁+ X₂ + X₃ + X₄ + X₅ as the random variable representing the number of units the first worker produces during the entire week.

We know that Mean =(Sum of all quantities)/(Number of quantities)

Mean=75 and number of quantities =5(given)

Therefore, from the formula

=>Sum of all quantities=75×5

or We can Say that X₁+ X₂ + X₃ + X₄ + X₅=375--------------------------------(eq1)

Now, talking about the standard deviation of first worker

We know that standard deviation = \(\frac{\sqrt{(Each quantity - Mean)^{2} } }{\sqrt{Total Number of quantities} }\)

We are given standard deviation of first worker as 20,

Therefore 20×\(\sqrt{Total Number of quantities}\) = \(\sqrt{(Eachquantity -Mean)^{2} }\)

20√5 = √[(X₁ - Mean)²+(X₂ - Mean)²+(X₃ - Mean)²+(X₄ - Mean)²+(X₅ - Mean)²]-(eq2)

Therefore, from eq1 and eq2,

we get Mean(µx) =375 and standard deviation(σ\(x\)) =20√5

Similarly, define random variables Y₁, Y₂, . . . , Y₅ representing the number of units produces by the second worker during each of the five days and define Y = Y₁ + Y₂ + Y₃ + Y₄ + Y₅.

From the Mean formula,

we get  Y₁ + Y₂ + Y₃ + Y₄ + Y₅=(65×5)--------------------------------(eq3)

Standard deviation of second worker = 21(given),

So using the standard deviation formula, we get

Therefore 21×\(\sqrt{Total Number of quantities}\)=\(\sqrt{(Eachquantity -Mean)^{2} }\)

21√5=√[(Y₁ - Mean)²+(Y₂ - Mean)²+(Y₃ - Mean)²+(Y₄ - Mean)²+(Y₅ - Mean)²]-(eq4)

Therefore, from eq3 and eq4,

we get Mean(µy) =325 and standard deviation(σy) =21√5

Of course, we assume that X and Y are independent. The problem asks for P(X > Y ) or in other words for P(X − Y > 0).

It is a quite surprising fact that the random variable U = X −Y , the difference between X and Y ,is also normally distributed with mean µU = µx−µy = 375−325 = 50 and standard deviation σu ,where σ\(u^{2}\) = σ\(x^{2}\)+σ\(y^{2}\) =400·5+441·5 = 841·5 = 4205

It follows that  σu=√4205.

Now probability of first worker(P₁)=375/√4205

probability of second worker(P₂) =325/√4205

We can clearly see P₁>P₂

Difference in Probability of both workers(P)=P₁-P₂

=>P=[(375/√4205)-(325/√4205)]

=>P=50/√4205

=>P=50/64.84

=>P=0.771

Hence, probability by which worker 1 will outproduce worker 2 is 0.771.

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Answer:

A 19.8

Step-by-step explanation:

Mr. McMahon expected a semi-annual probability of default of 35.7% on the bond.

How to solve?

To solve this problem, we can use the formula for the present value of a bond:

PV = (C/r) ×[1 - 1/(1+r)²n] + F/(1+r)²n

where PV is the present value of the bond, C is the semi-annual coupon payment, r is the semi-annual yield rate, n is the number of semi-annual periods, and F is the face value or redemption value of the bond.

We know that Mr. McMahon paid $880 for a $1000 bond, so the present value of the bond is PV = $880. The redemption value of the bond is F = $1000, and the yield rate that he desired was r = 8% per year, compounded semi-annually. Therefore, the semi-annual yield rate is:

i = 0.08/2 = 0.04

We can use the formula to solve for the number of semi-annual periods:

PV = (C/i) ×[1 - 1/(1+i)²n] + F/(1+i)²n

$880 = ($45/i) ×[1 - 1/(1+0.04)²(220)] + $1000/(1+0.04)²(220)

Solving for i gives:

i = 0.0517 or approximately 5.17%

This is the semi-annual yield rate that Mr. McMahon actually received on the bond. To find the semi-annual probability of default that he expected, we can use the formula for the expected yield rate of a bond:

yield = (1 - probability of default) ×(yield rate on the bond) + (probability of default) ×(recovery rate)

where the recovery rate is the percentage of the face value that would be recovered in the event of default.

Assuming that the recovery rate is zero (meaning that in the event of default, Mr. McMahon would receive nothing), we can solve for the probability of default:

0.08 = (1 - p) ×0.0517 + p ×0

Solving for p gives:

p = 0.357 or approximately 35.7%

Therefore, Mr. McMahon expected a semi-annual probability of default of 35.7% on the bond.

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Answer:

39

Step-by-step explanation:

f(x)=17x

f(3)=17(3)

f(x)=51

g(x)=4x

g(3)=4(3)

g(x)=12

f(x)-g(x)

51-12= 39

Dinesh needs to pay the total amount of Rs 11976.40.

What is the simple interest?

Simple interest is the interest calculated on the original amount (principal) of a loan, without compounding.

To calculate the amount Dinesh needs to pay, we first find the interest using the formula:

I = P * R * T

Where:

P = 9000 (principal)

R = 12% (interest rate)

T = (8th September 2016 - 27th June 2016) / 365 (time in years)

The interest would be:

I = 9000 * 0.12 * (83/365) = Rs 2976.40

The total amount Dinesh needs to pay would be:

9000 + 2976.40 = Rs 11976.40

Hence, Dinesh needs to pay the total amount of Rs 11976.40.

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\(\bold{\huge{\purple{\underline{ Solutions }}}}\)

\(\bold{\dfrac{ 7}{6}}{\bold{ + }}{\bold{\dfrac{ 2}{5}}}\)

\(\sf{ = \:}{\sf{\dfrac{ 35 + 12 }{30}}}\)

\(\sf{ =\: }{\sf{\red{\dfrac{ 47 }{30}}}}\)

Hence, The answer is 47/30

\(\bold{\dfrac{ 1}{7}}{\bold{ + }}{\bold{\dfrac{ 1}{8}}}\)

\(\sf{ =\: }{\sf{\dfrac{ 8 + 7 }{56}}}\)

\(\sf{ =\: }{\sf{\red{\dfrac{ 15}{56}}}}\)

Hence, The answer is 15/56

\(\bold{\dfrac{ 7}{13}}{\bold{ + }}{\bold{\dfrac{ 5}{10}}}\)

\(\sf{=\:}{\sf{\dfrac{ 70 + 65 }{130}}}\)

\(\sf{ = \:}{\sf{\dfrac{ 135}{130}}}\)

\(\sf{ =\:}{\sf{\red{\dfrac{ 27}{26}}}}\)

Hence, The answer is 27/26

\(\bold{\dfrac{ 7}{5}}{\bold{ - }}{\bold{\dfrac{ 1}{3}}}\)

\(\sf{ =\:}{\sf{\dfrac{ 21 - 5 }{15}}}\)

\(\sf{ = \:}{\sf{\red{\dfrac{ 16}{15}}}}\)

Hence, The answer is 16/15

\(\bold{\dfrac{ 8}{7}}{\bold{ - }}{\bold{\dfrac{ 9}{11}}}\)

\(\sf{=\:}{\sf{\dfrac{ 88 - 63}{77}}}\)

\(\sf{=\:}{\sf{\red{\dfrac{ 25}{77}}}}\)

Hence, The answer is 25/77

\(\bold{\dfrac{ 11}{4}}{\bold{ - }}{\bold{\dfrac{ 1}{9}}}\)

\(\sf{=\:}{\sf{\dfrac{ 99 - 4}{36}}}\)

\(\sf{ =\: }{\sf{\red{\dfrac{ 95}{36}}}}\)

Hence, The answer is 95/36

Answer:

Mt Bueno esta alejandro Si

To create a box plot, we need to first order the data from smallest to largest:

19%, 22%, 24%, 25%, 27%, 29%, 30%, 31%, 32%, 33%, 38%, 42%

Next, we find the median, the first and third quartiles, the interquartile range (IQR), and any potential outliers.

Median: The middle value is the average of the two middle values: (29% + 30%) / 2 = 29.5%

First quartile (Q1): The median of the lower half of the data: (24% + 25%) / 2 = 24.5%

Third quartile (Q3): The median of the upper half of the data: (33% + 38%) / 2 = 35.5%

Finally, we can draw the box plot. The box represents the middle 50% of the data, and the whiskers extend to the minimum and maximum values that are within the fences.

From the box plot, we can see that the middle 50% of customers (represented by the box) purchased cookies between 24.5% and 35.5% of the time.

The whiskers show that almost all customers (represented by the horizontal lines) purchased cookies between 19% and 42% of the time.

Based on Athena's data, we can expect between 24.5% and 35.5% of people to buy Girl Scout cookies at the grocery store.

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The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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Answer:  B   28√15

Step-by-step explanation:

They want you to find the Area of the quadrilateral.  But if you can find the area of 1 trangle then you can double it because the 2 triangles are congruent.

We know the 2 triangles are congruent from the theorem  (see diagram

We also know that  QR=TR=SR  They are all radius

Let's solve for triangle PRS

PR = hypotenuse = 10+7 =17

SR=7  radius

Use pythagorean to find PS

c²=a²+b²

17²=7²+b²

289 = 49 + b²

b²=289 -49

b² = 240

b=√240

b=\(\sqrt{16*15}\)

b= 4√15  This is PS

Area of triangle = 1/2 bh       b=PS   h=7

Area of triangle = 1/2 (4√15)(7)

Area of triangle = (2√15)(7)

Area of triangle = 14√15

Area of quadrilateral = 2 (14√15)        > 2 triangles make the quadrilateral

Area of quadrilateral =  28√15

Answer:

\(-16/5 < s < 4\)

Step-by-step explanation:

\(|5s-2|-6 < 12 \\ |5s-2| < 18 \\-(5s-2) < 18 \\ -5s+2 < 18 \\ -5s < 16 \\ -s < (16/5) \\ s > -(16/5) \\(5s-2) < 18 \\ 5s < 20 \\ s < 4 \\= -16/5 < s < 4\)

The zeros of the polynomial are: x = 1/2 (with multiplicity 1), x = 3 (with multiplicity 1), and x = 5/2 (with multiplicity 1).We have found all three real zeros of the polynomial, which confirms that there are no complex zeros.

f(x) = 2x³ - 112x² + 27x - 41x + 15

To find the zeros and their multiplicities of this polynomial, we can begin by using Descartes' Rule of Signs. Let's consider the sign changes in the coefficients:

There are 2 sign changes in the coefficients (from 2x³ to -112x² and then to 27x, and finally to -41x and 15), which means there are either 2 or 0 positive real zeros.

There are no sign changes when we replace x with -x, which means there are either 0 or 2 negative real zeros.

Thus, there can be either 0, 2, or 4 real zeros, but we cannot determine their exact number or location with Descartes' Rule of Signs alone.

Next, we can use the Upper and Lower Bound Theorem to limit our search for rational zeros. According to this theorem, any rational zero of the polynomial must be of the form p/q, where p is a factor of the constant term (15 in this case) and q is a factor of the leading coefficient (2 in this case). Therefore, the possible rational zeros of the polynomial are:

±1/2, ±1, ±3/2, ±5, ±15/2, ±30

We can use synthetic division or long division to check these possible rational zeros and see which ones are actually zeros of the polynomial. Doing so, we find that the rational zeros of the polynomial are:

x = 1/2 (with multiplicity 1), x = 3 (with multiplicity 1), and x = 5/2 (with multiplicity 1).

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Answer:

Original: $733 million

Sequel: $860 million

Step-by-step explanation:

Let's say the original movie grossed x dollars. Since the sequel grossed 127 million more than that, we can write the expression x + 127 to represent the sequel.

Their total is 1593 million, so let's add them up:

x + (x + 127) = 1593

2x + 127 = 1593

2x = 1466

x = 1466/2 = 733

To find the sequel gross amount, add 127 to 733:

127 + 733 = 860

So, the original movie grossed $733 million, while the sequel grossed $860 million.

Answer: ≈ 26 lb

Step-by-step explanation:

11,800 grams x \(\frac{1 kilograms}{1000 grams}\) x \(\frac{1 pound}{0.45kilograms}\) ≈ 26 lb

Answer:

put 1 orange in each group and then cut the last in thirds and each group will have 1 and 1/3 oranges

Step-by-step explanation:

A given shape that is bounded by three sides and has got three internal angles is referred to as a triangle. Thus the value of PB is 8.0 units.

A given shape that is bounded by three sides and has got three internal angles is referred to as a triangle. Types of triangles include right angle triangle, isosceles triangle, equilateral triangle, acute angle triangle, etc. The sum of the internal angles of any triangle is \(180^{o}\).

In the given question, point P is such that <APB = <APC = <BPC = \(120^{o}\). Also, line PB bisects <ABC into two equal measures. Thus;

<ABP = \(30^{o}\)

Thus,

<ABP + <APB + <BAP = \(180^{o}\)

30 + 120 + <BAP = \(180^{o}\)

<BAP = \(180^{o}\) - 150

<BAP = \(30^{o}\)

Apply the Sine rule to determine the value of PB, such that;

\(\frac{AP}{Sin B}\) = \(\frac{BP}{Sin30}\)

\(\frac{8}{Sin30}\) = \(\frac{BP}{Sin 30}\)

BP = \(\frac{8*Sin30}{Sin 30}\)

     = \(\frac{4}{0.5}\)

BP = 8.0

Therefore, the value of BP = 8 units.

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