use your knowledge of transformations to find matching graph f (x) = ½ √x - 1

The error that Martell made in determining the scale factor was using point K and point A when they weren't similar points.

The process that Martell used to find the scale factor was correct, however, he should not have used points A and K because they are not similar sides in the triangles.

Point A is similar to point H while point D is similar to point K.

Using the similar points of A (4, 2 ) and H ( 6, 3 ), we find the scale factor to be:

= 6 / 4

= 1. 5

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The data set that best describes the histogram is

(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)

We have,

The histogram shows that there are different intervals on the x-axis, and for each interval, there is a corresponding frequency on the y-axis.

From the given data, we can see that there are more passengers in the 11 to 20 interval than in the 1 to 10 interval, and so on.

Looking at the answer choices, we need to choose the data set that matches the histogram.

The first step is to check if the data set has the same range as the histogram.

The histogram has intervals from 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50.

Now,

The first answer choice has numbers less than 1 and greater than 50, so it cannot be the correct choice.

The second answer choice has a range from 4 to 42, which matches the histogram.

We can check if the frequencies in the data set match the heights of the bars in the histogram.

For example, the histogram has a bar for the 11 to 20 interval that stops at 4, which means there are 4 passengers in that interval.

The second data set has 4 passengers in the 11 to 20 interval, so it matches.

We can do the same for the other intervals and find that the second data set matches the histogram.

Therefore,

The data set that best describes the histogram is

(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)

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Answer:21y -78

Step-by-step explanation: Distribute the 7 to 3y and -10 to get 21y and -70.

Then combine like terms so the equation would be 21y -78

Step-by-step explanation:

-8+7(3y-10)

-8+21y-70

21y-70+8

21y-78

Last step because there is no more like terms to combine

Hope this helps

The range of the function f(x) = |x| + 5 include the following; B. R: {f(x) ∈ ℝ | f(x) ≥ 5}.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞} or -∞ ≤ x ≤ ∞.

Range = {5, ∞} or 5 ≤ f(x) ≤ ∞.

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Answer:

Step 1: Distributive Property

Step 2: Distributive Property

Step 3: Commutative Property

Step-by-step explanation:

Step 1: This is distributing the (x + 4y + z) into the (x - 7y), so each term in the prior expression is multiplied by (x - 7y). Hence, Distributive Property.

Step 2: This is doing the same thing but to each individual term. The x in the first term is multiplied by each term in the (x - 7y), the 4y in the second term is multiplied by each term in the (x - 7y), and the same for z. Hence, Distributive Property.

Step 3: This is reordering the variables in the terms. For example, 4yx is changed to 4xy, and that is possible because of the Commutative Property. zx is also reordered into a xz and 7zy into a 7yz.

Feel free to ask any more questions. Hope this helps!!!

The coordinates of the point that corresponds to -5π/4 on the unit circle is (-1/√2, 1/√2).

Given that,

We have to find the coordinates of the point that corresponds to -5π/4 on the unit circle.

We know that any point on the unit circle can be defined as,

(cos θ, sin θ)

where θ is the angle formed with the X axis.

-5π/4 will be the point the corresponds to -225°.

Cos(-5π/4) = cos (5π/4)

                  = cos (π + π/4)

                  = -cos (π/4)

                  = -1/√2

sin (-5π/4) = -sin (5π/4)

                  = -sin (π + π/4)

                  = sin (π/4)

                  = 1/√2

Hence the coordinate of the unit circle is (-1/√2, 1/√2).

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Probability of answering exactly 4 questions correctly = 0.206

P (More than 2) = 0.475

1.

ind P(4): Probability of answering exactly 4 questions correctly.

P(X=4) = (10C4) * (0.25^4) * (0.75^6)

10C4 = 10! / (4! * (10-4)!) = 210

P(X=4) = 210 * (0.25^4) * (0.75^6)

= 0.206

P(X=0) = (10C0) * (0.25^0) * (0.75^10) ≈ 0.056

P(X=1) = (10C1) * (0.25^1) * (0.75^9) ≈ 0.187

P(X=2) = (10C2) * (0.25^2) * (0.75^8) ≈ 0.282

Now, calculate P(X>2):

P(X>2)

= 1 - (P(X=0) + P(X=1) + P(X=2))

= 1 - (0.056 + 0.187 + 0.282)

= 1 - 0.525

= 0.475

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[tex]\sin^2(\theta)+\cos^2(\theta)=1\hspace{9em} \begin{array}{llll} \textit{Symmetry Identities} \\\\ \sin(-\theta )=-\sin(\theta) \\\\ \cos(-\theta )=\cos(\theta ) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\cot(-x)\cos(-x)+\sin(-x)\implies \cfrac{\cos(-x)}{\sin(-x)}\cos(-x)+\sin(-x) \\\\\\ \cfrac{\cos(x)}{-\sin(x)}\cos(x)+[-\sin(x)]\implies \cfrac{-\cos^2(x)}{\sin(x)}-\sin(x) \\\\\\ \cfrac{-\cos^2(x)-\sin^2(x)}{\sin(x)}\implies \cfrac{-( ~~ \cos^2(x)+\sin^2(x) ~~ )}{\sin(x)} \\\\\\ \cfrac{-( ~~ 1 ~~ )}{\sin(x)}\implies -\cfrac{1}{\sin(x)}\implies -\csc(x)[/tex]

The required, difference between the perimeters of the two rectangles is,

⇒ 46.03 in.

Since, rectangles LMNP and WXYZ are similar, their corresponding sides are proportional. Let's denote the scale factor as k.

Then, We get:

k = XY / LM

k = 2.22 / 19

To find the value of k, we can divide 2.22 by 19:

k ≈ 0.117

Hence, The area of rectangle LMNP is given as,

140.6 in².

We can use this to find the length of NP:

LM x NP = area of LMNP

19 x NP = 140.6

NP ≈ 7.4 in

Since, the sides of WXYZ are proportional to those of LMNP, we can find the length of YZ:

XY / YZ = LM / NP

2.22 / YZ = 19 / 7.4

YZ ≈ 1.167 in

Now we can calculate the perimeters of both rectangles:

Perimeter of LMNP = 2(LM + NP) = 2(19 + 7.4) = 52.8 in

Perimeter of WXYZ = 2(XY + YZ) = 2(2.22 +1.167) = 6.77in

Thus, The difference between the perimeters is:

52.8 - 6.77 = 46.03 in

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The amount of water needed is 72 liters.

Given that, the ratio of the alcohol and water in a mixture of 72 units is 2 ratio 1, we need to find the amount of water that must be added to the mixture in order to make this ratio 1 ratio 2,

So,

The quantity of water in it = 72 / 3 × 1 = 24

New ratio =

48 / 24+x = 1/2

96 = 24+x

x =72

Hence, the amount of water needed is 72 liters.

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The solution is , price of jeans = RD$ 1140 and, price of  handbag =

RD$ 2110.

Here, we have,

given that,

Margarita went to the store and bought a bag and some jeans for a total of RD$3,250.

Knowing that the handbag exceeds the jeans by RD$970,

now, we have to find that, how many do she pay for each article.

let, price of jeans = RD$ x

so, price of  handbag = RD$ (x +970)

ATQ, we get,

RD$ x + RD$ (x +970) = RD$3,250

or, RD$ 2x + 970 = RD$3,250

or, RD$ 2x = RD$ 2280

or, x = RD$ 1140

Hence, price of jeans = RD$ 1140 and, price of  handbag = RD$ 2110.

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Answer:

[tex]\sqrt{2}[/tex]

Step-by-step explanation:

When t = 0, the velocity is:

[tex]\begin{aligned}\vec{v}(t)&=3^t \vec{i}+e^{6t} \vec{j}\\\\t=0 \implies \vec{v}(0)&=3^0 \vec{i}+e^{(6 \cdot 0)} \vec{j}\\ &=1 \vec{i}+1 \vec{j} \end{aligned}[/tex]

Speed is the magnitude of the velocity of the object.

[tex]\boxed{\text{A vector $\binom{x}{y}$ has magnitude $\sqrt{x^2+y^2}$}}[/tex]

Therefore, the particle's speed at time t = 0 is:

[tex]\begin{aligned}\implies |v|&=\sqrt{1^2+1^2}\\&=\sqrt{1+1}\\&=\sqrt{2}\end{aligned}[/tex]

1.) [tex]6p=30[/tex]

2.) Sebastian bought a pack of 30 mechanical pencils and plans to give the same number of pencils each to 6 friends.

Let a varible such as p be the number of pencils given by him to each students.

Now we need to find p we need to divide 30 by 6, we get

[tex]p = \frac{30}{6}[/tex]    

 [tex]to[/tex]

[tex]6p = 30[/tex]

Thus, the equation can he use to find p, the number of pencils each friend will receive is: [tex]6p = 30[/tex]

Answer:

[tex]6p = 30[/tex]

Step-by-step explanation:

3dxnn have's the explanation.

The correlation coefficient which best matches the data plotted on the graph is 0.25, the correct option is C.

We are given that;

The graph of different values of x

Now,

we can see that there is a weak positive linear relationship between x and y, as the points are scattered around a slightly upward-sloping line. The closer the points are to the line, the stronger the correlation. The farther the points are from the line, the weaker the correlation. Hence, we can expect the correlation coefficient to be a small positive number, less than 1.

Therefore, by correlation coefficient the answer will be 0.25.

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Answer:

4 minutes and 44 seconds.

Answer:

8.) is D

9.) is B

10.) is A

Step-by-step explanation:

mark brainliest

Answer: D, B, A

Step-by-step explanation:

When multiplying or dividing - and + numbers, rules are as follows:

If the signs are the same, your answer will be +

[tex]\frac{-a}{-b} =+\frac{a}{b}[/tex]

[tex]\frac{+a}{+b} =+\frac{a}{b}[/tex]

If the signs are different, your answer will be -

[tex]\frac{-a}{+b} =-\frac{a}{b}[/tex]

[tex]\frac{+a}{-b} =-\frac{a}{b}[/tex]

If there is no sign in front of number, it is positive

8.

a. 18 / -9 = -2   negative because signs are diff

b. -35 / -7  +5   signs same so +

c.  -12 / -6 = +2          same signs so +

d. 70 / -10 = -7        diff signs so -

Order from least to greatest:

-7    -2   2   5

Answer: D

9.  Follow rules from above:

Be careful with fractions  1/5  is not the same as 5/1.

With the fraction problems they do not divide into the number because 1 cannot be divided by 5 evenly, leave as a fraction and we are only taking care of the signs.

a.  +1/5

b.  -1/5

c.  +1/10

d.  +1/10

Order from least to greatest:

-1/5    1/5   1/10    1/10

Answer: B

10.

a. -2/3

b.  +1/25

c.  +3/25

d.  +1/50

The smallest number is the negative number

Answer A

Based on the information, bIda would owe $3700 at the end of 12 months.

Ida would owe $3808 at the end of 12 months.

The formula will be:

I = P * r * t

I = 2500 * 0.04 * 12 = $1200

So, Ida would owe $2500 + $1200 = $3700 at the end of 12 months.

b. For option b, , the monthly interest rate is:

r = 0.01 * 4.33 = 0.0433

Using the same simple interest expression:

I = 2500 * 0.0433 * 12 = $1308

Ida would owe $2500 + $1308 = $3808 at the end of 12 months.

Therefore, option a is the better choice due to the fact she would owe less in total with a simple interest rate of 4% annually.

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Answer:

use symbolab it will help you with almost anything

well, presumably the best deal is the cheaper one, so let's check how much is it for each

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 45.99}}{\left( \cfrac{15}{100} \right)45.99} ~~ \approx ~~ 6.90\hspace{5em}\underset{ Store~1 }{\stackrel{ 45.99~~ - ~~6.90 }{\approx\text{\LARGE 39.09}}}\checkmark \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em} \stackrel{\textit{20\% of 52.99}}{\left( \cfrac{20}{100} \right)52.99} ~~ \approx ~~ 10.60\hspace{4em}\underset{ Store~2 }{\stackrel{ 52.99~~ - ~~10.60 }{\approx\text{\LARGE 42.39}}}[/tex]

The correct statements about the capacity of swimming pool are (a) and (d)

The capacity of a swimming pool is given by C = l × w × (d₁ + d₂)/2

where l is the length,

w is the width,

d₁ is the depth of the shallow end,

and d₂ is the depth of the deep end of the pool.

If C = 9,216 ft, l = 48 ft, w = 24 ft, and d₂ = 12 ft, then d₁  would be,

9216 = 48 × 24 × (d₁ + 12)/2

d₁ + 12 = (9216 × 2) / (48 × 24)

d₁ + 12 = 16

d₁ = 4 ft

And formula for the depth of the shallow end would be,

d₁ = (2C/lw) - d₂

Therefore, the correct statements are (a) and (d)

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The complete question is:

The capacity of a swimming pool is given by C = l × w × (d1 + d2)/2, where l is the length, w is the width, d 1 is the depth of the shallow end, and d 2 is the depth of the deep end of the pool.

Select all the correct statements.

a) The depth of the shallow end is given by d1 = 2C/lw - d2.

b) If C = 9,216 ft, l = 48 ft, w = 24 ft, and d2 = 16 ft, then d1 = 4 ft.

c) The depth of the shallow end is given by 2C - d2/lw .

d) If C = 9,216 ft, l = 48 ft, w = 24 ft, and d2 = 12 ft, then d1 = 4 ft.

The three numbers are -2, 42 and 16 these we obtained by solving the equations

Let the three numbers x, y, and z. We know that:

x + y + z = 56 (Equation 1)

z - x = 44 (Equation 2)

x + y = 16 (Equation 3)

From Equation 3, we can solve for one of the variables in terms of the other:

y = 16 - x

Substituting this into Equation 1, we get:

x + (16 - x) + z = 56

Simplifying this equation, we get:

z = 40 - x (Equation 4)

Substituting Equation 4 into Equation 2, we get:

(40 - x) - x = 44

Simplifying this equation, we get:

40 - 2x = 44

Subtracting 40 from both sides, we get:

-2x = 4

Dividing both sides by -2, we get:

x = -2

z = 40 - (-2) = 42

Finally, using Equation 1, we can solve for y:

-2 + y + 42 = 56

y=16

Hence, the three numbers are -2, 42 and 16

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The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

We have,

The angle between the tangent and the radius of a circle is 90.

So,

∠1 = 90

∠2 = 90

And,

48 + 90 + 90 + ∠3 = 360 ______(1)

Solve for ∠3 from (1).

48 + 90 + 90 + ∠3 = 360

48 + 180 + ∠3 = 360

∠3 = 360 - 228

∠3 = 132

Thus,

The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

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The range of the repairs to the cars is 241.

The sample variance is 11, 671.33

The sample standard deviation would be 108.03.

Range = Maximum repair cost - Minimum repair cost

= 456 - 215

= 241

Find mean :

= (422 + 456 + 401 + 215) / 4

= 373. 5

Sample variance :

= Sum of ( each repair cost - mean ) ² / (Number of cars - 1)

= ( 2, 340.25 + 6, 812.25 + 756.25 + 25, 105.25 ) / ( 4 - 1 )

= 11, 671. 33

Sample standard deviation:

= √sample variance

= √11, 671. 33

= 108. 03

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The value of solution of the equation is,

⇒ tan x = 1 / 3

We have to given that;

The expression is,

⇒ - 2 tan (-x) = 5 tan (x) - 1

Now,, We can simplify as;

⇒ - 2 tan (-x) = 5 tan (x) - 1

⇒ - 2 (-  tan (x) ) = 5 tan (x) - 1

⇒ 2 tan (x) = 5 tan (x) - 1

⇒ 5 tan x - 2 tan x = 1

⇒ 3 tan x = 1

⇒ tan x = 1 / 3

Thus, The value of solution of the equation is,

⇒ tan x = 1 / 3

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The  area of the reduced rectangle is 1.8 unit²

The correct answer is an option (b)

Here the length of the rectangle is 15 units.

And the width of the rectangle is 12 units.

The rectangle has been reduced by a scale of 1/10

so, the new length of the rectangle is:

l = 1/10 × 15

  = 1.5 units

And the new width of the rectangle is:

w = 1/10 × 12

   = 1.2 units

We need to determine the area of the reduced rectangle.

Using the formula for area of rectagle, the area of the reduced rectangle would be:

A = l × w

A = 1.5 × 1.2

A = 1.8 unit²

Therefore, the correct answer is an option (b)

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The complete question is:

The rectangle below has been reduced by a scale of StartFraction 1 over 10 EndFraction. A rectangle has a length of 15 and width of 12. [Not drawn to scale] What is the area of the reduced rectangle?

a) 0.18 square units

b) 1.8 square units

c) 18 square units

d) 180 square units

Answer:

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Hence, we use this formula to solve for the missing length:

c^2 = a^2 + b^2

Plugging in the given values, we get:

c^2 = 12^2 + 12^2 c^2 = 144 + 144 c^2 = 288 c ≈ √288

Rounding √288 to the nearest ten gives 17. Therefore, the missing length is approximately 17.

Hence, c ≈ 17 is the answer.

Step-by-step explanation:

The requried measure of the angles is given as:

(1) ∠OLQ = 32, (2) ∠NQP = 38°, (3) ∠NLP = 38°, and (4) ∠NPL = 52°.

As shown in the figure,
(1) Following the property of angle subtended by an arc on the center of the circle and at a point on the circumference of a circle,
∠OLQ = ∠OQL = 64/2 = 32°.

(2)

Following the figure,
∠NQP = ∠LQP - ∠LQN
          = ∠LQP-[∠OQL+∠MQN]
          = 90 - [32+20]
          = 38°

Similarly,
∠NLP = 38°
∠NPL = 52°

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If the sample size was increased, the 95% confidence interval would decrease. A larger sample size would provide more precise and accurate data, resulting in a narrower confidence interval.

A confidence interval is a range of values within which a population parameter is estimated to lie with a certain level of confidence. It is commonly used in statistical inference to estimate the true value of a population parameter based on a sample from that population.

If the sample size was increased, the 95% confidence interval would likely decrease. This is because a larger sample size typically leads to more precise estimates and less variability in the data, resulting in a narrower confidence interval. However, the exact size of the decrease would depend on various factors such as the amount of variability in the data and the level of statistical significance chosen for the study.

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