Write a function rule to describe this statement-

A model is %60 of the size of the real item.

Answer:

  ₹168 per hour

Step-by-step explanation:

The hourly rate at which Tamara is paid can be found by dividing her ₹1050 pay by the 6:15 hours that she worked.

We know there are 60 minutes in an hour, so the fraction of an hour represented by 15 minutes is ...

  (15 min)/(60 min/h) = (15/60) h = 1/4 h = 0.25 h

Added to the 6 whole hours Tamara worked, her pay is for 6.25 hours.

The pay per hour is found by dividing pay by hours.

  ₹1050/(6.25 h) = ₹168/h

Tamara's hourly rate of pay is ₹168 per hour.

Answer:

150 + 1.5d

Step-by-step explanation:

increase 120 by d%

d% = d/100

So, increasing 120 by d % means

120 + (d/100 * 120)

= 120 + 1.2d

Then increase this by 25%

= (120 + 1.2d) + 25/100(120 + 1.2d)

= 120 + 1.2d + (120+1.2d)/4

= 120 + 1.2d + 30 + 0.3d

= 120 + 30 + 1.2d + 0.3d

= 150 + 1.5d

The value of z-score for a score that is three standard deviations above the mean is 3.

In this question,

A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.

Let x be the score

let μ be the mean and

let σ be the standard deviations

Now, x =  μ + 3σ

The formula of z-score is

[tex]z_{score} = \frac{x-\mu}{\sigma}[/tex]

⇒ [tex]z_{score} = \frac{\mu + 3\sigma -\mu}{\sigma}[/tex]

⇒ [tex]z_{score} = \frac{ 3\sigma }{\sigma}[/tex]

⇒ [tex]z_{score} = 3[/tex]

Hence we can conclude that the value of z-score for a score that is three standard deviations above the mean is 3.

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Answer:

last choice

Step-by-step explanation:

The domain is the set of x values: from -3 to 3.

The range is the set of y values: from 1 to 10.

Answer: last choice

The median of an equilateral triangle are equal has been proved.

The medians are given as AD, BE, and CF.

Let AB = AC = BC = x unit.

In triangles, BFC and CEB, we've

BF = CE.

ABC = ACB since they're both 60°

BC = BC

By SAS congruence,

BFC = CEB = BE = CF.

Similarly, we've AB = BE

Therefore, AD = BE = CF

median of an equilateral triangle are equal has been proved.

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Answer:

(-4,-4)

Step-by-step explanation:

If the point is moved 2 units to the rights then we add 2 to the x value: -6+2 = -4

(-4,-4)

Answer:

last answer:

h(x) = 1/4 x

Step-by-step explanation:

First, change f(x) to y.

f(x) = 4x

y = 4x

Then switch the x and y.

y = 4x

x = 4y

Last, solve for y.

x = 4y

x/4 = 4y/4

x/4 = y

y = x/4

This is the same as:

y = 1/4 x

h(x) = 1/4 x

The geometric series which result in a sum of -69,905 is: D. [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]

Mathematically, the standard form of a geometric series can be represented by the following expression:

[tex]\sum^{n-1}_{k=0}a_1(r)^k[/tex]

Where:

Also, the sum of a geometric series is given by:

[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]

For option A, we have:

r = -5, n = 8, a₁ = 1/4 = 0.25

[tex]S=\frac{0.25(1-(-5)^8)}{1-(-5)}[/tex]

S = -24,414.

For option B, we have:

r = 5, n = 12, a₁ = -1/4 = -0.25

[tex]S=\frac{-0.25(1- 5)^{12})}{1-5}[/tex]

S = -15,258789.

For option C, we have:

r = -4, n = 11, a₁ = 1/5 = 0.2

[tex]S=\frac{0.2(1-(-4)^{11})}{1-(-4)}[/tex]

S = -279,620.

For option D, we have:

r = 4, n = 10, a₁ = -1/5 = -0.2

[tex]S=\frac{-0.2(1-4^{10})}{1-4}[/tex]

S = -69,905.

In conclusion, the geometric series which result in a sum of -69,905 is [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]

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Answer:

x < -41/6 or x > -13/6.

Step-by-step explanation:

5/2+x>1/3

x > 1/3 - 5/2

x > 2/6 - 15/6

x > -13/6

x+2 < -29/6

x < -29/6 - 2

x < -41/6

The answer is     x < -41/6 or x > -13/6.

Answer:

x > -13/6 or x < -41/6

Step-by-step explanation:

5/2+x>1/3 or x+2 < -29/6

x > 1/3 - 5/2 or x < -29/6 - 2

x > 2/6 - 15/6 or x < -29/6 - 12/6

x > -13/6 or x < -41/6

Answer:

875

Step-by-step explanation:

1-0.32=0.68 so its 0.68 of its original price.

x*0.68=595 x is the original price

x=595/0.68

x=875

Option C is the correct choice   [tex]-2x^4+4x^2+3x-2[/tex],

Remainder of a polynomial by substitution

For a polynomial f(x) to give a remainder of 24 when divided by x + 2:

f(-2) = 24

By testing, substitute x = -2 into the equation [tex]-2x^4+4x^2+3x-2[/tex]

[tex]f(x) = -2x^3+4x^2+3x-2\\\\f(-2)=-2(-2)^3+4(-2)^2+3(-2)-2\\\\f(-2)=-2(-8)+4(4)-6-2\\\\f(-2)=16+16-8\\\\f(-2)=32-8\\\\f(-2)=24[/tex]

Since f(-2) = 24 when x = -2 is substituted into  [tex]-2x^4+4x^2+3x-2[/tex], then  [tex]-2x^4+4x^2+3x-2[/tex] has a remainder of 24 when divided by x+2

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The t-test statistic is used to evaluate whether there is any significant difference between the mean hourly wages.

To evaluate whether there is a statistically significant difference between the means of two variables, a t-test is an inferential statistic that is utilized.

A statistical test for assessing hypotheses is the t-test.

The difference between the means from each data set, the standard deviation of each group, and the total number of data values are the three basic data values needed to do a t-test.

There are independent and dependent T-tests.

The problem statement is established mathematically by using a sample from each of the two sets in the t-test. It presupposes that the two means are equal, which is the null hypothesis.

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440 repeat 11 more times.

400+(400*.1)=440 repeat 11 more times. Remember to use a new value each time.

Vacations can get expensive fast. The average cost per person for a week-long vacation is about $1,200 annually. So, if you've got a family of five, you'll need to sock away at least $6,000 for transportation, hotels, meals, and amusement parks.

Financial experts suggest that the average family vacation costs between 5-10% of your total income. If your family makes $40,000 per year then experts say your yearly family vacation budget should average between $2,000-$4000.

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Answer:

C . Sixteen and four eighths.

Step-by-step explanation:

2 6/8 * 6

= 22/8 * 6

= 6*22 / 8

= 132/8

= 16 4/8.

Answer: plot points (0,-2) (1.-5) (2.-8) (-1.1) (-2.1) makes a upside down V

-3|0+2|+4=-2

-3|1 +2|+4= -5

-3|2+2|+4= -8

-3|-1+2|+4=1

+3|-2+2|+4=1

Step-by-step explanation:

Using the concept of an one-to-one function, it will be one-to-one for c = 13.

A function is said to be one-to-one if each output is mapped to only one input.

In this problem, outputs 2, 5 and 11 have already been matched to inputs 1, 3 and 5, respectively, hence the output for input 6 has to be c = 13 for a one-to-one function.

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Answer:

Step-by-step explanation:

Our equation will be 3x+8=20.6

3x=12.6

x=4.2

The given points on the final image A''B''C''D'', and the transformation gives;

The coordinates of the vertex A of square ABCD is the option;

D. A(-2, 1)

From the figure, we have;

A''(-5, -3), B''(-3, -1), C''(-1, -3), D''(-3, -5)

The given transformation is presented as follows;

[tex] T_{ (- 4 , \: - 1)} \circ \:R_ {( O , \: 90^{ \circ} )}[/tex]

The formula for a rotation of 90° about the origin is presented as follows;

Therefore;

Therefore;

A''(-5, -3) → A'(-5 + 4, -3 + 1) = A'(-1, -2)

B''(-3, -1) → B'(-3 + 4, -1 + 1) = B'(1, 0)

C''(-1, -3) → C'(-1 + 4, -3 + 1) = C'(3, -2)

D''(-3, -5) → D'(-3 + 4, -5 + 1) = D'(1, -4)

The coordinates of the vertex A of square ABCD is therefore;

D. A(-2, 1)

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Square A"B"C"D" has vertex A" at (-5, -3), the coordinates of vertex A before the transformation is A(-2, 1)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation.

Square A"B"C"D" has vertex A" at (-5, -3), the coordinates of vertex A before the transformation is A(-2, 1)

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The number from the grid that fulfills all the given clues is; 12

The grid is shown in the attached image.

Now, we are told that Manju and Arif are thinking of a number on the grid and the clues are;

It is a multiple of 3.

It is even.

It is in the third row.

Now, looking at the third row, we see the numbers as;

11, 12, 13, 14, 15

Now, the only number that fulfills all the given clues is 12.

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Answer:

27 cm³

Step-by-step explanation:

To find the volume, multiply the length, the width, and the depth together.

3*3*3=27

The volume of the cube is 27 cm³

Hope this helps!

If the test gives positive results for 95% of those having disease and correctly gives negative results for 90% of those who don't have disease and the incidence of the disease is 1% then the chance of having disease is 0.0105.

Given that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease.

We have to calculate the chance of having disease.

Probability that test is correct in determining the disease when person is suffering from it is 0.95.

Probability that test is not correct in determining the disease when person is suffering from it is 1-0.95=0.05.

Probability that test is correct in determining that the person is not suffering from disease  when person is not suffering from it is 0.90.

Probability that test is not correct in determining that the person is not suffering from disease  when person is not suffering from it is 1-0.9=0.10.

The chance of having disease is equal to incidence of disease multiplied by probabilities that the test has corectly determined disease when personis suffering from it and when test is not able to determine the disease when person is suffering from it.

Chance=0.01*0.95+0.01*0.10

=0.0095+0.001

=0.0105.

Hence the chance of having disease is 0.0105.

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The answer is 8300.

Divide 91300 by 11 you will get the answer.

Problem-solving is the act of defining trouble; figuring out the cause of the problem; figuring out, prioritizing, and choosing alternatives for an answer; and enforcing a solution.

Problem-fixing starts with identifying the difficulty. For instance, a teacher might want to discern the way to improve student performance on a writing talent test. To do that, the trainer will assess the writing checks looking for areas of development.

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Answer:

A

Step-by-step explanation:

[tex]\cos \theta=\frac{3}{8} \\ \\ \theta=\cos^{-1} \left(\frac{3}{8} \right) \\ \\ \theta \approx 68^{\circ}[/tex]

The minimum possible distance that Fyodor could be from Alyosha is 4 meters.

Given Information and Deduction

It is given that Fyodor is 3 meters in distance away from Dmitri and 5 meters from Ivan.

Now, since we know that the longest side of a right angle triangle formed by the dividing the rectangular room into two parts using a diagonal is the hypotenuse. Thus, if we want to find the minimum possible distance between Fyodor and Alyosha, we will have to assume that Ivan is standing diagonally opposite to Fyodor, as shown in the figure below.

Calculating the Minimum Distance

According to Pythagoras Theorem,

(hypotenuse)² = (base)² + (perpendicular)²

Here, the hypotenuse is the distance between Fyodor and Ivan.

Perpendicular and the base are the distances between Fyodor and Dmitri, and Fyodor and Alyosha respectively.

⇒ base = √(hypotenuse)² -(perpendicular)²

⇒ base = √(5)²-(3)²

⇒ base = √(25-9)

⇒ base = √16

⇒ base = 4 meters

Therefore, the minimum possible distance between Fyodor and Alyosha is 4 meters.

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The calculated probabilities are

Probability = 60/110

= 0.5455

probability = 65/110

= 0.5909

Probability = 30/65

= 0.4615

25/45

= 0.5556

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Answer:

1540

Step-by-step explanation:

This is an arithmetic progression.

a = first term = 10

Common difference = d = second term - first term

                                         = 12 - 10

                                     d  = 2

Last term = l = 78

First we have to find how many terms are there in the sequence using the formula:  l = a + (n-1)*d

                   78 = 10 + (n -1) * 2

               78 -10 = (n -1)*2

                     68 = (n -1) *2

               68 ÷2 =  n -1

                      34 = n - 1

                 34 + 1 = n

                         n = 35

There are 35 terms.

  [tex]\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}}[/tex][tex]\sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}[/tex]

            [tex]\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540[/tex]

Step-by-step explanation:

This is an arithmetic progression.

a = first term = 10

Common difference = d = second term - first term

= 12 - 10

d = 2

Last term = l = 78

First we have to find how many terms are there in the sequence using the formula: l = a + (n-1)*d

78 = 10 + (n -1) * 2

78 -10 = (n -1)*2

68 = (n -1) *2

68 ÷2 = n -1

34 = n - 1

34 + 1 = n

n = 35

There are 35 terms.

\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}} \sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}

Sum =

2

n

(a+l)

\begin{gathered}\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540\end{gathered}

=

2

35

(10+78)

=

2

35

∗88

=35∗44

=1540

The given statement is True for the scoring rule in bowling.

Scoring Rule in Bowling

The number of frames in a game of bowling is ten. According to the scoring rule in bowling, the bowler will have two opportunities to use their bowling ball to remove as many pins as they can throughout each frame.

Every bowler will complete their frame in a predefined order before the next frame starts in games with more than one bowler, which is typical.

Rule for Spare

A bowler is given a strike if they can remove all 10 pins with their first ball. A spare is achieved when the bowler uses both of the two balls in a frame to remove all 10 pins.

Depending on whether the next two balls (for a strike) or the next ball (for a goal) are scored, bonus points are given for both of these (for a spare), as per the scoring rule.

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Answer: Yes

Step-by-step explanation:

Since ABCD is a rectangle, [tex]\angle AXY[/tex], [tex]\angle YBZ[/tex], [tex]\angle WCZ[/tex], and [tex]\angle WDX[/tex] are all right angles, and are thus all congruent because all right angles are congruent. Furthermore, because ABCD is a rectangle, we know that [tex]\overline{AB} \cong \overline{CD}[/tex] and [tex]\overline{AD} \cong \overline{BC}[/tex]. Because we are given that X, Y, Z, and W are midpoints, using the fact that halves of congruent segments are congruent, we can conclude that [tex]\overline{AY} \cong \overline{YB} \cong \overline{CW} \cong \overline{WD}[/tex] and that [tex]\overline{AX} \cong \overline{XD} \cong \overline{BZ} \cong \overline{ZC}[/tex]. As a result, we can conclude that [tex]\triangle AYX \cong \triangle DXW \cong \triangle CWZ \cong \triangle BYZ[/tex] by SAS, and thus by CPCTC, [tex]\overline{AY} \cong \overline{XW} \cong \overline{ZW} \cong \overline{YZ}[/tex]. Therefore, since the quadrilateral formed by the midpoints has four congruent sides, it must be a rhombus.

Answer: 120 days

Step-by-step explanation:

A can complete it in 16 days.

=100/16 =6.25%/day.

B has ten days to do it.

10% every day is equal to 100/10.

So they would each contribute 16.25 percent per day as a group.

then for six days,

16.25*6 =97.50percent

97.50% of the work has been finished, in other words.

The amount of work left is now 100-97.5 = 2.5.

C finishes up the remaining job in 3 days

3.5% in 3 days, to be exact.

Consequently, he will finish his entire project in 120 days.

[2.5 * 40 = 100 percent; 40 * 3 = 120 days]

There are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence. This can be obtained by forming the arithmetic sequence, equating by Pythagoras theorem and finding numbers divisible by the integral.

Let the arithmetic sequence be (a - d), a, (a+d)

Using Pythagoras theorem,

(a - d)² + a² = (a+d)²

a² -2ad + d² + a² = a² + 2ad + d²

2a² - 2ad + d² = a² + 2ad + d²

2a² - a² + d² - d² = 2ad + 2ad

a² = 4ad

a = 4d

Thus hypotenuse will be (a + d) = 4d + d = 5d

Since the value of hypotenuse is 5d, the total numbers divisible by 5 between 1 and 2020 will be the number of possible sides of the hypotenuse.

There are 2020 numbers between 1 and 2020 inclusive

The numbers divisible by 5 = 2020/5 = 404

Hence there are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence.

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