Translate the sentence into an inequality.
Eight times the sum of a number and 29 is less than 17
Use the variable for the unknown number.

Answer:

if sample of 30 bulbs has 2 defective bulbs so,

there is one defective bulb every

[tex] \frac{30}{2} = 15[/tex]

bulbs.

total defective bulbs in 450 bulbs =

[tex] \frac{450}{15} = 30[/tex]

To determine the number of different ways the prizes can be awarded, we need to use the concept of combinations.

To determine the number of different ways the prizes can be awarded, we need to use the concept of combinations. Since there are 40 people purchasing raffle tickets, and 3 winning tickets are selected at random, we can find the number of ways the prizes can be awarded using the formula for combinations:

C(n, r) = n! / ((n-r)! * r!)

Where n is the total number of items and r is the number of items chosen at a time. In this case, n = 40 and r = 3:

C(40, 3) = 40! / ((40-3)! * 3!)

= 40! / (37! * 3!)

= (40 * 39 * 38) / (3 * 2 * 1)

= 9880

Therefore, there are 9,880 different ways the prizes can be awarded.

The function f(x)=ln(9.2x) is a horizontal compression of the parent function by a factor of 1/9.2

Step-by-step explanation:

The multiplication of a function by a number compresses or stretches the function vertically while to compress or stretch the function horizontally, the input variable is multiplied with a number.

i.e.

[tex]For\ f(x) => g = f(bx)[/tex]

where b is a constant.

Now

If b>0 then the function is compressed horizontally

The given function is:

[tex]f(x) = ln\ x\\Transformed\ to\\f(x) = ln\ (9.2x)[/tex]

As the variable in function is multiplied with a number greater than zero, the function will stretch horizontally.

The function f(x)=ln(9.2x) is a horizontal compression of the parent function by a factor of 1/9.2

Keywords: Transformation

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Answer:

The function f(x)=In (9.2x) is a horizontal compression of the parent function by a factor of 5/46

Step-by-step explanation:

I just took this test and that was the correct answer :( good luck everyone

Given a ratio of cheese to turkey slices is 2:3, Mr. Lynch spent $18 on cheese and $27 on turkey slices out of a total of $45.

Mr. Lynch is faced with a real-world example of the concept of ratios. In this case, the ratio of cheese to turkey slices is 2:3, meaning for every 2 parts of cheese, he's spending on 3 parts of turkey slices. The total amount spent is $45. We can solve this ratio problem to identify the individual costs for cheese and turkey slices by using a simple mathematical method.

Firstly, let's understand how a ratio works. It's a way to compare amounts of different things. Given the ratio 2:3 (cheese to turkey), add the ratio numbers together to get the total parts, i.e., 2 + 3 = 5. These 5 parts represent the total amount of $45 spent.

Next, we need to find the value of one part. To do this, divide the total amount spent by the total parts: $45/5 parts gives us 9: this determines that each part is worth $9.

Finally, to find the amounts spent on cheese and turkey slices, multiply the number of parts each item has in the ratio by the value of one part. So, for cheese, it's 2 parts x $9 = $18, and for turkey slices, it's 3 parts x $9 = $27.

In conclusion, Mr. Lynch spent $18 on cheese and $27 on turkey slices.

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Answer:

D. Reject the null hypothesis as the test statistic is greater than the critical value of z.

Step-by-step explanation:

[tex]H_{0}:[/tex] welders earn $50,000 annually

[tex]H_{a}:[/tex] welders' income does not equal $50,000 annually

Sample size 100>30, therefore we need to calculate z-values of sample mean and significance.

z-critical at 0.10 significance is 1.65

z-score of sample mean (test statistic) can be calculated as follows:

[tex]\frac{X-M}{\frac{s}{\sqrt{N} } }[/tex] where

Then z=[tex]\frac{50,350-50,000}{\frac{2,000}{\sqrt{100} } }[/tex] =

1.75.

Since test statistic is bigger than z-critical, (1.75>1.65), we reject the null hypothesis.

To answer the question, a z-test was performed comparing the sample mean income of welders to the population mean. The test statistic (1.75) was found to be greater than the critical z-value (±1.645) for a 0.10 alpha level, therefore we reject the null hypothesis.

The question is asking us to conduct a hypothesis test to determine whether shipbuilders' welders earn more or less than the population mean income of certified welders, which is $50,000. In statistics, we normally use a z-test for such a comparison when we know the population standard deviation. Given that the level of significance (alpha) is 0.10, we must find the critical z-value that corresponds to this alpha level, calculate the test statistic for the sample mean of $50,350, then compare our test statistic with the critical value to make our decision.

Since we have a large sample size (n=100) and the population standard deviation is known, a z-test is appropriate. The test statistic is calculated using the formula:

z = (X_bar- μ) / (σ/√n)

Where X_bar is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the values:

z = ($50,350 - $50,000) / ($2,000/√100) = $350 / $200 = 1.75

To determine whether to reject the null hypothesis, we must compare the test statistic to the critical value of z for a significance level of 0.10. For a two-tailed test (since we want to know if it's more or less, not just more), the critical z-values are approximately ±1.645. Since our test statistic of 1.75 is greater than 1.645, we reject the null hypothesis, implying that there is enough evidence to suggest the mean annual income of the sample of welders is different from $50,000. However, as the question does not specify the direction of the alternative hypothesis (whether we were testing for higher or lower earnings, specifically), we cannot conclude that welders earn more than $50,000 without further information.

Answer: Total amount of money earned last month = $2608.75

Step-by-step explanation:

Miguel earns 2,456.75 every month. This is his constant pay for the month. He also earns an extra 4.75 every time he sells a new gym membership.

Last month, Miguel sold 32 new gym membership. This means that the extra money that he earned for last month will be the number of new gym membership sold times the amount her earns per new gym membership sold. It becomes

32 × 4.75 = 152

Total amount of money earned last month will be sum of his monthly salary + the extra earned. It becomes

2456.75 + 152 = $2608.75

Answer:

The number of pitchers produced by each container = 16 .

Step-by-step explanation:

Given,

⇒∴ The number of cups of mix in brand A = [tex]x+4[/tex];

Number of pitchers produced by the containers :

Since both are equal:

⇒[tex]2x+8 = 4x\\8=2x\\x=4[/tex]

Thus the number of cups of mix in Brand B = [tex]x=4[/tex];

The number of pitchers produced by each container :

= [tex]\frac{4}{\frac{1}{4} } \\= 4*4\\=16[/tex]

∴The number of pitchers produced by each container = 16.

Each container can make 16 pitchers.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole.

As per the given data:

For making a pitcher of brand, A 1/2 cup of a mix is required.

For making a pitcher of brand, B 1/4 cup of a mix is required.

For brand A, 4 more cups than brand B .

Let's assume the number of cups for brand B as x

∴ Number of cups for brand A = x + 4

Total number of pitchers = Total number of cups / cups for one pitcher

For brand A number of pitchers:

= [tex]\frac{x + 4}{\frac12}[/tex] = 2(x + 4)

For brand B number of pitchers:

= [tex]\frac{x}{\frac14}[/tex] = 4x

The number of pitchers will be same for both brand A and B

∴ 2(x + 4) = 4x

= 2x + 8 = 4x

x = 4

The number of pitchers = [tex]\frac{4}{\frac14}[/tex] = 16

Hence, each container can make 16 pitchers.

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Answer:

  x² +9x +14 = 0

Step-by-step explanation:

Since the roots are integers, we can write the equation in the given form using a=1. Then b is the opposite of the sum of the roots:

  b = -((-7) +(-2)) = 9

And c is the product of the roots:

  c = (-7)(-2) = 14

So, the desired quadratic equation is ...

  x² +9x +14 = 0

_____

The attached graph confirms the roots of this equation.

_____

Another way

For root r, a factor of the equation is (x -r). For the given two roots, the factors are ...

  (x -(-7))(x -(-2)) = (x +7)(x +2)

When expanded, this expression is ...

  x(x +2) +7(x +2) = x² +2x +7x +14

  = x² +9x +14

We want the equation where this is set to zero:

  x² +9x +14 = 0

___

If a root is a fraction, say p/q, then the factor (x -p/q) can also be written as (qx -p). In this case, expanding the product of binomial factors will result in a value for "a" that is not 1.

Answer:

Step-by-step explanation:

First find the equations of the lines, then fill in the proper inequality sign.  The upper line has a y-intercept of 1 and a slope of 1/2, so the equation, in slope-intercept form is

[tex]y=\frac{1}{2}x+1[/tex]

Since the shading is below the line, the inequality sign is less than or equal to.  The inequality, then, is

[tex]y\leq \frac{1}{2}x+1[/tex]

But the solutions are in standard form, so let's do that:

[tex]-\frac{1}{2}x+y\leq  1[/tex]

AND they do not like to lead with negatives, apparently, so let's change the signs and the way the inequality is facing, as well:

[tex]\frac{1}{2}x-y\geq  -1[/tex]

Let's do the sae with the lower line.  The equation, in slope-intercept form is

[tex]y=\frac{3}{2}x-3[/tex] since the slope is 3/2 and the y-intercept is -3.  Now, since the shading is above the line, the inequality is greater than or equal to:

[tex]y\geq \frac{3}{2}x-3[/tex]

In standard form:

[tex]-\frac{3}{2}x+y\geq  -3[/tex] and not leading with a negative gives us

[tex]\frac{3}{2}x-y\leq  3[/tex]

Those 2 solutions are in choice B, I do believe.

Answer:

0.9953, 3.3629<x<4.0371

Step-by-step explanation:

Given that slader the internal revenue service claims it takes an average of 3.7 hours to complete a 1040 tax form, assuming th4e time to complete the form is normally distributed witha standard devait of the 30 minutes:

If X represents the time to complete then

X is N(3.7, 0.5) (we convert into uniform units in hours)

a) percent of people would you expect to complete the form in less than 5 hours

=[tex]100*P(x<5)\\= 0.9953[/tex]

b) P(b<x<c) = 0.50

we find that here

c = 4.0371 and

b = 3.3629

Interval would be

[tex](3.3629, 4.0371)[/tex]

Answer:

Volume of wax for 210 candles=18463.2 cubic inches

Step-by-step explanation:

Each wax candle has a cylindrical shape with

Number of candles to be made=210

Volume of one wax candle =π × [tex]r^{2}[/tex] × h

                                             =π ×[tex]2^{2}[/tex] × 7

                                             =3.14×4×7

                                             =87.92 cubic inches

Volume of 210 wax candles=210×87.92

                                              =18,463.2 cubic inches

Answer:

18,471.6

Step-by-step explanation:

Answer:

Option C) corner point or extreme point

Step-by-step explanation:

Linear Programming:

Corner Point Theorem:

Thus,

The mathematical theory behind linear programming states that an optimal solution to any problem will lie at corner point or extreme point of the feasible region

Answer:

Maximum = 540 at (6,14)

Minimum = 300 at (0,10) or (12,2).

Step-by-step explanation:

The given linear programming problem is

Minimize and maximize: P = 20x + 30y

Subject to constraint,

[tex]2x+3y\ge 30[/tex]            .... (1)

[tex]2x+y\le 26[/tex]            .... (2)

[tex]-2x+3y\le 30[/tex]            .... (3)

[tex]x,y\geq 0[/tex]

The related equation of given inequalities are

[tex]2x+3y=30[/tex]

[tex]2x+y=26[/tex]

[tex]-2x+3y=30[/tex]

Table of values are:

For inequality (1).

x      y

0     10

15     0

For inequality (2).

x      y

0     26

13     0

For inequality (3).

x      y

0     10

15     0

Pot these ordered pairs on a coordinate plane and connect them draw the corresponding related line.

Check each inequality by (0,0).

[tex]2(0)+3(0)\ge 30\Rightarrow 0\ge 30[/tex]    False

[tex]2(0)+(0)\le 26\Rightarrow 0\le 26[/tex]     True

[tex]-2(0)+3(0)\le 30\Rightarrow 0\le 30[/tex]    True

It means (0,0) is included in the shaded region of inequality (2) and (3), and (0,0) is not included in the shaded region of inequality (1).

From the below graph it is clear that the vertices of feasible region are (0,10), (6,14) and (12,2).

Calculate the values of objective function on vertices of feasible region.

Point           P = 20x + 30y

(0,10)           P = 20(0) + 30(10) = 300

(6,14)           P = 20(6) + 30(14) = 540

(12,2)           P = 20(12) + 30(2) = 300

It means objective function is maximum at (6,14) and minimum at (0,10) or (12,2).

\Given :

x^{3} +x^{2} -20x

Solution:

x^{3} +x^{2} -20x

taking x common from the given polynomial

⇒x(x^{2} +x-20)=0

⇒x(x(x+5)-4(x+5))=0

⇒x(x+5)(x-4)=0

⇒ x=0 , x+5=0 , x-4=0

⇒x = 0 , x = -5 , x = 4

The zeros of the polynomial function f(x) = x³ - x² - 20x are x = 0, x = 5, and x = -4.

To find the remaining zeros, we can use polynomial division or factoring techniques. Since the given polynomial is already in its factored form, we can use the zero-product property to find the other zeros.

The given polynomial f(x) = x³ - x² - 20x can be factored as

f(x) = x(x² - x - 20).

Now, we have two factors: x and (x² - x - 20).

To find the zeros of the second factor, we can set it equal to zero and solve for x. So, we have

x² - x - 20 = 0.

We can factor this quadratic equation by splitting the middle term:

x² - x - 20 = (x - 5)(x + 4).

Now, we have three factors: x, (x - 5), and (x + 4). To find the zeros, we set each factor equal to zero and solve for x:

x = 0 (given) x - 5 = 0 => x = 5 x + 4 = 0 => x = -4

Therefore, the zeros of the polynomial function

f(x) = x³ - x² - 20x are x = 0, x = 5, and x = -4.

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Answer:

The answer to your question is 43

Step-by-step explanation:

                  2x³  + 8x² - 5x + 5 / x - 2

Process

1.- Use synthetic division

                      2   8    -5    5     2

                           4    24  38                          

                      2  12    19   43

Quotient    2x² + 12x + 19

Remainder     43

Answer: 70

Step-by-step explanation:

8x+6=4x+38

4x=32

x=8

<B=4x+38=4*8+38=70

Answer:

x = 8

∠B = 70°

Step-by-step explanation:

∠A = ∠B through alternate exterior angles.

∠A = ∠B

8x + 6 = 4x + 38

8x - 4x + 6 = 38

4x + 6 = 38

4x = 38 - 6

4x = 32

x = 32 ÷ 4

x = 8

∠B = 4x + 38

4(8) + 38

32 + 38

= 70

Answer:

The over payment amount after 36 months is $ 0.37

Step-by-step explanation:

Given as :

The cost of the Car = $ 26,555

The number of times payment done for 36 month = 36

So, The the cost of car for 36 equal payment = [tex]\dfrac{\textrm Total cost of car}{\textrm number of times payment done }[/tex]

i.e The the cost of car for 36 equal payment = [tex]\frac{26,555}{36}[/tex]

∴ The the cost of car for 36 equal payment = $ 737.6389

Now rounding this value to nearest whole dollar = $ 738

Note - A) If after decimal , number are above 4 then round it to 1 above digit

B) If after decimal , number 4 or less then simply remove all number   after       decimal

So, The over payment after 36 months = $ 738 - $ 737.63 = $ 0.37

Hence The over payment amount after 36 months is $ 0.37   Answer

Answer:

The answers should be c. 120° and e. 240°

Step-by-step explanation:

Consider the provided information.

Equilateral triangle has 3 equal sides.

Now we need to rotate the equilateral triangle so that the equilateral triangle to map it onto itself.

For this we need to rotate each of those sides to an adjacent side. (Shown in figure)

This can be happen 3 times as there are 3 sides,

A circle has 360° and [tex]\dfrac{1}{3}\times 360^{\circ}=120^{\circ}[/tex].

Thus, a 120° rotation map it onto itself.

Any other angle multiple of 120° will do the same.

Hence, the answers should be c. 120° and e. 240°

Answer:

20

Step-by-step explanation:

Given that the area of the rectangle is equal to that of the triangle

Area of triangle $ABC$

= 1/2 (bh)

Given that the sides of the triangle are $6$ units, $8$ units, and $10$ units,

The base and the heights are $6$ units and $8$ units. The $10$ units is the hypotenuse

From Pythagoras theorem,

6^2 + 8^2 = 10^2

Therefore, area of triangle

=1/2 (6 × 8)

= $24$ units^2

Area of rectangle = L × W

Where L = Length, W = Width

Area of the rectangle = area of triangle

L × 4 = 24

L= 24/4

L = $6$ Units

Perimeter of rectangle

=2 (L + B)

= 2(6 + 4)

= $20$ Units

Answer:

20

Step-by-step explanation:

We use the Pythagorean Theorem to verify that triangle $ABC$ is a right triangle, or we recognize that $(6,8,10)$ is a multiple of the Pythagorean triple $(3,4,5)$. The area of a right triangle is $\frac{1}{2}bh$ where $b$ and $h$ are the lengths of the two legs, so the area of triangle $ABC$ is $\frac{1}{2}(6)(8)=24$. If the area of the rectangle is $24$ square units and the width is $4$ units, then the length is $\frac{24}{4}=6$ units. That makes the perimeter $6+6+4+4=\boxed{20}$ units.

Answer:

A(max)  =  42.43 in²

Dimensions:

a   =  7 in

b   =  6,06  in

Step-by-step explanation:  See annex

Equilateral triangle  side  L  = 14 in,  internal angles all equal to 60°

Let  A  area of rectangle     A  = a*b

side   b        tan∠60°  = √3    tan∠60° = b/x     b  =  √3  * x

side  a   a = L  - 2x      a =  14  - 2x

A(x) = a*b        A(x) = ( 14  -  2x  ) *  √3  * x

A(x) =  14*√3*x  - 2√3 * x²

Taking derivatives both sides of the equation

A´(x)  =  14√3  -  4√3*x

A´(x)  = 0     ⇒    14√3  -  4√3*x  =  0     ⇒ 14  - 4x  = 0    x = 14/4

x  = 3,5  in

Then  

a =   14  - 2x          a = 14 - 7       a =  7 in

b  = √3*3,5               b = *√3 *3,5      b  = 6,06 in

A(max)  =  7 *6,06  

A(max)  =  42.43 in²

Answer: length of the drive way = 56 feet

Width of the driveway = 12 feet

Step-by-step explanation:

The rectangular driveway has two equal lengths and two equal widths. The area of the driveway is expressed as

length,l × width,w

The area is 672 feet squared. It means that

L×W = 672

The length of the rectangular driveway is four feet less than five times the width. It means that

L = 5W - 4

Substituting L = 5W - 4 into LW = 672

W(5W - 4) = 672

5W^2 - 4W - 672 = 0

5W^2 + 56W - 60W - 672 = 0

W(5W + 56) - 12(5W + 56) = 0

(W - 12)(5W + 56) = 0

W - 12 = 0 or 5W + 56 = 0

W = 12 or 5W = -56

W= 12 or W = - 56/5

The Width cannot be negative , so

W = 12

LW = 672

12L = 672

L = 672/12 = 56

Answer:

0.08

Step-by-step explanation:

A standard deck contains 52 cards. There are 4 aces and 12 kings/queens/jacks. This means that there is a 4/52 (or 1/13) chance of you winning 5$, and a 12/52 (or 3/13) chance of you winning 3$. To find the expected value, we can simply find the average amount of winnings. This can be done by adding the possible winning values for each card.. Since there is a 1/13 chance that you win 5$, we can add 5*1=5 to the sum. For the kings/jacks/queens, we can add 3*3=9 to the sum. Then, since we win nothing for anything else, we can find the expected value to be 14/13 = 1.08 (approximately). Subtracting the 1$ pay, the expected net winning is 0.08, or 8 cents.

Answer: = [tex]0.444\pm 0.111[/tex]

Step-by-step explanation:

The confidence interval for population proportion(p) is given by :-

[tex]\hat{p}-E<p<\hat{p}+E[/tex]  (1)

It is also written as : [tex]\hat{p}\pm E[/tex]         (*)

The given confidence interval for population proportion :

[tex]0.333<p<0.555[/tex] (2)

Comparing (1) and (2) , we get

Lower limit = [tex]\hat{p}-E=0.333[/tex] (3)

Upper limit = [tex]\hat{p}+E=0.555[/tex]  (4)

Adding (3) and (4) , we get

[tex]2\hat{p}=0.888\\\Rightarrow\ \hat{p}=\dfrac{0.888}{2}=0.444[/tex]

Put value of [tex]\hat{p}=0.444[/tex] in (2) , we get

[tex]0.444+E=0.555\\\\\Rightarrow\ E=0.555-0.444=0.111[/tex]

Put values of [tex]\hat{p}=0.444[/tex]  and E= 0.111 in (*) , we get

Required form = [tex]0.444\pm 0.111[/tex]

The confidence interval 0.333 to 0.555 can be written in the form 0.444 +/- 0.111 This helps to clearly represent the sample proportion and its margin of error.

The confidence interval 0.333 less than p less than 0.555 can be expressed in the form Modifying Above p with caret plus or minus Upper E. To do this, we need to find the middle point of the interval, which represents the sample proportion and the margin of error (E").

The confidence interval can be written as 0.444 plus or minus 0.111.

Answer:

segment

Step-by-step explanation:

We know that a line has no end points.

If we take a part from the line then it is called line segment.

The line segment has starting point and end point.

A part of a line consisting of two endpoints and all the points between them is called segment.

Therefore, the answer is segment

Line segment

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Answer:

28.27 cm/s

Step-by-step explanation:

Though Process:

Solution:

the area of the exposed circle is

[tex]A =\pi a^2 [/tex]

the rate of change of this area can be, (using chain rule)

[tex]\frac{dA}{dt} = 2 \pi a \frac{da}{dt}[/tex] we can call this Eq(2)

what we are really concerned about is how [tex]a[/tex] changes as the punch is being poured into the bowl i.e [tex]\frac{da}{dh}[/tex]

So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:

[tex]r = \frac{a^2 + h^2}{2h}[/tex]

and rearrage the formula so that a is the subject:

[tex]a^2 = 2rh - h^2[/tex]

now we can derivate a with respect to h to get [tex]\frac{da}{dh}[/tex]

[tex]2a \frac{da}{dh} = 2r - 2h[/tex]

simplify

[tex]\frac{da}{dh} = \frac{r-h}{a}[/tex]

we can put this in Eq(1) in place of [tex]\frac{da}{dh}[/tex]

[tex]\frac{da}{dt} = \frac{r-h}{a} . \frac{dh}{dt}[/tex]

and since we know [tex]\frac{dh}{dt} = 1.5[/tex]

[tex]\frac{da}{dt} = \frac{(r-h)(1.5)}{a} [/tex]

and now we use substitute this [tex]\frac{da}{dt}[/tex]. in Eq(2)

[tex]\frac{dA}{dt} = 2 \pi a \frac{(r-h)(1.5)}{a}[/tex]

simplify,

[tex]\frac{dA}{dt} = 3 \pi (r-h)[/tex]

This is the rate of change of area, this is being asked in the quesiton!

Finally, we can put our known values:

[tex]r = 5cm[/tex]

[tex]h = 2cm[/tex] from the question

[tex]\frac{dA}{dt} = 3 \pi (5-2)[/tex]

[tex]\frac{dA}{dt} = 9 \pi cm/s// or//\frac{dA}{dt} = 28.27 cm/s[/tex]

The given graph displays a periodic function with a [tex]5[/tex]-unit period and a [tex]3[/tex]-unit amplitude. Therefore, option C is correct, accurately describing the function's characteristics based on the observed graph.

The given graph indicates a periodic function with repeating patterns. The period is the horizontal distance between two successive peaks or troughs. In this case, the graph repeats every [tex]5[/tex] units horizontally, so the period is indeed [tex]5[/tex]. The amplitude is the vertical distance from the midline to the peak or trough.

Here, the vertical distance is [tex]3[/tex] units, confirming the amplitude as [tex]3[/tex].

Therefore, according to the graph, option C is correct with a period of [tex]5[/tex] and an amplitude of [tex]3[/tex], aligning with the observed characteristics of the function's periodicity and vertical range.

Answer:

Ik sorry but you can

Step-by-step explanation:

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The student needs to find the decryption exponent 'd' for the RSA algorithm by computing the modular multiplicative inverse of e modulo φ(n), and then use that to decrypt the message.

The student is asking how to decrypt a message that was encrypted using the RSA algorithm. The given public key consists of n = 43 · 59 and e = 13, and the encrypted message is 0667 1947 0671. To decrypt the message, we need to find the private key, which includes the decryption exponent d. The decryption exponent is the modular multiplicative inverse of e modulo φ(n), where φ(n) is the Euler's totient function of n. Since n is the product of two primes, 43 and 59, φ(n) is (43-1)(59-1) which equals 42 · 58. Now, we need to find d such that it satisfies the congruence ed ≡ 1 (mod φ(n)), which will be d = 13⁻¹ mod 42 · 58. Once d is computed, we can decrypt each part of the message using the formula M = C^d mod n, where M is the original message and C is each part of the encrypted message.

Answer:

The Total distance she travel fro work is 30 miles  .

Step-by-step explanation:

Given as :

the total time taken to cover distance = 45 minutes

Let The total distance cover = D miles

The distance cover at the speed of 32 mph = [tex]D_1[/tex] miles

The time taken to cover [tex]D_1[/tex] miles distance = [tex]\frac{1}{2}[/tex] hour

Distance = Speed × Time

∴  [tex]D_1[/tex] = 32 mph  ×  [tex]\frac{1}{2}[/tex] h

or, [tex]D_1[/tex] = 16 miles

Again ,

The distance cover at the speed of 56 mph = [tex]D_2[/tex] miles

The time taken to cover [tex]D_2[/tex] miles distance =  [tex]\frac{1}{4}[/tex] hour

∴  [tex]D_2[/tex] = 56 mph  ×  [tex]\frac{1}{4}[/tex] h

or, [tex]D_2[/tex] = 14 miles

So , The total distance she travel for work =  [tex]D_1[/tex]  +  [tex]D_2[/tex]

Or, The total distance she travel for work = 16 miles + 14 miles = 30 miles

Hence The Total distance she travel fro work is 30 miles  . Answer

Answer:

Step-by-step explanation:

Area of rectangle = Length × Width

The given rectangle has a length if x meters

The width of the triangle is (x-3) meters

The area of the rectangle is given as 10 square meters.

Area if rectangle = x(x-3) = 10

Multiplying each term in the parentheses,

x^2 -3x = 10

x^2 -3x -10 = 0

This is a quadratic equation

We will look for two numbers such that when they are multiplied, it will give us -10x^2 and when they are added, it will give -3x. It becomes

x^2 + 2x - 5x -10 = 0

x(x+2)-5(x+2) =0

( x + 2)(x-5) = 0

x = -2 or x = 5

The length of the rectangle cannot be negative so the length is 5 meters

Widith = x+3 = 5-3 = 2 meters

Final answer:

The dimensions of the rectangle are found by solving the quadratic equation derived from the area. The length is 5 meters, and the width is 2 meters, as negative dimensions are not possible.

Explanation:

To find the dimensions of the rectangle with an area of 10 square meters and the sides defined as x and x
- 3, we have derived a quadratic equation x^2 - 3x - 10 = 0 which factors down to (x + 2)(x - 5) = 0. This gives us two possible solutions for x: either x + 2 = 0 or x - 5 = 0. Solving these equations, we find x = -2 or x = 5. Since a rectangle cannot have a negative dimension, we disregard x = -2. Therefore, the length of the rectangle is x = 5 meters and the width is x - 3 = 2 meters.

Answer:

47.5%

Step-by-step explanation: