What is the rule for the reflection?
rx-axis (x, y) - (-x, y)
ry-axis (x, y) (-x, y)
rx-axis (x, y) - (x, y)
ry-axis (x, y) (x, −y)

Answer:

  8 cylinders

Step-by-step explanation:

The surface area of a cylinder is given by the formula ...

  A = 2πr(r +l) . . . . . for radius r and length l

__

The cylinders Rufus has each have an area of ...

  A = 2π(5 cm)(5 cm +4 cm) = 90π cm² ≈ 282.74 cm²

That means 2500 cm² of paint will cover ...

  2500 cm²/(282.74 cm²/cylinder) ≈ 8.84 cylinders

Rufus has enough paint to cover 8 cylinders completely.

Answer:

16П or approximately 50.3)

Step-by-step explanation:

The area of a circle is equal to П*r²

Since the circle is inside a rectangle with side that is equal to 8, we know that d = 8

2r = d

r = 8/2

r = 4

A = П*r²

A = П*16

А = 16П ( or 16*3.141592653589793238... = 50.26548... ≈ 50.3)

Answer:

area = 50.27 [tex]cm^2[/tex]

Step-by-step explanation:

In the diagram, we see that the diameter of the circle is 8cm. Therefore the radius of the circle is 8/2 = 4cm.

[tex]area \hspace{0.15cm}of \hspace{0.15cm}circle = $\pi$r^2[/tex]

                        = π [tex](4)^2[/tex]

                        = 50.27 [tex]cm^2[/tex]

Using the permutation formula, it is found that there are 57,120 ways to fill the 4 positions.

There are different roles, hence the order is important, which means that the permutation formula is used.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 4 roles are chosen from a set of 17, hence the number of ways is given by:

[tex]P_{17,4} = \frac{17!}{13!} = 57120[/tex].

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She should spend 1 hour working on problems , 3 hour reading , Option B is the right answer.

The gain of the desired effect with respect to the previous gain is called margin gain

The marginal gain from 8:00 am to 9:00 am is

(40-0) = 40 problems

The marginal gain from 9:00 am to 10:00 am is

= 70-40 = 30 problems

The marginal gain from 10:00 am to 11:00 am is

(90-70) = 20 problems

As if she does more than one hour of problem solving her productivity decreases to 30 which is less than 1 hour of reading textbook

Therefore she should not spend more than 1 hour on problem solving.

Therefore Option B is the right answer.

1 hour working on problems , 3 hour reading

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:f(4)= -1 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

If a point point (x , y) satifys a function, then it can be written as :

[tex]\qquad \tt \rightarrow \: f(x) = y[/tex]

Here, point (x , y) is replaced by (4 , -1)

[tex]\qquad \tt \rightarrow \: f(4) = - 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.

If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.

We have:

The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67.

As we know, from the empirical rule, 68% of the data will lie in one standard deviation of the mean, i.e., in the interval with the endpoints x±s

for samples and with endpoints u±б for the population.

x = 91.9

s = 4.67

x - s = 91.9 - 4.67 = 87.23

x + s = 91.9 + 4.67 = 96.57

68% of the day's sales will be between 87.23 and 96.57

95% of the data will lie within two standard deviations of the mean, which means in the interval with the endpoints  x±2s for samples and with endpoints  u±б population.

x - 2s = 82.56

x + 2s = 101.24

On 95% of the days, sales will be between 82.56 and 101.24

Thus, 68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.

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Answer:

A = 5, B = 9, C = 6

Step-by-step explanation:

let me know if you want an explanation :))

The values are x= -2 and x =4 of the given function f (x) =-5|x+1| +3

Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

According to the question,

The given function is

[tex]f(x) = -5|x + 1| + 3[/tex]

Here f(x) = -12

Substitute f(x) and solve for x

[tex]- 12 = -5|x + 1| + 3[/tex]

By subtracting 3 on both sides

[tex]- 12 - 3 = -5|x + 1| + 3 - 3[/tex]

[tex]- 15 = -5|x + 1|[/tex]

By dividing -5 on both sides

[tex]3 = |x + 1|[/tex]

We get absolute values for the function.

[tex]x + 1 = 3 , x + 1 = -3[/tex]

By subtracting 1 on both sides

[tex]x + 1 - 1 = 3 - 1 = 2\\\\x + 1 - 1 = - 3 - 1 = -4\\\\x = 2 , x = - 4[/tex]

Therefore, the values of x are 2 and - 4 of the given function f (x) =-5|x+1| +3

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Answer:

x=0

Step-by-step explanation:

when the reflection falls on the y-axis the answer is x=0

Answer:

area of a parallelogram equals to 1/2 x base x perpendicular height and area of a triangle equals to 1/2 base times height so you ought to search for the base in order to get the area of the triangle needed that's how I got the answer bye.

You are given the equation

A(t) = P*e^(rt)

Where P = Principal

r = interest rate

t = time

e is a mathematical constant equivalent to approx 2.71828

You're told the initial Principal is $500, the interest rate is 3%, over 6 years. So you have everything that you need to solve the problem, just plug in the values and solve for A(6)

A(t) = P*e^(rt)

A(6) = 500 * e^(0.03 * 6)

A(6) = 500 * e^(0.18)

A(6) = 500 * 2.71828^(0.18)

A(6) = 500 * 1.19721

A(6) = 598.60861

So $500 invested 6 years ago at 3% would be worth $598.61 today.

The measure of the angles are Z = 90, X = 90, V = 90, Y = ∠20, W = ∠8 and W = ∠20

The sum of angles on a straight line is 180 degrees.

This means that:

Z + 90 = 180

X + 90 = 180

V + 90 = 180

Solve for the variables

Z = 90;

X = 90

V = 90

Also, alternate angles are equal.

This means that:

Y = ∠20

W = ∠8

This is so because the above angles are alternate angles.

Lastly, corresponding angles are equal.

So, we have:

W = ∠20

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Answer:

B

Step-by-step explanation:

when x is 0 y=4(0)+12 y=12

y is 0 y=4(-3) +12 = 12=12

Answer:

3

Step-by-step explanation:

1: Turn the mixed fraction into improper.

2: Multiply 3/5 to each side

3: The you get x = 3

You need to multiply the fraction instead of division because multiplying by the reciprocal is the same as dividing the normal fraction.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5 = 1\dfrac{2}{3}x}[/tex]

[tex]\mathsf{1\dfrac{2}{3}x = 5}[/tex]

[tex]\mathsf{\dfrac{1\times3 + 2}{3}x = 5}[/tex]

[tex]\mathsf{\dfrac{3 + 2}{3}x = 5}[/tex]

[tex]\mathsf{\dfrac{5}{3}x = 5}[/tex]

[tex]\large\textbf{MULTIPLY }\rm{\bf \dfrac{3}{5}}\large\textbf{ to BOTH SIDES}[/tex]

[tex]\mathsf{{\dfrac{3}{5}\times\dfrac{5}{3}x= \dfrac{3}{5}\times 5}}[/tex]

[tex]\large\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathsf{x = \dfrac{3}{5}\times5}[/tex]

[tex]\mathsf{x = \dfrac{3}{5}\times\dfrac{5}{1}}[/tex]

[tex]\mathsf{x = \dfrac{3\times5}{5\times1}}[/tex]

[tex]\mathsf{x = \dfrac{15}{5}}[/tex]

[tex]\mathsf{x = 15\div5}[/tex]

[tex]\mathsf{x = 3}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Part A

Part B

Two figures are congruent if they have the same shape and size.  (They are allowed to be rotated, reflected and translated, but not resized).

Therefore, ABCD and A'B'C'D' are congruent.  They are the same shape and size as they have only be reflected and translated.

Answer:

Correct answer is B, 69.3 feet

Step-by-step explanation:

Since we have a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg, so the length of the shorter leg is 1/√3, or √3/3 times the length of the longer leg.

[tex]120( \frac{ \sqrt{3} }{3}) = 40 \sqrt{3} = 69.3[/tex]

Answer:

[tex]\boxed {C. -2}[/tex]

Step-by-step explanation:

[tex]\textsf {Substitute x = 5 in the expression :}[/tex]

[tex]\longrightarrow \mathsf{\frac{15 - x}{x - 10}}[/tex]

[tex]\longrightarrow \mathsf{\frac{15 - 5}{5 - 10}}[/tex]

[tex]\longrightarrow \mathsf{\frac{10}{-5}}[/tex]

[tex]\longrightarrow \mathsf{-2}[/tex]

Answer:

[tex]360xy^2|xz^3|[/tex]

Step-by-step explanation:

Given expression:

[tex]12x \sqrt{900x^2y^4z^6}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 12x \sqrt{900}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}[/tex]

Replace 900 with 30² :

[tex]\implies 12x \sqrt{30^2}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies 12x \cdot 30|x|\sqrt{y^4}\sqrt{z^6}[/tex]

[tex]\implies 360x|x|\sqrt{y^4}\sqrt{z^6}[/tex]

(We need to use the absolute value of √x² since the x term was originally to the power of 2, which means the value of x² is always positive since the exponent is even).

[tex]\textsf{Apply exponent rule} \quad \sqrt{a^m}=a^{\frac{m}{2}}:[/tex]

[tex]\implies 360x|x|\cdot y^{\frac{4}{2}}\cdot z^{\frac{6}{2}}[/tex]

Simplify:

[tex]\implies 360xy^2|xz^3|[/tex]

(We need to use the absolute value of z³ since the z term was original to the power of 6, which means the value of z⁶ is always positive since the exponent is even).

Explanation:

Add up the given decimal values

0.03+0.14+0.65+0.08 = 0.90

Recall that all of the P(X) values must add to 1 to represent 100% of all possible outcomes. So far we added to 0.90, so we're missing 1 - 0.90 = 0.10

As a check,

0.03+0.14+0.65+0.08 + 0.10 = 1

All the equations have been solved

A quadratic equation is what can be represented by

ax² +bx+c = f(x)

It is given to solve the given quadratic equations

1.  x² = 25

x = ± 5

2. 16x² = 25

x² = 25/16

x = ± 5/4

3. (3x+2)²= 25

9x² +4+12x = 25

9x² +12x -21 = 0

3x(3x+7) -3(3x+7) = 0

x =1

x = -7/3

4. x² = 11x

x² -11x = 0

x (x-11) = 0

x = 0, 11

5. 3x²= 14x

3x² -14x = 0

x (3x - 14) = 0

x = 0 , 14/3

6. x²+2x = 3

x²+2x -3 = 0

x (x+3) -1(x+3) = 0

x = 1 ,-3

7.x²+2x -5 = 0

determined from the formula for the roots

x=−1±√6

x=1.44949

x=−3.44949

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L1 and L2 are parallel

so the interior alternate angles are equal

4y - 40 = 3y ( interior alternate angles)

4y - 40 = x + 15 ( vertically opposite angles).

solving the first equation, we get

4y - 3y = 40

y = 40°

putting values of y= 40° in eq. 2, we get

4y - 40= x + 15

4(40) - 40 = x + 15

160 -40 = x + 15

120 - 15 = x

105° = x

Answer:

18

Step-by-step explanation:

Using order of operations:

[tex] \frac{15 - 9}{3} (19 - 10)[/tex]

[tex] \frac{6}{3} (9)[/tex]

[tex]2(9) = 18[/tex]

Answer:

[tex]\boxed {1)log_{b}(75) = 4.317}[/tex]

[tex]\boxed {2)ln(20) = 2.9957}[/tex]

Step-by-step explanation:

[tex]\textsf {Question l :}[/tex]

[tex]\longrightarrow \mathsf {log_{b}(3) = 1.099}[/tex]

[tex]\longrightarrow \mathsf {log_{b}(5) = 1.609}[/tex]

[tex]\textsf {Identities applied :}[/tex]

[tex]\boxed {log(ab) = loga + logb}[/tex]

[tex]\boxed {log(a)^{x} = xloga}[/tex]

[tex]\textsf {We can rewrite the problem as :}[/tex]

[tex]\longrightarrow \mathsf {log_{b}(75)}[/tex]

[tex]\longrightarrow \mathsf {log_{b}(25 \times 3)}[/tex]

[tex]\longrightarrow \mathsf {log_{b}(5^{2} \times 3)}[/tex]

[tex]\longrightarrow \mathsf {log_{b}(5)^{2} + log_{b}(3)}[/tex]

[tex]\longrightarrow \mathsf {2log_{b}(5) + log_{b}(3)}[/tex]

[tex]\textsf {Now, substitute the values :}[/tex]

[tex]\longrightarrow \mathsf {2(1.609) + (1.099)}[/tex]

[tex]\longrightarrow \mathsf {3.218 + 1.099}[/tex]

[tex]\longrightarrow \mathsf {4.317}[/tex]

[tex]\boxed {log_{b}(75) = 4.317}[/tex]

[tex]\textsf {Question ll :}[/tex]

[tex]\longrightarrow \mathsf {ln(4) = 1.3863}[/tex]

[tex]\longrightarrow \mathsf {ln(5) = 1.6094}[/tex]

[tex]\textsf {Rewriting the problem :}[/tex]

[tex]\longrightarrow \mathsf {ln(20)}[/tex]

[tex]\longrightarrow \mathsf {ln(4 \times 5)}[/tex]

[tex]\longrightarrow \mathsf {ln(4) + ln(5)}[/tex]

[tex]\longrightarrow \mathsf {1.3863 + 1.6094}[/tex]

[tex]\longrightarrow \mathsf {2.9957}[/tex]

[tex]\boxed {ln(20) = 2.9957}[/tex]

Answer:

[tex]\sf \log_b(75)=4.317[/tex]

[tex]\sf \ln (20)=2.9957[/tex]

Step-by-step explanation:

Question 1

Given:

  [tex]\sf \log_b(3)=1.099[/tex]

  [tex]\sf \log_b(5)=1.609[/tex]

To evaluate [tex]\sf \log_b(75)[/tex],  replace 75 with (5 × 5 × 3):

[tex]\implies \sf \log_b(5 \cdot 5 \cdot 3)[/tex]

[tex]\textsf{Apply the Product log law}: \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\implies \sf \log_b5+\log_b5+\log_b3[/tex]

Substitute the given values to solve:

[tex]\implies \sf 1.609 + 1.609 + 1.099=4.317[/tex]

Question 2

Given:

  [tex]\sf \ln(4)=1.3863[/tex]

  [tex]\sf \ln(5)=1.6094[/tex]

To evaluate ln(20) replace 20 with (4 × 5):

[tex]\implies \sf \ln (4 \cdot 5)[/tex]

[tex]\textsf{Apply the Product log law}: \quad \ln xy=\ln x + \ln y[/tex]

[tex]\implies \sf \ln (4)+\ln (5)[/tex]

Substitute the given values to solve:

[tex]\implies \sf 1.3863+1.6094=2.9957[/tex]

If [tex]m=-4[/tex]

and a point is [tex](2,3)[/tex]

[tex]y=mx+b[/tex]

[tex]3=(-4)(2)+b[/tex] using the point and the slope

[tex]3=-8+b[/tex]

[tex]b=8+3[/tex]

[tex]b=11[/tex]

Therefore, the equation of the line will be [tex]y=-4x+11[/tex]

Answer:

y = C/h - 2

Step-by-step explanation:

Equation

C = (2 + y)*h

Solution

C = (2 + y)*h                          Divide by h

C/h = (2 + y)*h/h

C/h = 2 + y                            Subtract 2 from both sides

C/h-2 = 2-2+ y                      Combine

C/h - 2 = y

Answer:

here you go

Step-by-step explanation:

no of times he failed = -3

points he losed = -3 x 4 = -12

no of times he need to hit the target to get 48 points = 6x

equation

-12 + 6x = 48

6x = 60

x = 10

no of points he  will  gain = 10 x 6 = 60