A student survey his classmates to determine their favorite movies

the price of the watch plus tax = 100% + 7% = 107%

Divide the total cost by 107%:

234.33 / 1.07 = 219.00

The original price was $219.00

Answer:

The relationship between the scale factor and perimeter of an image and its pre-image is a, b = perimeter = 2a + 2b. the relationship between the scale factor and area of an image and its pre-image is k∧2 (ab).

Step-by-step explanation:

Relationship between the scale factor and perimeter of an image and its pre-image.

Scale factor = k

Pre-image lengths: a, b = perimeter = 2a + 2b

Image lengths: ka, kb = perimeter = 2ka + 2 kb = k (2a + 2b) = 2 * preimage perimeter.

She has to say that the perimeter of the image is the perimeter of the preimage times the same scale factor.

What should she say about the relationship between the scale factor and area of an image and its pre-image?

area of the pre-image = ab

are of the image = (ka)(kb) = k^2 (ab)

The area of the image is the area of the preimage times the square of the scale factor.

Support her statements using scale factors of 5 and 6.

Scale factor 5

length of the pre-image = 3 x 4 = perimeter = 2 (3 + 4) = 2(7) = 14

length of the image = 3*5 x 4*5 = 15 x 20 = perimeter = 2 (15 + 20) = 2 (35) = 70

14 * 5 = 70 which shows the prediction

area of the pre-image = 3 * 4 = 12

area of the image = 15 * 20 = 300

12 * (5^2) = 12*25 = 300 which is the value predicted.

Now you can do the same using scale factor 6.

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Answer:

Step-by-step explanation:

Let the total distance be x.

We have:

Set this as equation and solve for x:

Total distance from the park to the station is approximately 311 m.

Let that be d

Answer:

the second option listed

(A = 53 degrees)

(a = 13.3)

(c = 16.6)

Step-by-step explanation:

SOH CAH TOA

(sin = opposite / hypotenuse)

(cos = adjacent / hypotenuse)

(tan = opposite / adjacent)

For this question, you are provided an angle (37), and its opposite (10)

so, we can solve for either sin or tan first.

tan = opposite / adjacent

tan 37 = 0.7535540501

0.7535540501 = 10/a  [multiply by a]

0.7535540501a = 10 [divide by [0.7535540501]

a = 13.2704482163

rounded to the nearest tenth, a = 13.3

we know that the three angles shown here must add up to 180

so,

90 + 37 + A = 180

127 + A = 180

- 127           - 127

A = 53

--this is enough information to answer, but I will also solve side c to prove my answer

c = hypotenuse

a²+ b²=c²

[13.3]² + [10]² = c²

176.89 + 100 = c²

276.89 = c²

√276.89 = √c²

16.6400120192 = c

c = 16.6 (rounded to the nearest tenth)

**I am assuming this is a right triangle, otherwise there wouldn't be a matching answer

The simplification form of the provided expression is 6/5x¹⁰ option first is correct.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

[tex]\rm = \sqrt{\dfrac{72x^{16}}{50x^{36}}}[/tex]

[tex]\rm = \sqrt{\dfrac{72}{50}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]

[tex]\rm = \sqrt{\dfrac{36\times2}{25\times2}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]

[tex]\rm ={\dfrac{6x^{8}}{5x^{18}}}[/tex]

[tex]\rm ={\dfrac{6}{5x^{10}}}[/tex]

Thus, the simplification form of the provided expression is 6/5x¹⁰ option first is correct.

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Answer:

6x3

Step-by-step explanation:

Edge 2023

The probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328

The given parameters are:

Start by calculating the mean:

[tex]\mu = np[/tex]

[tex]\mu = 100 * 82\%[/tex]

[tex]\mu = 82[/tex]

Calculate the standard deviation:

[tex]\sigma = \sqrt{\mu(1 - p)[/tex]

[tex]\sigma = \sqrt{82 * (1 - 82\%)[/tex]

[tex]\sigma = 3.84[/tex]

Within ± 0.02 of the population proportion are:

[tex]x_{min} = 82 * (1 - 0.02) = 80.38[/tex]

[tex]x_{max} = 82 * (1 + 0.02) = 83.64[/tex]

Calculate the z-scores at these points using:

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

So, we have:

[tex]z_1 = \frac{80.36 - 82}{3.84} = -0.43[/tex]

[tex]z_2 = \frac{83.64 - 82}{3.84} = 0.43[/tex]

The probability is then represented as:

P(x ± 0.02) = P(-0.43 < z < 0.43)

Using the z table of probabilities, we have:

P(x ± 0.02) = 0.3328

Hence, the probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328

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Answer:

898

Step-by-step explanation:

898999

Answer:One of the factors of the given expression is (2h + 1).

Step-by-step explanation:

ed

Answer:

C on edge 23

Step-by-step explanation:

because i said so

Answer:

f(x) = (x + 1)^2 + 2

Step-by-step explanation:

A parabola function has different forms:

standard form: f(x) = ax + bx + c^2

vertex form:  f(x) = a (x − h)^2 + k

Our equation that includes a horizontal translation is h

- negative h shifts right

- positive h shifts left

this graph shows a shift to the left by 1 so h = 1

Our equation that includes a vertical translation is k

- negative k shifts down

- positive k shifts up

this graph shows a shift to the up by 2 so k = 2

- a represents a compression / stretch which seems not to be in this graph

combine, f(x) = (x + 1)^2 + 2

Step-by-step explanation:

The roots of the polynomial are done by using a calculator will be -2.3671, 2.1835 + 1.2527i, and 2.1835 – 1.2527i.

The polynomial is given below.

[tex]\rm f(x) = a_0x^n + a_1 x^{n - 1}+ ....+ a_{n-2}x^2 + a_{n-1}x + a_nx^0[/tex]

The roots of the polynomial are equal to n or less than n.

And if one imaginary root is a + bi, then the other imaginary root will be a – bi.

The roots of the polynomial are done by using a calculator.

x = -2.3671, 2.1835 + 1.2527i, 2.1835 – 1.2527i

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Answer:

80

Step-by-step explanation:

when you do the math you get two answers, -90 and 80

we dont use -90 because -90 units cannot be manufactured

Of the food donated, 1 lb 6 oz of vegetables, 2 lb 3 oz of meat, and 8 oz of condiments were weighed, the total weight of food donated is 65 ounces.

Units are used to measure and express quantities. In the context of the given problem, units are used to indicate the weight of the donated food items.

Pounds (lb) and ounces (oz) are units of weight commonly used in the United States. One pound is equal to 16 ounces.

To add these weights together, we need to make sure they are all in the same units. Let's convert everything to ounces:

- 1 lb 6 oz = 22 oz (since 1 lb = 16 oz, and 6 oz + 16 oz = 22 oz)

- 2 lb 3 oz = 35 oz (since 2 lb = 32 oz, and 3 oz + 32 oz = 35 oz)

- 8 oz = 8 oz

Now we can add the weights:

22 oz + 35 oz + 8 oz = 65 oz

Therefore, the total weight of food donated is 65 ounces.

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Answer:

The minimum cost of the X-ray machines is 12,197dollars.

Step-by-step explanation:

First, we check whether it’s a Quadratic Equation or not

The general form of the Quadratic equation [tex]f(x) =[/tex] [tex]ax^{2} + bx + c[/tex]

Let’s compare it with the given equation, we get

a = 1

b = -520

c = 79,79

Hence, it’s a quadratic equation.

Now, we will use the VERTEX FORMULA as we are asked to find the ‘minimum’ unit cost.

X = [tex]\frac{-b}\[2a[/tex]  =  [tex]\frac{-(-520)}\[2(1)[/tex] = [tex]260[/tex]

So , number of X-ray machines are = 260 (value of x)

To find the minimum unit cost, plug the value of x into the given equation, and we get

[tex]f(260) = (260)^{2} -520(260) + 79,797[/tex]

[tex]=12,197[/tex]

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(i) The Maclaurin's series is:

1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........

(ii) Integral of limit o to 1∫ e^sinx is 0

Maclaurin's expansion is as follows:

y(x) = y₀ ₊ x y₁(0) ₊ x²/2! y₂(0) ₊ x³/3! y₃(0) ₊ ........

y = e^sinx

y(0) = e^sin0

y(0) = 1

Differentiate y with respect to x

y₁(x) = e^sinx . cos x

y₁(0) = 1 [i.e y₁ = cosx.y]

y₁(0) = 1

Differentiate y₁ with respect to x

y₂(x) = cosc . y₁ ₋ sinx . y

∴ y₂(0) = 1 ₋ 0 = 1

Differentiate y₂ with respect to x

y₃ = cosx . y₂ ₋ (2 sinx ₊ cosx)y₁

y₃(0) = 1 ₋(0 ₊ 1)1

y₃(0) = 0

Differentiate y₃ with respect to x

y₄ = cosx . y₃ sinx . y₃ ₋ (2sinx ₊ cosx)y₂ ₋ (2cos x ₋ sinx) y₁

y₄(0) = 0 ₋ (3 . 0 ₊ 1)1 ₋ (2 ₋ o) 1

y₄(0) = -3

∴ From maclaurin's equation we get:

e^sinx = 1 ₊ x . 1 ₊ x²/2! . 1 ₊ x³/3! (0) ₊ x⁴/4! (₋3) ₊ ....

           =1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........

Hence we get the the series expansion as 1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........

(ii) limit 0 to 1∫e^sinx

integration formula ∫e^x dx = e^x + c

                    limit 0 to 1 ∫e^sinx = [e^sinx + c ]limit 0 to 1

                                                 = e^sin0 ₋ e^sin1

                                                 = 1 ₋ 1

                                                 = 0

Hence we get the answer as 0

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Answer:

4/15

Step-by-step explanation:

in fractions, the number that goes on top is the dividend (the first number in the division problem) which is 4 in this case and the number that goes on the bottom of the fraction is the divisor, which is 15 in this case. therefore, the answer is 4/15.

Answer:

The first sequence is correct being (6)^k

Step-by-step explanation:

To find a ratio divide a term by its previous member such as 36/6 to give you r=6.

Taking into account the definition of a system of linear equations, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that

Galen sold tickets of his church’s carnival for a total of $2,820. Children’s tickets cost $3 each and adult tickets cost $5 each. The number of children’s tickets sold was 30 more than 3 times the number of adult tickets sold.

So, the system of equations to be solved is

[tex]\left \{ {{3x+5y=2820} \atop {x=3y+30}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first you get:

3×(3y+30)+5y=2820

Solving:

3×3y+3×30+5y=2820

9y+90+5y=2820

9y+5y=2820 - 90

14y= 2730

y= 2730÷ 14

y= 195

Remembering that x=3y +30, then:

x= 3×195 + 30

Solving

x=585 +30

x=615

Finally, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.

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Answer:

57905.8

Step-by-step explanation:

Plug in:

V = 4/3 * 24³π

= 4/3 * 13824π

= 18432π

= 57905.83579cm³

Rounded to nearest tenth:

57905.8

Answer: 18,432

Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO

Answer:

c. x/7

Step-by-step explanation:

seven is dividing something, and X is the placeholder in this equation.

So, since x is being divided by seven, that rules out B., because that's backwards.

A. and D. don't involve division, so they're both incorrect as well.

Thus we are left with C. x/7

Answer:

y=3x-21

Step-by-step explanation:

Given points A(2,5) and B(8,3), line AB must contain them.

To calculate the slope, [tex]m_{\text{AB}}[/tex], of line AB, use the slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m_{\text{AB}}=\dfrac{(3)-(5)}{(8)-(2)}[/tex]

[tex]m_{\text{AB}}=\dfrac{-2}{6}[/tex]

[tex]m_{\text{AB}}=-\frac{1}{3}[/tex]

Since the slope isn't undefined, line AB must cross the y-axis somewhere.  To find the y-intercept, build and equation in slope-intercept form:

[tex]y=m_{\text{AB}}x+b_{\text{AB}}[/tex]

[tex]y=\left(-\frac{1}{3} \right) x+b_{\text{AB}}[/tex]

Substituting values for a known point (point A) on line AB...

[tex](5)=\left(-\frac{1}{3} \right) (2)+b_{\text{AB}}[/tex]

[tex]5=-\frac{2}{3} +b_{\text{AB}}[/tex]

[tex](5)+\frac{2}{3} =(-\frac{2}{3} +b_{\text{AB}})+\frac{2}{3}[/tex]

Finding a common denominator...

[tex]\frac{3}{3}*5+\frac{2}{3} =b_{\text{AB}}[/tex]

[tex]\frac{15}{3}+\frac{2}{3} =b_{\text{AB}}[/tex]

[tex]\frac{17}{3}=b_{\text{AB}}[/tex]

So, the equation for line AB is  [tex]y=-\frac{1}{3} x +\frac{17}{3}[/tex]

Since line AB and line BC form a right angle, they are perpendicular.  Perpendicular lines have slopes that are opposite (opposite sign) reciprocals (fraction flipped upside-down) of each other.  Stated another way, the slopes multiply to make negative 1.

[tex]m_{\text{AB}}*m_{\text{BC}}=-1[/tex]

[tex]\left( -\frac{1}{3} \right) *m_{\text{BC}}=-1[/tex]

[tex]-3*\left( -\frac{1}{3} *m_{\text{BC}} \right) =-3*(-1)[/tex]

[tex]m_{\text{BC}} =3[/tex]

Since the slope isn't undefined, line BC must also cross the y-axis somewhere.  To find the y-intercept, build and equation in slope-intercept form:

[tex]y=m_{\text{BC}}x+b_{\text{BC}}[/tex]

[tex]y=(3) x+b_{\text{BC}}[/tex]

Substituting values for a known point (point B) on line BC...

[tex](3)=3 * (8)+b_{\text{BC}}[/tex]

[tex]3=24+b_{\text{BC}}[/tex]

[tex](3)-24=(24+b_{\text{BC}})-24[/tex]

[tex]-21=b_{\text{BC}}[/tex]

So, the equation for line BC is  [tex]y=3 x -21[/tex]

Answer:

a computer is an electronic device,which input data/instruction,store and processes it and produces output in the desired from

The probability is 0.2153.

It is a branch of mathematics that deals with the occurrence of a random event.

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]^{n}C_x* P^{x}* (1-p)^{n-x}[/tex]

n=18, p=0.8

So,

[tex]^{18}C_{14}* 0.8^{14}* (1-0.8)^{18-14}[/tex]

=0.2153

Hence, the probability is 0.2153.

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The answer will be Rs. 4330.

Step-by-step explanation:

Because if you subtract 340 from 4670, you will get the answer which is 4330.

The trip to the lake took  4 hours.

The first step is to determine the distance of the trip.

Distance = average speed x time

24 km/h x 5 = 120 km

Time = distance / average speed

120 / 30 = 4 hours

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The probability that among the first 2 songs played ;a) 6% , not unusual b) 40% and c) 48.4%

Probability refers to a possibility that deals with the occurrence of random events.

We have the following information from the statement:

n = 6, r = 2

a)  

P (like both of them) = P (like first song) x P (like second song)

P = 2/6 x 1/5

P = 0.06 = 6%

The probability that among the first 2 songs played and You like both of them is 6%.

b)

P (like neither) = P (not like first song) x P (not like second song)

P = 4/6 x  3/5

P = 0.4 = 40%

c) P (like exactly one of them) = P (first song liked) x P (second song not liked) + P (first song not liked) x P (second song liked)

P = ( 2/6 x 1/5) + (4/6 x  3/5)

P = 0.484 = 48.4%

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Answer:

b

Step-by-step explanation:

The value of x and y from the given figure are 3 and 36

From the given similar triangles, the following expression is true

4/6 = x/54

Cross multiply

6x = 4 *54

x = 4 * 9

x = 36

Similarly

y/6 = 27/54
y/6 = 1/2

x =3

Hence the value of x and y from the given figure are 3 and 36

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Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.

To determine whether Mr. Tan bases his decision on instinct, mean, median, or mode, we need to consider the given information that Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts.

Instinct refers to a natural or intuitive decision-making process that is not based on specific calculations or statistical measures. While Mr. Tan's decision-making process could involve some level of instinct, it is unlikely to be the primary basis for his decision.

The mean is the average value calculated by summing up all the values and dividing by the total number of values. However, the mean does not provide any information about the distribution of the sizes or the fact that Mr. Tan produces more medium-sized shirts.

The median is the middle value when the data is arranged in ascending or descending order. However, we do not have any information about specific values or the distribution of sizes, so we cannot determine the median.

The mode refers to the value or values that appear most frequently in a set of data. Since Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts, it implies that medium-sized shirts are the mode in his production. This suggests that Mr. Tan's decision is based on the mode, as he produces more shirts of this size than any other size.

Therefore, based on the given information, it can be inferred that Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.

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