Kayla's mom left a 20% tip for a restaurant bill that was $35. She used the expression 1. 20(35) to find the total cost.


Which equivalent expression could she also use to find the total cost?


A. 35 + 0. 2

B. 1+0. 2(35)

C. 1. 02(35)

D. (1+0. 2)35

The margin of error for estimating the true population proportion of adult office workers who have worn a Halloween costume to the office at least once, using a 95% confidence level, is approximately 0.02633 .

A random variable is a variable whose value is unknown, or a function that assigns values to each of an experiment's outcomes.

A proportion is an equation in which two ratios are set equal to each other.

The margin of error for estimating the true population proportion can be calculated using the formula:

Margin of Error = Critical Value * Standard Deviation

where the Critical Value is determined based on the desired confidence level and the Standard Deviation is an estimate of the variability of the population proportion.

Given that the sample size is large (n = 1200) and we are using a 95% confidence level, we can use the standard normal distribution (Z-distribution) for the Critical Value. The critical value for a 95% confidence level in a standard normal distribution is approximately 1.96.

The Standard Deviation can be estimated using the sample proportion, which is given as 32% or 0.32 in this case. The sample proportion is a point estimate of the population proportion.

Using these values, we can calculate the margin of error as follows:

Margin of Error = 1.96 * √( (0.32 * (1 - 0.32)) / 1200 )

= 1.96 * √( 0.2176 / 1200 )

= 1.96 * √( 0.00018133333 )

= 1.96 * 0.01345451543

= 0.02633 (rounded to 5 decimal places)

So, the margin of error for estimating the true population proportion of adult office workers who have worn a Halloween costume to the office at least once, using a 95% confidence level, is approximately 0.02633 .

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In the given cirlce, the value of x is 15

From the question, we are to determine the value of x in the given diagram

From the given information,

We have a circle and we are given the angles subtended by the arcs at the center of the circle.

We know that the sum of angles in a circle is 360°.

Then,

We can write that

(8x - 10)° + (6x)° + (10x + 10)°  = 360°

Solving for x

8x - 10 + 6x + 10x + 10  = 360

Collect like terms

8x + 6x + 10x - 10 + 10 = 360

24x = 360

Divide both sides by 24

24x / 24 = 360 / 24

x = 15

Hence, the value of x is 15

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The probability that the mean of a sample of 77 computers would be greater than 82.59 months, assuming the population mean is 80 months and the variance is 64, is approximately 0.0606

The situation described can be modeled using a normal distribution, with a mean of 80 months and a standard deviation of the square root of the variance, which is 8 months (since variance = standard deviation squared).

To find the probability that the mean of a sample of 77 computers would be greater than 82.59 months, we need to standardize the sample mean using the formula

z = (x - μ) / (σ / √n)

where

x is the sample mean

μ is the population mean (believed to be 80 months)

σ is the population standard deviation (8 months)

n is the sample size (77)

Plugging in the values, we get

z = (82.59 - 80) / (8 / √77) ≈ 1.55

To find the probability of a z-score being greater than 1.55, we can use a standard normal distribution table or calculator. From the table, we find that the probability of z being greater than 1.55 is approximately 0.0606.

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The probability that the product of the two chosen numbers will be even and greater than 2 is 9/25.

Probability is a measure of the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event that will not occur, and 1 represents a certain event that will always occur.

According to the given information:

There are 5 balls numbered 1 through 5 in the bowl. The total number of possible outcomes, when Josh chooses a ball, is 5, as there are 5 balls in the bowl.

Now let's consider the probability of choosing a ball with an even number. There are 3 even numbers (2, 4, and 5) out of the 5 possible numbers, so the probability of choosing a ball with an even number is 3/5.

Next, let's consider the probability of choosing a ball with a number greater than 2. There are 3 numbers (3, 4, and 5) greater than 2 out of the 5 possible numbers, so the probability of choosing a ball with a number greater than 2 is also 3/5.

To find the probability that the product of the two chosen numbers will be even and greater than 2, we need to multiply the probabilities of choosing an even number and choosing a number greater than 2.

Probability of choosing an even number: 3/5

Probability of choosing a number greater than 2: 3/5

Multiplying these probabilities, we get:

(3/5) * (3/5) = 9/25

So, the probability that the product of the two chosen numbers will be even and greater than 2 is 9/25.

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Answer:

Same equation just using the assocaitive property

Step-by-step explanation:

For example, 8 + (2 + 3) = (8 + 2) + 3 = 13

Hope this helps! =D

Step-by-step explanation:

Given:

The damage to the parked car was

$4,300and the damage to the store

was

$50,400.

Objective:

The objective is to determine the

amount will the insurance company pay

for Susan's car accident.

Explanation:

Having a 100/300/50 insurance policy

means you have $100,000 in coverage

for bodily injury liability per person,

$300,000 for bodily injury liability per

accident, and $50,000 for property

damage liability.

The anmount insurance company

will pay $4,300 for car damage and

$50,000 for property damage.

So total amount that must be paid is

$50000+$4300=$54300

mark brainly

fraction wise, a whole is always simplified to 1, so

[tex]\cfrac{4}{4}\implies \cfrac{1000}{1000}\implies \cfrac{9999}{9999}\implies \cfrac{17}{17}\implies \text{\LARGE 1} ~~ whole[/tex]

so, we can say the whole of the players, namely all of them, expressed in fourth is well, 4/4, that's the whole lot,  and we also know that 3/4 of that is 12, the guys who chose the bottle of water

[tex]\begin{array}{ccll} fraction&value\\ \cline{1-2} \frac{4}{4}&p\\[1em] \frac{3}{4}&12 \end{array}\implies \cfrac{~~ \frac{4 }{4 } ~~}{\frac{3}{4}}~~ = ~~\cfrac{p}{12}\implies \cfrac{~~ 1 ~~}{\frac{3}{4}} = \cfrac{p}{12}\implies \cfrac{4}{3}=\cfrac{p}{12} \\\\\\ (4)(12)=3p\implies \cfrac{(4)(12)}{3}=p\implies 16=p[/tex]

Arun is not correct - he has just under $5 in total, not just over.

Let's start by finding out how many 5-cent and 10-cent coins Arun has.

Let the number of 5-cent coins be 5x and the number of 10-cent coins be 3x (since the coins are in the ratio 5:3).

Then the total value of the 5-cent coins is 5x0.05 = 0.25x dollars, and the total value of the 10-cent coins is 3x0.1 = 0.3x dollars.

So the total value of all the coins is 0.25x + 0.3x = 0.55x dollars.

Since Arun has 72 coins, we know that 5x + 3x = 72, or 8x = 72, or x = 9.

Therefore, Arun has 5x = 59 = 45 5-cent coins and 3x = 39 = 27 10-cent coins.

The total value of these coins is 450.05 + 270.1 = 2.25 + 2.7 = 4.95 dollars.

So Arun is not correct - he has just under $5 in total, not just over.

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Step-by-step explanation:

'Range' is the 'y' values a graph can have....

 this one goes from a high of -8   down through - inf

-8 <= y < -inf

(-inf, -8]  

The runtime of the algorithm is primarily determined by the dominant term, which is the constant value of [tex]1 x 10^36[/tex].

To determine the dominant term given the computational complexity 0.00001 * n * log(n), 300n, and

[tex]1 x 10^36[/tex], you

need to compare the growth rates of these terms as n approaches infinity.

0.00001 × n × log(n):

This term grows at a rate of n × log(n), which is a function of both n and its logarithm.

300n:

This term grows linearly with n.

[tex]1 x 10^36[/tex]:

This term is a constant and does not grow with n.

As n approaches infinity, the term with the highest growth rate is the dominant term.

In this case, the dominant term is 0.00001 × n × log(n) since it grows at a rate of n × log(n), which is faster than the linear

growth of 300n and the constant [tex]1 x 10^36[/tex].

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The cost of 1 dou of corn is 9 coins and the cost of 1 dou of sesame is 3 coins.

Let x be the cost of 1 dou of corn and y be the cost of 1 dou of sesame.

Using the first set of information, we can create the following equation

4x + 12y = 72

Simplifying this equation by dividing by 4, we get

x + 3y = 18

Using the second set of information, we can create another equation

5x + 10y = 75

Simplifying this equation by dividing by 5, we get

x + 2y = 15

Now we have two equations with two variables

x + 3y = 18

x + 2y = 15

Subtracting the second equation from the first, we get

y = 3 coins

Substituting this value of y back into either of the two equations, we get

x + 3(3) = 18

x + 9 = 18

x = 9 coins

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Answer:

mean: 101 (add all the numbers then divide by 7)

mode: 102 (the most frequent number in the set)

median: 102 (the number in the middle of the set)

range: 20 (the difference between the largest and smallest number)

Mean = 101

Mode = 102

Median = 102

Range = 20

MEAN: Add up all the numbers, then divide by how many numbers there are.

102 + 107 + 99 + 102 + 111 + 95 + 91 = 707

707 ÷ 7 = 101

MODE: Arrange all numbers in order from lowest to highest or highest to lowest and then count how many times each number appears in the set. The one that appears the most is the mode.

91,95,99,102,102,107,111

MEDIAN: Arrange the numbers from smallest to largest. If the amount of numbers is odd, the median is the middle number. If it is even, the median is the average of the two middle numbers in the list.

91,95,99,102,102,107,111

RANGE: Subtract the lowest number from the highest number

111 - 91 = 20

Answer:

Set your calculator to degree mode.

[tex] \tan(39) = \frac{12}{x} [/tex]

[tex]x \tan(39) = 12[/tex]

[tex]x = \frac{12}{ \tan(39) } = 14.818766[/tex]

So the area of this triangle is

(1/2)(14.818766)(12) = 88.91 (B)

The equation that represents the distance traveled is d = 50t

To find the time it takes the car to travel a certain distance, we can use the formula:

time = distance / speed

where speed is the constant speed of the car, which is 50 miles per hour.

Using this formula, we can fill in the table:

Time (hours) Distance (miles)

2 100

1.5 75

2.5 125

20 1000

To write an equation that represents the distance traveled by the car, d, for an amount of time, t, we can rearrange the formula to:

distance = speed x time

Substituting the value of the speed, we get:

distance = 50t

In this equation, the dependent variable is the distance traveled, which depends on the value of the independent variable, which is the time elapsed.

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Answer:

6.862745098%

Step-by-step explanation:

8/18x7/17x6/16=0.06862745098

0.06862745098 * 100 = 6.862745098%

When x is 2, the value of the expression is 9.

An algebraic expression is a mathematical phrase that contains one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can also contain exponents, roots, and trigonometric functions.

Algebraic expressions are used to represent mathematical relationships and solve problems in a wide range of fields, including physics, engineering, finance, and statistics. They can be used to model real-world phenomena and to make predictions based on data.

Algebraic expressions can be simplified by combining like terms and using mathematical rules and properties. They can also be evaluated by substituting values for the variables and simplifying the expression. Solving equations involving algebraic expressions often involves manipulating the expression to isolate a variable and find its value.

When x is 2, the value of the expression 12/4+3(8−x)-12 can be found by substituting 2 for x and simplifying the expression:

12/4 + 3(8 - 2) - 12

= 3 + 3(6) - 12

= 3 + 18 - 12

= 9

Therefore, when x is 2, the value of the expression is 9.

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The complete question is :

When x is 2, what is the value of the expression 12/4+3(8−x)-12?

A number of

convergence tests

can be used to examine a Taylor series' convergence, but the Ratio Test is one that is frequently employed. According to the

ratio test, the series converges absolutely if the limit of the

absolute value

of the ratio of the (n+1)th term to the nth term is smaller than 1. In mathematics, this is expressed as:

lim┬(n→∞)⁡〖|a_(n+1)/a_n |<1〗

where a n is the

series' nth term. The series

diverges

if the limit is bigger than 1, and extra tests must be employed if the limit is equal to 1.

Although the

Ratio Test

is a frequently used test for

Taylor series

convergence, it is not always appropriate and other tests can be required based on the unique characteristics of the series.

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The balloon payment at the end of 7 years would be $173,819.97, which is option A.

A 7/23 balloon mortgage means that April will make payments on the loan as if it were a 23-year mortgage, but the remaining balance of the loan will be due in full after 7 years.

To find the balloon payment at the end of 7 years, we can first calculate the monthly payment using the loan amount, interest rate, and loan term:

n = 23 * 12 = 276 (total number of payments)

r = 4.15% / 12 = 0.003458 (monthly interest rate)

P = (r * PV) / (1 - (1 + r)^(-n))

where

PV = $197,000

P = (0.003458 * $197,000) / (1 - (1 + 0.003458)^(-276)) = $1,007.14 (monthly payment)

Now we can calculate the remaining balance on the loan after 7 years. Since April is making payments as if it were a 23-year mortgage, she will have made 7 * 12 = 84 payments by the end of the 7th year.

Using the formula for the remaining balance of a loan after t payments:

B = PV * (1 + r)^t - (P / r) * ((1 + r)^t - 1)

Where

t = 84 (number of payments made)

B = $197,000 * (1 + 0.003458)^84 - ($1,007.14 / 0.003458) * ((1 + 0.003458)^84 - 1)

B = $173,819.97

Therefore, the balloon payment at the end of 7 years would be $173,819.97, which is option A.

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The sine function that describes the child's apparent distance from the center of the merry-go-round is d(t) = 5.3 sin(2π/15 * t)

To write a sine function that describes the child's apparent distance from the center of the merry-go-round as a function of time t, we can start by finding the amplitude, period, and phase shift of the motion.

Amplitude:

The amplitude of the motion is half the diameter of the merry-go-round, which is 10.6/2 = 5.3 feet. This is because the child moves back and forth across the diameter of the merry-go-round.

Period:

The period of the motion is the time it takes for the child to complete one full cycle of back-and-forth motion, which is equal to the time it takes for the merry-go-round to complete one full rotation.

From the given information, the child completes 8 rotations in 120 seconds, so the period is T = 120/8 = 15 seconds.

Phase shift:

The phase shift of the motion is the amount of time by which the sine function is shifted horizontally (to the right or left).

In this case, the child starts at one end of the diameter and moves to the other end, so the sine function starts at its maximum value when t = 0. Thus, the phase shift is 0.

With these values, we can write the sine function that describes the child's apparent distance from the center of the merry-go-round as:

d(t) = 5.3 sin(2π/15 * t)

where d is the child's distance from the center of the merry-go-round in feet, and t is the time in seconds. The factor 2π/15 is the angular frequency of the motion, which is equal to 2π/T.

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Answer:

D. y ≥ x² - 4x - 5

Step-by-step explanation:

We can observe two characteristics of this graphed inequality:

1. its shading is above it, therefore the inequality sign must be greater than

2. its boundary line is continuous, not dotted, so the inequality sign must include or equal to

From these two observations, we can assert that D. x² - 4x - 5 is the correct answer because it is the only one which has a greater than or equal to sign.

____________

Note:

We can also check that the equation for the inequality is correct by converting it to vertex form by completing the square, then graphing it ourselves:

[tex]y \ge (x-2)^2 - 9[/tex]

Answer:

The answer is y≥ x²-4x-5

Step-by-step explanation:

x=a,x=b

where a,b are roots of the equation

a= -1 b=5

x= -1,x=5

x+1=0,x-5=0

(x+1)(x-5)=0

x²-5x+x-5=0

x²-4x-5=0

Answer:

The answer that you're looking for is approximately 9202.77 and in terms of π it is 2929.33π

Step-by-step explanation:

Using the equation [tex]\frac{4}{3}\pi r^{3}[/tex] you can replace r with 13 to get [tex]\frac{4}{3} \pi 13^{3}[/tex] you then multiply them all to get 9202.77 and divide by π to find the terms of pi which is 2929.33π.

I hope this was helpful!

Answer:

To determine if (-1, 4) is a solution to y < -3x + 2, we need to substitute x = -1 and y = 4 into the inequality and see if the inequality is true:

4 < -3(-1) + 2

4 < 3 + 2

4 < 5

Since 4 is not less than 5, the inequality is false when we substitute x = -1 and y = 4. Therefore, (-1, 4) is not a solution to y < -3x + 2.

To graph the inequality y < -3x + 2, we can first graph the line y = -3x + 2 (which has a y-intercept of 2 and a slope of -3) as a dashed line (since the inequality is "less than" and not "less than or equal to"). Then, we can shade the region below the line to represent all the points that satisfy the inequality.

Here is a graph of y < -3x + 2:

    |

    |

    |

    |

    |         /

    |       /

    |     /

    |   /

    | /

-----+----------------

    |   |   |   |

   -2   0   2   4

The dashed line represents the line y = -3x + 2, and the shaded region represents all the points that satisfy y < -3x + 2.

The statement which  is true for the quadrilateral is B.

To dilate a figure by a scale factor of 2, each point of the original figure is multiplied by 2.

So the coordinates of each vertex of A'B'C'D' are twice the coordinates of the corresponding vertex of ABCD.

The coordinates of A' are (4,10), B' are (4,4), C' are (8,6), and D' are (8,12).

To determine which statements are true, we can compare the angles and side lengths of the two quadrilaterals:

A) None of the answers apply. This may be a valid answer, but we should check the other options before concluding that none of them apply.

B) The angles of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same. This is true because dilation does not change angles. The corresponding angles of the two quadrilaterals are congruent.

C) The side lengths of Quadrilateral ABCD and Quadrilateral A'B'C'D' are not the same. We can see this by calculating the length of each side of both quadrilaterals.

Therefore, the correct answer is B.

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The probability that Neta is chosen first and Jinita is chosen second is:

1/56(or approximately 0.018.)

There are 8 students in class, so there are 8 choices for first person and 7 choices for second person.

Since we want to calculate probability that Neta is chosen first and Jinita is chosen second, we need to consider the number of ways in which these two students can be chosen in that order.

There is only one way for Neta to be chosen first and Jinita to be chosen second, so the total number of possible outcomes is:

8 x 7 = 56

Therefore, the probability that Neta is chosen first and Jinita is chosen second is: 1/56 or approximately 0.018.

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Answer:  7.7

Step-by-step explanation:  is how much you save because when you intact 20% from 38.5 you get 30.8 and if you add 7.7 you get 38.5

Step-by-step explanation:

x = -4     ( the value of the x-coordinate of the vertex is the axis of symmetry for normal up or down opening parabolas)

Answer:

The perimeter of this trapezoid is

7 + 5 + 3 + 7 + 4 = 26 cm

rectangle, A = lw, 4 × 7 = 28 square cm

triangle, A = (1/2)bh, (1/2) × 3 × 4 =

6 square cm

(1/2)(4)(7 + 10) = (1/2)(4)(17) = 34 square cm = 28 square cm + 6 square cm

Answer:

£12063.57

Step-by-step explanation:

The value of Alfred’s car after 12 years can be calculated using the formula for exponential decay: Final Value = Initial Value * (1 - rate of depreciation)^(number of years). Plugging in the values we get: Final Value = 13960 * (1 - 0.0075)^12. Therefore, after 12 years, Alfred’s car will be worth approximately £12063.57.

Answer:

Step-by-step explanation:

Let A be the area of the surface of the cube.

When the side length changes from s to 4s, the new area A' can be calculated as:

A' = 6(4s)^2 = 96s^2

The change in area is then:

ΔA = A' - A = 96s^2 - 6s^2 = 90s^2

To find the integral that quantifies the change in area, we can integrate the expression for ΔA with respect to s, from s to 4s:

∫(90s^2)ds from s to 4s

= [30s^3] from s to 4s

= 30(4s)^3 - 30s^3

= 1920s^3 - 30s^3

= 1890s^3

Therefore, the integral that quantifies the change in area of the surface of a cube when its side length quadruples from s units to 4s units is:

∫(90s^2)ds from s to 4s

= 1890s^3 from s to 4s

= 1890(4s)^3 - 1890s^3

= 477,840s^3 - 1890s^3