The graph below shows the number of hours Dario
worked and the amount he earned.
Earnings (in dollars)
100
90
80
70
60
50
40
30
DARIO'S EARNINGS
(2, 24)
(5, 60)
(8, 96)
0 1 2 3 4 5 6 7 8 9 10
Time (in hours)
What was Dario's hourly wage?
A $10
B $12
$24
D $54

The each monthly loan payment is given by A = $ 414.03

Given data ,

The Liang family wants to buy a family car at a cost of $22700.

They pay a deposit of $4500 and borrow the balance at an interest rate of 11.5% p.a.

And , loan will be paid off with 48 equal monthly payments

The amount borrowed by the Liang family is:

$22700 - $4500 = $18200

The interest rate is 11.5% per annum, which means that the monthly interest rate is:

11.5% / 12 = 0.95833%

To calculate the interest paid, we need to find the total interest over the 48-month loan period. We can use the formula for calculating the total amount paid on a loan with equal monthly payments:

Total amount paid = Monthly payment x Number of payments

The monthly payment can be calculated using the formula for the present value of an annuity:

Monthly payment = PV x (r / (1 - (1 + r)^-n))

Where PV is the present value of the loan, r is the monthly interest rate, and n is the number of payments.

Using the values we have:

PV = $18200

r = 0.95833%

n = 48

Monthly payment = $414.03

Total amount paid = $414.03 x 48 = $19,873.44

Total interest paid = $19,873.44 - $18,200 = $1,673.44

Therefore, the Liang family will pay $1,673.44 in interest over the 48-month loan period.

The total cost of the car, including interest, will be:

$22,700 + $1,673.44 = $24,373.44

Each loan repayment will be A = $19,873.44 / 48 = $ 414.03

Hence , the monthly loan repayment is A = $ 414.03

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The length of the line segment AB is 11/2 mm.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know a line segment parallel to one side of a triangle divides the other two sides in the same ratio.

Therefore, AC/AB = EC/ED.

22/AB = 44/11.

2/AB = 4/11.

4AB = 22.

AB = 11/2.

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Answer:

6 or 7/6

Step-by-step explanation:

they are both prime so 2*3=6

4/6+3/6=7/6

Answer:

21/31/6/2/34861/27651/7266163)

Answer:

UHHHHHH

Step-by-step explanation:

Answer:

6:7

Step-by-step explanation:

Divide 12 and 14 by 2 to simplify the ratio.

Answer: 6:7

Step-by-step explanation:

The number of red balloons in 12 and the number of blue ones is 14, which can be written as 12:14. 12:14 can be simplified to 6:7

Answer:i haven't learned this yet sorry

Step-by-step explanation:

The appropriate measure of variability depends on the characteristics of the data and the research question being addressed and the IQR is a more robust measure than the range if the data is skewed, and a large IQR indicates a wide range of expenses, requiring more funds. (option c)

Firstly, the IQR of 10 is the most accurate to use if the data is skewed. IQR is a measure of variability that measures the spread of the middle 50% of the data, thus, reducing the influence of outliers. Therefore, if the data is skewed, the IQR provides a more robust measure of variability than the range. The range is the difference between the largest and smallest value in a dataset and is sensitive to extreme values, which can distort the results.

Secondly, the IQR of 45 is the most accurate to use if the charity wants to show that they need more money. If the IQR is large, it means that there is a large variation in the data, and the spread is significant. Therefore, in this scenario, a large IQR indicates that the charity has a wide range of expenditures, and some expenses are significantly higher than others. Thus, the charity needs more funds to cover these expenses adequately.

Finally, the range of 45 is the most accurate to use if the charity wants to show that they have plenty of money. A large range indicates that the data points are spread out, and there is a significant variation in the expenses.

Therefore, in this scenario, a large range indicates that the charity has a wide range of expenses, and some expenses are higher than others, but overall, they have enough money to cover these expenses.

Hence the correct option is (c).

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If X is a normal random variable with mean of 85 and a standard deviation of 10, the following probabilities by standardizing,

a. P(X ≤ 80) = 0.3085.

b. P(X ≤ 100) = 0.9332.

c. P(65 ≤ X ≤ 100) = 0.8964.

d. P(X ≥ 70) = 0.9332.

e. P(85 ≤ X ≤ 95) = 0.3413.

f. P(| X − 80 | ≤ 10) = 0.6247.

a. P(X ≤ 80)

Z = (X - μ) / σ = (80 - 85) / 10 = -0.5

Using a standard normal distribution table or a calculator, we can find:

P(Z ≤ -0.5) = 0.3085

Therefore, P(X ≤ 80) = P(Z ≤ -0.5) = 0.3085.

b. P(X ≤ 100)

Z = (X - μ) / σ = (100 - 85) / 10 = 1.5

Using a standard normal distribution table or a calculator, we can find:

P(Z ≤ 1.5) = 0.9332

Therefore, P(X ≤ 100) = P(Z ≤ 1.5) = 0.9332.

c. P(65 ≤ X ≤ 100)

Z for X = 65: Z = (65 - 85) / 10 = -2

Z for X = 100: Z = (100 - 85) / 10 = 1.5

Using a standard normal distribution table or a calculator, we can find:

P(-2 ≤ Z ≤ 1.5) = 0.9192 - 0.0228 = 0.8964

Therefore, P(65 ≤ X ≤ 100) = P(-2 ≤ Z ≤ 1.5) = 0.8964.

d. P(X ≥ 70)

P(X ≥ 70) = 1 - P(X < 70)

Z = (70 - 85) / 10 = -1.5

Using a standard normal distribution table or a calculator, we can find:

P(Z < -1.5) = 0.0668

Therefore, P(X ≥ 70) = 1 - P(Z < -1.5) = 0.9332.

e. P(85 ≤ X ≤ 95)

Z for X = 85: Z = (85 - 85) / 10 = 0

Z for X = 95: Z = (95 - 85) / 10 = 1

Using a standard normal distribution table or a calculator, we can find:

P(0 ≤ Z ≤ 1) = 0.3413

Therefore, P(85 ≤ X ≤ 95) = P(0 ≤ Z ≤ 1) = 0.3413.

f. P(|X − 80| ≤ 10)

We can rewrite the inequality as -10 ≤ X - 80 ≤ 10, or 70 ≤ X ≤ 90.

Z for X = 70: Z = (70 - 85) / 10 = -1.5

Z for X = 90: Z = (90 - 85) / 10 = 0.5

Using a standard normal distribution table or a calculator, we can find:

P(-1.5 ≤ Z ≤ 0.5) = 0.6915 - 0.0668 = 0.6247

Therefore, P(|X − 80| ≤ 10) = P(-1.5 ≤ Z ≤ 0.5) = 0.6247.

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Answer:

Step-by-step explanation:

Answer: 1608.48

Step-by-step explanation:

From this proportion of days he does the activities, sometimes they will meet in one day.

He will do both in the same day when the day is a common factor of 3 and 4.

Since today he did both, the next time he will do so will be in the least common factor of 3 and 4.

To get the least common factor of these, we can identify the divisors of each and makes the divisions until both get to 1. If one of the divisiors is divisior for both, we don't repeat it.

So, from 3 and 4, we can start by the divisior of 2. 2 Is a divisior of 4, but not of 3, so we divide only the number for:

3, 4 | 2

3, 2 |

Now, we have 3 and 2, so we can divide for 2 again:

3, 4 | 2

3, 2 | 2

3, 1 |

Now, we have 3 and 1, so we can only divide by 3 now:

3, 4 | 2

3, 2 | 2

3, 1 | 3

1 , 1 |

So, in the end we have 2, 2 and 3, so the least common factor is 2*2*3 = 12.

Since the common factor of 3 and 4 is 12, Tyler will lift and jog on the same day 12 days after today.

We need to know about ratio to solve the problem. Lonnie is not correct, the correct ratio is 5:6.Two ratios for the information given is 3:7 and 7:3.

Ratio shows how many times one number contains another. In the given question we know the number of boys and number of girls in sixth grade. Lonnie found the ratio of number of boys to number of girls to be 5:7, inorder to find the ratio we need to divide the number of boys by the number of girls and cancel out the common factors which gives us

35/42=5/6

The ratio of number of boys to number of girls is 5:6 and Lonnie was wrong. With the information given in the question that there are 15 male teachers and 35 female teachers we can find the ratio of number of male teachers to female teachers and vice versa.

15/35=3:7

Therefore Lonnie was wrong about the ratio and the correct ratio of number of boys to number of girls is 5:6 and with the given information we know that the ratio of number of male teachers to number of female teachers is 3:7 and the ratio of number of female teachers to male teachers is 7:3.

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The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

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56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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The equation of the path to find the dimensions of the patio is x² + (x + 5)² = 841.

Here we have to find the equation of the dimensions of the patio.

Data provided:

the path = 29 meters

length of the path is 5 meters more than the width of the path.

So let us assume that the length of the path is x

with this, the width of the path is x + 5

The formula for the diagonal:

Diagonal²  = length² + width²

Putting the data we have:

29² = x² + (x +5)²

841 = x² + (x+5)²

Therefore we get the equation as x² +(x + 5)² = 841.

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Answer: B

Step-by-step explanation:

a. probabilities using the binomial table:  0.0225

b.  standard deviation of a binomial random variable is given by:  0.4975

a. Calculation of probabilities using the binomial table:

The probability of X=0, P(X=0) can be found using the binomial table.

The probability of X=1 and X=2 can be found using the formula:

P(X = k) = (n choose k) * (p)^k * (1-p)^(n-k)

Where n = 25 and p = 0.01.

P(X = 0) = (25 choose 0) * (0.01)^0 * (0.99)^(25-0)= (1) * (1) * (0.78) = 0.78

P(X = 1) = (25 choose 1) * (0.01)^1 * (0.99)^(25-1)= (25) * (0.01) * (0.77) = 0.1925

P(X = 2) = (25 choose 2) * (0.01)^2 * (0.99)^(25-2)= (300) * (0.0001) * (0.75) = 0.0225

b. Calculation of the variance and standard deviation of X:

The variance of a binomial random variable is given by:

Var(X) = np(1-p)

Where n = 25 and p = 0.01.

Var(X) = 25 * 0.01 * (1 - 0.01) = 0.2475

The standard deviation of a binomial random variable is given by:

SD(X) = sqrt(np(1-p))

SD(X) = sqrt(25 * 0.01 * (1 - 0.01))

= sqrt(0.2475) = 0.4975 (rounded to 4 decimal places)

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Answer:

Step-by-step explanation:

To construct an equilateral triangle so that segment AB is one of the sides of the triangle we will follow the following steps.

1). Set a distance equal to the segment AB in the compass and draw two arcs on the same side of AB.

2). Join the point of intersection of these arcs to A and B with the help of a straightedge.

3). Hence an equilateral triangle (with all equal sides) is constructed.

To sort the people seated in a row of chairs by their first names without having them move, you would need to retrieve their names, sort them externally, and then update the seating arrangement accordingly.

To sort the 100 people by their first names without them moving from their seats, you can follow these steps:

1. Assign each person a number from 1 to 100 based on their current seat position. The person in the first chair will be assigned number 1, the person in the second chair number 2, and so on.

2. Create a list or array of 100 elements to represent the chairs. Each element will store the name of the person sitting in that chair.

3. Ask each person for their first name and assign it to the corresponding element in the list/array based on their assigned number. For example, if person number 1 is named "John," assign "John" to the first element in the list/array.

4. Once you have gathered all the first names and assigned them to the correct elements in the list/array, you can sort the list/array alphabetically based on the first names.

5. Finally, you can print or display the sorted list/array to show the order of the people sorted by their first names without them having to move from their seats.

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Answer:

2700ft³ or 76455.49 litre

Step-by-step explanation:

Given

Length = 25 feet

Width = 18 feet

Height = 6 feet

Formula for Volume of cuboid = Length×Width×Height

So,

Volume of the pool = 25×18×6 = 2700ft³ or 76455.49 liters aprox.

Answer: 0.86 or 86%

Step-by-step explanation:

To calculate the probability that a new insured with an unknown accident history will be accident-free in the second year of coverage, we can use conditional probability.

Let's define the following events:

A: Insured had no accidents last year

B: Insured is accident-free this year

Given information:

i) P(A) = 0.70 (probability that a new insured had no accidents last year)

ii) P(B | A) = 0.80 (probability that an insured who was accident-free last year will be accident-free this year)

iii) P(B | A') = 0.60 (probability that an insured who was not accident-free last year will be accident-free this year)

We want to find P(B), which is the probability that an insured is accident-free this year, regardless of their accident history last year.

We can use the law of total probability to calculate P(B):

P(B) = P(A) * P(B | A) + P(A') * P(B | A')

P(B) = 0.70 * 0.80 + (1 - 0.70) * 0.60

P(B) = 0.56 + 0.30

P(B) = 0.86

Therefore, the probability that a new insured with an unknown accident history will be accident-free in the second year of coverage is 0.86.

Answer:

24

Step-by-step explanation:

The range is the biggest number subtracted by the smallest number.

45-21=24

I hope this helped <3

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

Considering the data:

Dilation by a scale factor of 4 from the origin in the form of an A'B'C' reflection over x = 1

<=> The two triangles are comparable to one another since triangles can have the same shape but differ in size, so A′′B′′C′′ is 4 times larger than ABC.

=> the connection between "ABC" and "A"B"C" .

\(\frac{AB}{A"B"} = \frac{1}{4}\)

We settle on C.

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

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Answer:

x = 11.4 m

y = 21 m

man's shadow =  9.6 m

Step-by-step explanation:

measure of third angle must be 50 degrees (180 - (40 + 90))

you can take tan50° = 15/y and 'y' will equal approx. 21

to find 'x' you can take tan21° = (21-x) /25 and 21 - x = 25 · tan21°

21 - x = 9.6

-x = -11.4

x = 11.4

man's shadow is the difference of 21 and 11.4, which is 9.6

Answer: (1,2)

Step-by-step explanation:

1)

x+y=3

y=-x+3

x | 0 | 3 |

y | 3 | 0 |

2)

3x+y=5

y=-3x+5

x | 0 | 2 |

y | 5 | -1 |

After answering the provided question, we can conclude that  Each inequality person will receive three portions, for a total of three-eighths of a candy bar.

In mathematics, an inequality is a non-equal relationship between two expressions or values. As a result, imbalance leads to inequality. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal sign is commonly used (). Different inequalities, no matter how small or large, are used to contrast values. Many simple inequalities can be solved by modifying the two sides until only the variables remain. However, a number of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.  

Each person will be given 3/8 of a candy bar.

Words: If Sam has three candy bars and wants to divide them into eight equal portions to give to his friends, each will receive one-eighth of a candy bar.

Diagram:

Candy bar 1     Candy bar 2     Candy bar 3

----------     ----------     ----------

|          |   |          |   |          |

|          |   |          |   |          |

|          |   |          |   |          |

----------     ----------     ----------

    1/8            1/8            1/8

The diagram above depicts three candy bars, each divided into eight equal portions. Each portion represents 1/8 of a candy bar, and each person will receive one. Each person will receive three portions, for a total of three-eighths of a candy bar.

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The area of the base of the cube is 9 square inches.

To find the area of the base of a cube, we can use the formula:

\(Area $ of base = (Volume)^{(2/3)\)

Given that the volume of the cube is 27 cubic inches, we substitute this value into the formula:

\(Area $ of base = (27)^{(2/3) }\)

To simplify the expression, we can rewrite 27 as (3^3):

\(Area $ of base = (3^3)^{(2/3)\)

Applying the exponent rule, we multiply the exponents:

\(Area $ of base = 3^{(3\times (2/3))\)

The exponent \(3\times (2/3)\) simplifies to 2:

\(Area $ of base = 3^2\)

Evaluating \(3^2,\) we get:

Area of base = 9 square inches.

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Hey there! I'm happy to help!

The greatest common factor is the largest factor that both numbers contain. Let's look at the factors of these terms.

12x²: 1, 12, 2, 6, 3, 4, x, x

15x³: 1, 15, 3, 5, x, x ,x

We see that both of these numbers contain a 3 and 2 x's, so our GCF would be 3x².

Have a wonderful day!

Answer:

c=27

Step-by-step explanation:

9-c=-18

-c = -18 -9

-c = -27

change the signs

c = 27