The unemployment compensation is calculated by finding the total of the quarterly wages of two consecutive quarters and dividing by 26. The weekly employment is 60% of that amount. In the quarter of January, February, and March, Roger made a total of $12,950.80. In the quarter of April,May, and June, he made a total of $12,250.10. Find Roger’s weekly unemployment amount.

On solving the provided question, we can say that equation for Quinn  = > 625 + 12x and equation for Ryan =>  627 - 10x.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Quinn has $625 in his retirement account, and Ryan has $627

Quinn is adding $12 per day

equation for Quinn  = > 625 + 12x, x is no. of days

Ryan is contributing $10 per day

equation for Ryan =>  627 - 10x, x is no. of days

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The two digit number is 35.

Writing a mathematical statement in the form of a mathematical equation for the correct analysis, measurement and solutions.

Given is that Elizabeth is thinking of a two - digit number. When the tens digit is subtracted from the ones digit, the difference is 2. One-fifth of the number is 1 less than the sun of the digits.

Let the number be (xy).

We can write the two digit number as -

xy = 10x + y                                                   ... Eq { 1 }

Now, it is given that when the tens digit is subtracted from the ones digit, the difference is 2. We can write -

y - x = 2                                                              ... Eq { 2 }

Also, one - fifth of the number is 1 less than the sun of the digits. We can write -

(1/5)(10x + y) = (x + y) - 1                                         ... Eq { 3 }

Now, from eq { 1 } and eq { 2 }, we have -

y - x = 2    

y = x + 2

and

(1/5)(10x + y) = (x + y) - 1    

(1/5)(10x + x + 2) = (x + x + 2) - 1

(1/5)(11x + 2) = 2x - 1

11x + 2 = 10x - 5

x = - 7

y = -5

So, the number would be -

xy = 35

Therefore, the two digit number is 35.

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Answer:

Step-by-step explanation:

12.

1+|-11|=12

lol

The value of [tex]log_35 \times log_{25}9[/tex] is 1.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]log_35 \times log_{25}9[/tex]

[tex]log_ab = \frac{logb}{loga}[/tex]

So,

= log 5 / log 3 x log 9 / log 25

= log 5 / log 3 x log 3² / log 5²

[tex]logm^n = n~logm[/tex]

So,

= log 5 / log 3 x log 3² / log 5²

= (log 5 / log 3) x (2 log 3 / 2 log 5)

= (log 5 / log 3) x (log 3 / log 5)

= 1

Thus,

1 is the value.

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Answer: First, calculate the total value of the shares after the price fall to $80:

value = 200 shares * $80/share = $16,000

Then, calculate the amount of money borrowed:

borrowed = $14,000 / (1 - margin requirement)

= $14,000 / (1 - 0.20)

= $14,000 / 0.80

= $17,500

Finally, calculate the percentage return on investment:

return = (value - borrowed) / borrowed * 100%

= ($16,000 - $17,500) / $17,500 * 100%

= -6.06%

The return on investment is -6.06%, meaning that the investment lost 6.06% of its value.

Step-by-step explanation:

The actual diameter of the gazebo is 12.75 feet and has an area of

127.6 square inches.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, The blueprint for a circular gazebo has a scale of 2 inches = 5 feet.

So, The scale factor is (5/2) = 2.5 or 1 inch = 2.5 feet.

Also given, The gazebo has a diameter of 5.1 inches.

Therefore, The actual diameter of the gazebo is = 5.1×2.5 = 12.75 feet.

The area of the gazebo is π(12.75/2)² = 127.6 square inches.

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The scale factor is: 1.8

because of :

[tex]\frac{36}{20}=1.8\\ \\\\\frac{25.2}{14}=1.8[/tex]

The mean of the combined group can be calculated as follows:

   Calculate the total sum of test scores of both classes:

   Class 1: 36 students * 73.1 mean = 2631.6

   Class 2: 28 students * 67.4 mean = 1888.32

   Total: 2631.6 + 1888.32 = 4519.92

   Calculate the total number of students:

   Total students = 36 + 28 = 64

   Divide the total sum of test scores by the number of students to find the mean:

   Mean = 4519.92 / 64 = 70.9375.

Therefore, the mean of the combined group of 64 students is 70.9375.

The inequality that represents the graph is option D: 13x - 3y - 14 < 0.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The x-intercept is a = 1.077

The y-intercept is b = -4.677

The equation of line having x-intercept a and y-intercept b is -

x/a + y/b = 1

The equation of line having x-intercept 1.077 and y-intercept -4.677 is -

x/1.077 + y/-4.677 = 1

y/-4.677 = 1 - x/1.077

y = (1 - x/1.077)-4.677

y = -4.677 + 4.677x/1.077

y = -4.677 + 4.342x

Multiply both sides by 3 -

3y = 3(-4.677 + 4.342x)

3y = -14.031 + 13.026x

Now, the line 3y = -14.031 + 13.026x divide the xy-plane in two regions and the region given in the graph is satisfied by the origin.

Also, the line 3y = 14.031 + 13.026x is dotted and not dark ,therefore, the points on the line are not included in the shaded region.

Therefore, the inequality that represents the shaded region is -

0 > - 3y - 14.031 + 13.026x ≈ 13x - 3y - 14 < 0

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Answer:

Below

Step-by-step explanation:

Each pound has two 8 oz servings     so three pounds is 6 servings

6 x 544 =3264 cal

Answer:

B) False

In most job, you will get paid on a weekly basis, usually on a Friday.

Step-by-step explanation:

Hope it helps! =D

Answer:

(+7)[(-12)-(+8)]

Step-by-step explanation:

(+7)[(-12)-(+8)

Answer:

solution

given,

length =6cm

breadth =5cm

height =4cm

Now,

area of cuboid =l×b×h

=6cm ×5cm×4cm

=120cm^3

Hence, the total surface area of the given figure of cuboid is 120cm^3

Step-by-step explanation:

given above

The loss is given as difference of cost price and selling price and the selling price is R750.

Mathematicians use the profit and loss formula to calculate market prices for goods and to assess how lucrative a company is. There is a selling price and a cost price for every goods. We can determine the profit made or loss suffered for a certain product based on the values of these prices. Cost price, fixed, variable, and semi-variable costs, selling price, marked price, list price, margin, etc. are some of the key words that are addressed in this article.

Given that the cost price is R600, and the profit is R150.

The profit is given as:

P = SP - CP

150 = SP - 600

SP = 150 + 600

SP = 750

The loss is given as:

L = CP- SP

Hence, the loss is given as difference of cost price and selling price and the selling price is R750.

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Based on each given parallelogram, the correct answers are:

Let's try to solve each parallelogram problems

1. In paralellogram, each parallel sides have equal lengths; then:

x // 9; then x = 9

y // 15; then y = 15

2.  In paralellogram, each parallel sides have equal lengths; then:

m + 1 // 5; then m + 1 = 5

m = 4

n // 10; then n = 10

3.  In paralellogram, each parallel sides have equal lengths; then:

z - 8 // 20; then z - 8 = 20

z = 28

Opposite angles share the same size; then:

d - 21 = 105

d = 126

4. Uncomplete screenshot

5. In parallelogram, adjacent angles is supplementary to each other; then:

∠A + ∠B = 180°

51 + ∠B = 180°

∠B = 129°

6. In parallelogram, adjacent angles is supplementary to each other; then:

∠M + ∠N = 180°

95 + ∠N = 180°

∠N = 85°

In the given parallelogram LMNQ, the length of MP is 8.2 and PN is 7. Angle ∠MQN is 29° and ∠MLQ is 100°.

7. LM can be calculated by focusing on triangle MLQ. Under the Sinus Law, we can find that:

LM / sin LQM = MQ / sin MLQ

MQ is one of the parallelogram diagonal. MP is the mid point, then MQ is twice of MP.

MQ = 2(8.2) = 16.4

∠MLQ = 100°

∠LQN = 180° - 100°

∠LQN = 80°

∠LQN = ∠LQM + ∠MQN

80° = ∠LQM + 29°

∠LQM = 51°

LM / sin 51 = 16.4 / sin 100

LM / 0.78 = 16.4 / 0.98

LM = 12.9 = 13

8. LQ is parallel with MN; then they share the same length.

LQ = MN

MN can be calculated by focusing on triangle QMN. Under the Sinus Law:

MN / sin MQN = MQ / sin MNQ

∠MNQ is the opposite angle of ∠LMQ, then ∠MNQ = ∠LMQ = 100

MN / sin 29 = 16.4 / sin 100

MN = 8.07

9. LP = PN = 7

10. MQ = 2 x MP

MQ = 2(8.2)

MQ = 16.4

11. ∠LMN = ∠LQN = 80°

12. ∠NQL = 80°

13. ∠MNQ = ∠MLQ = 100°

14. ∠LMQ is the alternate interior angle of ∠MQN; then ∠LMQ = ∠MQN = 29°

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The better option to choose is MVR 20 per kg

A parcel can be sent by a freighter at a cost of MVR 20 per kg . The same parcel can be sent by cargo boat at a cost of MVR 280 per parcel .

The weight of the parcel is 13 kg. Let's find the better options as follows:

Therefore, let's convert

Hence, the cost of using cargo boat is  MVR 280 per parcel.

Recall

1 parcel = 13 kg

This means the cargo ship cost MVR 280 for 13 kilograms of the goods.

Therefore, the better option is the cost of MVR 20 per kg .

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The journal entry for the issuing of 1, 000 shares of common stock as payment for legal fees is:

Date               Account title                                  Debit                 Credit

July 1              Organizational expenses           $ 25, 000

                      Common stock                                                   $ 25, 000

The first thing to do is to find the par value of the common stock that was exchanged. This amount is :

= 1, 000 x 25

= $ 25, 000

This amount will be debited to organizational expenses because expenses are debited when incurred. This same amount is to be credited to common stock to show that the attorney is now a shareholder in the firm.

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The question is:

Jul. 1. Issued 1,000 shares of common stock at par to an attorney in payment of legal fees for organizing the corporation.

An inverse variation function with a small value for k. Therefore, option C is  the correct answer.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

The association between x and y can be classified in two ways, as follows:

Direct proportional: when the input x increases, the output y also increases.

Inverse proportional: when the input x increases, the output y decreases.

For this problem, we need an inverse proportional function, that has the following format:

y = k/x.

The lower the value of k, the lower the value of y when x goes to infinity.

Therefore, option C is  the correct answer.

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According to statistics, Land O' Lake's 2021 average annual household income was given at $84,146. Thus, the correct answer is Option B which indicates that the amount is approximately $84,000.

Average Annual Household Income is the average amount of money earned annually by a household, calculated by dividing the total household income by the number of households. It provides a measure of the economic well-being of a particular group or population.

Average Annual Household Income is useful because it provides a broad overview of the economic well-being of a population and can be used to compare the standard of living across different regions, demographic groups, and over time. It is an important indicator of the economy's health and the distribution of wealth.

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Answer:

581 divided by 8 should be 72 with a remainder of 5

Step-by-step explanation:

to check if i was correct i did 72 times 8 plus 5 and got 581

Answer: 2 would be on the 3rd number on the number line, 1 would be before that, and negative one is 1 below 0 means it would be the one in between -2 and 0. Have a nice day ;)

The value of interest after 3 years is  £2,304.

Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it is the kind of interest that banks give their customers on their savings accounts.

Given amount invested = principal = £9600

rate = 8% per year

time = 3 years

simple interest is,

SI = (Prt)/100

SI = (9600*8*3)100

SI = £2,304

Hence value after 3 years is £2,304.

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Answer: [tex]80\%[/tex]

Step-by-step explanation:

[tex]\frac{90-50}{50} \times 100=80\%[/tex]

The table is given as,

Z- Score     -0.299

Q₁                  36.47

Q₂                  38.45

Q₃                  41.2

IQR               4.25

Lower fourth   30.375

Upper fourth       47.375

An illustration of a standardised score is the z-score. A z-score calculates how far a data point deviates from the distribution's mean by standard deviation.

Given:

Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3

(a) The value of z-score is calculated as follows,

μ =[tex]\sum_{i=1}^n X_i[/tex]/ n = 933.1 /24 = 38.88

σ = 3.61

z = X - μ / σ  

  = 37.8 - 38.88/3.61

  = −  0.299

Therefore, the value of z-score is -0.299.

(b) Quartile:

Recalling the values: 31.5, 36, 37.8 ,38.5, 40.1 ,42.2, 34.2 ,36.2, 38.1, 38.7, 40.6 ,42.5, 34.7, 37.3 ,38.2, 39.5 ,41.4, 43.4, 35.6, 37.6 ,38.4 ,39.6 ,41.7, 49.3

Q₁ = ( n+1/4)th value

= (24+1/4)th value

= 6.25th value  

=  36.2 + 0.25 x ( 37.3 −  36.2 )  

= 36.47

and, M = ( n+1/2)th value

= (24+1/2)th value

= (24+1/4)th value

=  12.5 t h

= 38.4 + 38.5/2

= 38.45

Q₃ = 3( n+1/4)th value

= 3(24+1/4)th value

= 18.75 t h  v a l u e

= 40.6 + 0.75 x ( 41.4  −  40.6 )  

= 41.2

(c) Interquartile​ range =  Q ₃ −  Q ₁  

= 41.2  −  36.47  

= 4.25

Therefore, the IQR value is measure of spread of data, and here the value of IQR = 4.25.

(d) Lower fences =  Q₁− 1.5 ( I Q R )  

                            =  36.75 −  1.5  ( 4.25 )  

                            =   30.375  

Upper fences = Q ₃+1.5

                       =  41 + 1.5( 4.25 )  

                       = 47.375

Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.

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Answer:

x=65°

Step-by-step explanation:

Solution Given:

let the point having angle 115° be e.

and point having side containing a and c be f.

we have

∡bec+115°= 180° being linear pair

∡bec=180°-115°=65°

again

∡bec= ∡afc=65° being corresponding angle

again

∡afc=x°=65° being corresponding angle

Both Lily and Charlotte biked 9 miles in a day. They biked 48 miles within the space of 3 days

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Every day last week, Lily biked 7 miles and Charlotte biked 9 miles.

The total distance both biked in a day = 7 miles + 9 miles = 16 miles

Both Lily and Charlotte biked 9 miles in a day

They biked the same number of miles each day for 3 days, hence:

Total distance biked = 16 miles per day * 3 days = 48 miles

They biked 48 miles within the space of 3 days

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The slope of the linear relationship is equal to: A. negative five halves.

In Mathematics, the slope of a linear relationship can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following slope and data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (-2 - 3)/(2 - 0)

Slope, m = -5/2

Note: -5/2 is negative five halves.

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Answer: The Answer is A. -5/2

Step-by-step explanation: I took the test.

Lydia invested an amount of $1110 in the 12% savings account and $1960 in the 13% savings account.

Let's assume the amount invested in the 12% savings account "x". Then, the amount invested in the 13% savings account would be "x + 850".

The total interest earned is $388, so we can write the following two equations to represent the interest earned in each account:

0.12x + 0.13(x + 850) = 388

Expanding the second equation, we get:

0.12x + 0.13x + 110.5 = 388

Combining like terms and simplifying, we get:

0.25x = 277.5

Dividing both sides by 0.25, we get:

x = 1110

So, she invested $1106 in the 12% savings account and $1110 + 850 = $1960 in the 13% savings account.

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The mean of the histogram is 904.8

The mean of the histogram is calculated as

Mean = Sum of the product of carrying load and frequency/Sum of frequency

Using the above as a guide, we have the following:

Mean = (870 * 5 + 890 * 7 + 910 * 8 + 930 * 4 + 950 * 3)/(5 + 7 + 8 + 4 + 3)

Evaluate

Mean = 904.8

Hence, the mean is 904.8

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Answer: $50

Step-by-step explanation:

Let's denote the amount of money Gabriella had before buying the cake as "a". Then we can write an equation to find "a":

a - $25.52 = $24.48

Adding $25.52 to both sides:

a = $25.52 + $24.48

So,

a = $50

Therefore, Gabriella had $50 before buying the cake.