Complete the equation so that it has infinitely many solutions.
5(6b-3)-3b =___
b____

The height where the pumpkin lands on the hill is given as follows:

36 meters.

The equation for the pumpkin's height is given as follows:

y = -0.1x² + 4.9x.

The equation for the hill's height is given as follows:

y = 0.9x.

Hence the pumpkin will land on the hill at a time of:

-0.1x² + 4.9x = 0.9x.

Hence:

0.1x² - 4x = 0.

x(0.1x - 4) = 0.

0.1x - 4 = 0

x = 40.

The height is then given as follows:

y = 0.9(40)

y = 36 meters.

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

Step-by-step explanation:

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

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 ;)

Answer:

Below

Step-by-step explanation:

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

6 x 544 =3264 cal

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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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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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.

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.

If  Health and Fitness Tyler does squats and pushups. He wants to increase the number of each type of exercise by 20% by the end of the month. The equation is 0.2(x+25)=13 and the number of squats is 40.

Let x represent  the number of squats Tyler currently have

Given the equation:

0.2(x + 25) = 13

Expanding the parentheses on the left side:

0.2x + 5 = 13

Subtracting 5 from both sides:

0.2x = 8.

Dividing both sides by 0.2 to isolate x:

x = 8/0.2

x = 40

Therefore  Tyler currently does 40 squats.

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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]

Answer:

D. 29

Step-by-step explanation:

A. 10 = 2 × 5   not prime

B. 15 = 3 × 5   not prime

C. 27 = 3³   not prime

D. 29 = 1 × 29    prime

Answer:

29

Step-by-step explanation:

A prime number is a number that can't be divided by any number other than itself or 1.

10

1*10

2*5

5*2

10*1

NOT A PRIME NUMBER

15

1*15

3*5

5*3

15*1

NOT A PRIME NUMBER

27

1*27

3*9

9*3

27*1

NOT A PRIME NUMBER

29

1*29

29*1

PRIME NUMBER

Hence Sequences 4, 16, 36, 64,.. are not arithmetic, however 40, 30, 20, 10,... are, with a common difference of -10 and the 52nd term being -490.

An arithmetic progression is defined as a constant discrepancy between terms that follow one another through a series. For instance, the number sequence 5, 7, 9, 11, 13, and 15 is an example of either an exponential manner with a limitation of two. A progression with a set tolerance between any consecutive numbers is referred to as a "arithmetic progression" (A.P.). Two types of mathematical progression are possible: series in mathematics with a finite length A finite geographic progression is a serie with a finite number of terms. The early, delayed, tolerance, and frequency of terms may all be calculated using the terms in the series.

given

First succession

4, 16, 36, 64,

The common difference must be the same for it to be considered AP.

It is not AP since 16 - 4  ≠  36 - 16.

Second succession;

40, 30, 20, 10, ...

common distinction =30 - 40 = 20 - 30 = 10 - 20 = -10

As a result, it will be an AP because the common difference is -10 and the same.

Now, The nth phrase of AP equals a plus (n - 1) d, where d is a typical difference and an is the initial term.

So, 52nd term = 40 + (52 - 1) (-10), which is -490.

Hence Sequences 4, 16, 36, 64,.. are not arithmetic, however 40, 30, 20, 10,... are, with a common difference of -10 and the 52nd term being -490.

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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 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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44 tourists only visited LEGOLAND (of these three).

Let's call the number of tourists who visited only LEGOLAND x.

From the information given, we know that:

258 tourists had visited the Magic Kingdom

299 tourists had visited Universal Studios

100 tourists had visited both the Magic Kingdom and LEGOLAND

82 tourists had visited both the Magic Kingdom and Universal Studios

76 tourists had visited both LEGOLAND and Universal Studios

12 tourists had visited all three theme parks

68 tourists did not visit any of these theme parks

We can calculate x as follows:

x = number of tourists who visited LEGOLAND only

number of tourists who visited LEGOLAND - number of tourists who visited LEGOLAND and Magic Kingdom - number of tourists who visited LEGOLAND and Universal Studios + number of tourists who visited all three parks

= 100 - 82 - 76 + 12

= 44

Hence, 44 tourists only visited LEGOLAND (of these three).

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Answer:

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

Step-by-step explanation:

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

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 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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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.

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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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

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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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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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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To isolate the variable on one side of the equal sign, divide both sides of the equation by the coefficient of the variable.

The equivalent of a gallon (gal) is 16 cups, 8 pints, or 4 quarts. The biggest liquid measurement is this one.

The complete question is

What is the biggest measurement of liquid?

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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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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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Answer:

The class raised $45 x 23 = $1035.

Step-by-step explanation:

To find the total amount of money raised by the class:

Identify the amount raised by one student: $45.

Multiply the amount raised by one student by the number of students: $45 * 23.

The total amount raised by the class is $45 * 23 = $1035.

Answer:

ehhhh

Step-by-step explanation: