A tank of water is being drained. Due to a problem, the sensor does not start working until some time into the draining process. The sensor starts its recording at time zero when there are 770 liters in the tank.

The solution to the given quadratic equation is x = -1 + 3i OR x = -1 - 3i

From the question, we are to solve the given quadratic equation

From the given information,

The quadratic equation is

x² + 2x + 10 = 0

Using the Quadratic formula,

x = [-b ± √(b² - 4ac)] / 2a

From the equation,

a = 1, b = 2, and c = 10

Then,

x = [-b ± √(b² - 4ac)] / 2a

x = [-(2) ± √((2)² - 4(1)(10))] / 2(1)

x = [-2 ± √(4 - 40)] / 2

x = [-2 ± √(-36)] / 2

x = [-2 ± -6i] / 2

x = -1 ± 3i

x = -1 + 3i OR x = -1 - 3i

Hence, the solution is x = -1 + 3i OR x = -1 - 3i

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She traveled 6.375 miles by train.

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here as per question the formula is x × (4+3×4)=34

∴ x×16=34

       x= 6.375

Hence, She traveled 6.375 miles by train.

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If the perimeter of the triangle is 64 units, then the length of the side PR is 24 units.

This is referred to as a three-sided polygon that consists of three edges and three vertices and the longest side is referred to as the hypotenuse.

The perimeter of a triangle is the sum of all the sides which is:

P = a + b + c

64 = 3x +4x - 1 + x + 1

64 = 8x

x = 64/8 = 8 units

Therefore the length of side PR is :

3x = 3 (8) = 24 units.

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The baker can make 13 loafs of bread using 85 cups of flour using 6 1/4 c of flour for each loaf of bread.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A baker has 85 cups (c) of flour to make bread she uses 6 1/4 c of flour for each loaf of bread.

Now, The fraction 6 1/4 can be written as 25/4.

Therefore, The number of bread loaf the baker can make is,

= (85/25/4).

= 85×(4/25).

= (17×4)/5.

= 68/5.

= 65/5 + 3/5.

= 13 + 3/5.

So, he can make 13 bread loafs.

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The table is completed as shown below and total earnings of Lori is found.

What exactly is total earnings of a person?

The wages paid for both regular working hours and other working hours, including extra work or tips are referred to as total earnings.

Consider Tuesday

Hours worked = 4

Base salary = 4 × 7 ( $7 per hour given)

                     = $28

Tips = 18% of food sales = 0.18 × 300 = $54

Total earnings on Tuesday = 28 + 54 = $82

In the similar way the table can be completed as below.

1) The total earnings of Lori for the week = 82+138.9+218.5+173 = $612.4

2) Total earnings in a year = 52 × 612.4 = $31844.8

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Answer:

A) Angle A. Angle EG.

B) Angle A and Angle F.

C) Angle EG and Angle D.

I hope this helped you!

The set of rational expressions are closed under subtraction because the subtraction will result to a rational expression

The ratio of two polynomials is a rational expression.

A rational expression can be expressed in the form p/q, where p and q are polynomials,

Closure property of rational expression

According to the closure property, a - b is also a rational number for any pair of two rational numbers, a and b. The outcome is a rational number. Therefore, under subtraction, the rational numbers are closed.

In the polynomial subtraction

= P(x) /q(x) - r(x)/s(x)

= (P(x) * s(x) - r(x) * q(x)) / (q(x) * r(x))) also a rational number

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Answer:

Question 1: 29

Question 2: 50

Question 3: AD≅BC

Step-by-step explanation:

question 1: Since it's a parallelogram opposite sides are equal.

4x+5=5x-1   add one to both sides

4x+6 =5x subtract 4x from both sides

6 = x

So AD is equal to 5(6) - 1 = 30-1 =  29=AD

Question 2: Since diagonals in a parallelogram bisect each other AE = EC

So...

5x+5 = 8x- 7 add 7 to both sides

5x+12 = 8x subtract 5x from both sides

12=3x divide both sides by 3

4=x

AC= 5(4) + 5 + 8(4) - 7

AC= 20 + 5 + 32 - 7

AC= 50

Question 3: Lines can only be congruent, represented by ≅, not equal which is represented by =. Values can be equal.

By using the elimination method you get the answer  line AD ≅ line BC

Answer:

x=2/3

Step-by-step explanation:

when the three turned into a 2 it removed one third, so we need to remove one third from 1, which gives us 2/3.

Basically, if a rectangle side goes from x to y, we figure out the percent decrease, and subtract that percent from the other side to find the variable we need to find on the other rectangle

The total number of satsumas eated by George are 2[tex]\frac{1}{6}[/tex].

Fractions represent the parts of a whole or collection of objects. A fraction has two parts namely numerator (upper part) and denominator (lower part).

Given is that George peels and eats 2 whole satsumas. He then splits another satsuma into 6 equal segments and eats 1 of these segments.

The total number of satsumas eated by him can be written as -

2 + 1/6

2[tex]\frac{1}{6}[/tex]

Therefore, the total number of satsumas eated by George are 2[tex]\frac{1}{6}[/tex].

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Complete the puzzles with values -4, 0, -3 and 2

Since each row, column, and diagonal adds up to the same total.

For the 1st row, the total is:

3 + (-2) + (-1) = 0

That means each row, column, and diagonal will always adds up to 0.

3 + w + 1 = 0

w = -3-1

w = -4

w + y + 4 = 0

-4 + y + 4 = 0

y = 0

-1 + 4 + t = 0

3 + t = 0

t = -3

1 + h + t = 0

1 + h + (-3) = 0

h -2 = 0

h = 2

(Check the attached image for labeling)

Thus, complete the puzzle with the values accordingly

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The value of x is 10 yards. The given shape is a trapezoid.

What are trigonometry ratios?

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Draw a line parallel to the base.

Name the corner point of the shape.

Assume that ∠ADG = θ.

Consider △BDF:

BD = 6 + x

DF = 8 + 4.8 = 12.8 yrds.

The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.

cos θ = DF/BD

cos θ = 12.8 /(6+x)  .....(i)

Consider △CDE:

cos θ = DE/CD

cos θ = 8/x  .....(ii)

Now equate equations (i) and (ii):

12.8 /(6+x) = 8/x

Cross multiply:

12.8 × x = 8(6+x)

12.8x = 48 + 8x

12.8x - 8x = 48

4.8x = 48

Divide both sides by 4.8:

x = 48/4.8

x = 10

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The value of x is 10 yards. The given shape is a trapezoid.

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Draw a line parallel to the base.

Name the corner point of the shape.

Assume that ∠ADG = θ.

Consider △BDF:

BD = 6 + x

DF = 8 + 4.8 = 12.8 yrds.

The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.

cos θ = DF/BD

cos θ = 12.8 /(6+x)  .....(i)

Consider △CDE:

cos θ = DE/CD

cos θ = 8/x  .....(ii)

Now equate equations (i) and (ii):

12.8 /(6+x) = 8/x

Cross multiply:

12.8 × x = 8(6+x)

12.8x = 48 + 8x

12.8x - 8x = 48

4.8x = 48

Divide both sides by 4.8:

x = 48/4.8

x = 10

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The cost of the shirts after the discount is $43.20.

A 5% tax adds an additional $2.16 so the total bill comes to  45.36.

Kayla does not have enough money to buy the three shirts.

The first step is to determine the total cost of the three shirts.

Total cost of the three shirts = cost of one shirt x total number of shirts

$18 x 3 = $54

Cost of the shirt after the sale = (1 - discount/100) x total cost of the shirt

(1 - 20/100) x $54

(1 - 0.2) x $54

= 0.8 x $54

= $43.20

Price after the tax : (1 + tax/100) x cost of the shirt after the discount

(1 + 5/100) x $43.20

(1 + 0.05) x $43.20

1.05 x $43.20 = 45.36

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The range of days to have 500 pounds left is 30 - 17.5 days

The range is the difference between the highest and lowest values in a set of numbers. To find it, subtract the lowest number in the distribution from the highest.

For example the range in the ages 10,15,11,12,18 of students in a class is 18-10 = 8

The maximum days to feed the giant panda if the giant panda feeds on 30pounds per day is 900/30 = 30days

but due to accident 125 pounds are not good

Therefore the new pound of bamboo = 900- 125 = 875 pounds

The range of pounds when the minimum pound is 500 = 875-500 = 375 pounds

therefore no of days on 375 pounds = 375/30 = 12.5

Therefore the range of days to have more thanq 500 pounds = 30-12.5 = 17.5 days

The range of days the zoo has more than 500 pounds of bamboo is 30 - 17.5days

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Answer: The solution to the system of equations is (1/3,-4/3).

Step-by-step explanation: Yes

Answer:

231 employees

Step-by-step explanation:

The ratio of men to women working for the company is 6 to 5, which means that for every 5 women working at the company, there are 6 men working at the company.

Since there are 105 women working at the company,

there are 6/5 * 105 = 126 men working at the company.

In total, there are 126 men + 105 women = 231 employees working for the company.

The complete program is

intInput = int(input("Integer between 32 and 126: "))

floatInput = float(input("Float input: "))

charInput = input("Character input: ")[0]

strInput = input("String input: ")

print(intInput, floatInput, charInput, strInput)

From the question, we have the following parameters:

The program that does this is:

intInput = int(input("Integer between 32 and 126: "))

floatInput = float(input("Float input: "))

charInput = input("Character input: ")[0]

strInput = input("String input: ")

print(intInput, floatInput, charInput, strInput)

See attachment for complete program and the output of the program execution

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5a) The total cost of buying the car, priced at $32,000 with the harmonized sales tax (HST) of 13%, is $36,160.

5b) Through the lease, the customer saves $14,760.

5c) The lease options for the lessee after returning the car include:

6a) The after-tax cost of the Honda Civic is $32,199.35.

6b) The value of the vehicle that needs to be financed is $26,199.35.

6c) The monthly payment will be $567.26 for 4 years.

6d) After four years, the total amount paid for the vehicle is $33,228.48.

A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.

A car purchase can also be financed through loans, like home mortgages.

Value of the car = $32,000

Harmonized Sales Tax (HST) = 13%

Cost of the car with HST = $36,160 ($32,000 x 1.13)

Down payment = $1,000

Financing part = $35,160 ($36,160 - $1,000)

Installment payments = 48

Periodic payments = $425

Total lease cost = $21,400 ($1,000 + 48 x $425)

Savings (advantages) from leasing = $14,760 ($36,160 - $21,400)

The value of the Honda Civic = $28,495

Harmonized Sales Tax (HST) = 13%

After-tax cost = $32,199.35 ($28,495 x 1.13)

Annual interest rate = 1.9% compounded monthly

Down payment = $6,000

Financing part = $26,199.35 ($32,199.35 -$6,000)

Financing period = 4 years

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 1.9%

PV (Present Value) = $26,199.35

FV (Future Value) = $0

P/Y (# of periods per year) = 12

C/Y (# of times interest compound per year) = 12

Results:

Monthly Payments (PMT) = $567.26

Sum of all periodic payments = $27,228.48

Total Interest $1,029.13

Total amount paid over 4 years = $33,228.48 ($27,228.48 + $6,000)

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Producing written and visual content for social media can be divided into two items that can be developed as a one-person small business in a little amount of time.

Social media is internet communication that enables real-time information sharing and customer interaction. Social networking can help you: better connect with your audience. building online networks sell and publicise the goods and services you offer.

Social media's effects on business

The social media presence of businesses in order to boost visibility, engagement, positioning, and value creation for their intended audience has been facilitated by the digital revolution.

In order to help businesses establish their strategy in the digital environment, marketing and advertising agencies can quickly produce digital media such posters and catalogues in addition to advertising text as their core offerings.

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If we compare the given values then we can find that database B is more likely to have a smaller standard deviation.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.

While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

Given that the values in database A are 0 from 100 and have a mean of 50 and Database B has entries from 49 to 51 and also has a mean of 50.

We are required to find the database whose standard deviation is lower.

Standard deviation measures the variation of values. It is calculated after finding the mean. The square of a standard deviation is known as a variance.

Database A has values from 0 to 100 and has a mean of 50. Because the values are somewhat very larger than 50 and database B has values from 49 to 51, there are more chances that the standard deviation of database B will have a smaller value than the standard deviation of database A.

Hence if we compare the given values then we can find that database B is more likely to have a smaller standard deviation.

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The length of PZ is 7 units.

According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the side midpoints.

Given:

As, Centroid is the point where all median of a Triangle intersect.

Here, we have centroid 'P'.

Now, using the property of Centroid that the Centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.

So, SP = 1/3 SZ => SZ = 3SP

and, PZ = 2/3 SZ => SZ = 3/2 PZ

Then, 3SP = 3/2 PZ

3(3.5) = 3/2 PZ

10.5 x 2 = 3 PZ

21 = 3PZ

PZ = 7 units

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The total cost of the item after the sales tax of 8 % is given by the equation t = 1.08p , where p is the initial price of the item

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost price of the item be represented as t

Let the initial cost price of the item be represented as p

Now , the sales tax percentage = 8 %

So , the equation will be

The total cost price of the item t = sales tax percentage ( initial cost price of the item ) + initial cost price of the item

Substituting the values in the equation , we get

The total cost price of the item t = 8 % ( p ) + p

On simplifying the equation , we get

The total cost price of the item t = ( 8/100 ) p + p

The total cost price of the item t = 0.08p + p

The total cost price of the item t = 1.08p

Hence , the equation is t = 1.08p , where p is the initial price of the item

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The requried other factors of the given function are (x - 2) and (x - 3).

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

here,
Given function, f(x) = x³-19x+30,
One of the factors of function is x = -5 or x + 5 = 0
Following the remainder theorem to determine the others factor,
= given function / one of the factor
=  [x³-19x+30] / [x + 5]
= (x - 2)(x - 3)

Thus, the requried other factors of the given function are (x - 2) and (x - 3).

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Answer: To find the percent increase in pay, you can use the following formula:

percent increase = ((new pay - old pay)/old pay) * 100

Plugging in the values given in the question, you get:

percent increase = ((11.75 - 10.50)/10.50) * 100

= (1.25/10.50) * 100

= 0.119047619 * 100

= 11.9047619%

Therefore, the percent increase in pay is approximately 11.9%.

Step-by-step explanation:

Yogurt production is affected by the production technological conditions.

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Using the values for x and y and substituting these values in the expression of equations provided, The answer is 23 and 1728.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.

When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated.

x=3 and y=4

[tex]x^2 + 2(x+y)\\=3^2 + 2* (3+4)\\=9+2*7\\=9+14\\=23[/tex]

[tex](xy)^3\\=(3*4)^3\\=12^3\\=1728[/tex]

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The length of 9/16 of an inch threaded section of the pipe indicates that the new length of the threaded section after 4/32 of an inch is trimmed off obtained by the difference between the fractions is; C. 7/16 of an inch

A fraction is the representation of only a part of a whole of an item in the form of a quotient, consisting of a numerator, being divided by a denominator.

The length of the threaded section of the pipe = 9/16 of an inch

The length of the threaded part trimmed off due to an error = 4/32 of an inch

The new length of the threaded section following the trimming off of 4/32 is therefore;

New length of the threaded section = 9/16 - 4/32

The value of the difference between the fractions is found as follows;

[tex]\dfrac{9}{16} -\dfrac{4}{32} =\dfrac{2 \times 9 - 4}{32} = \dfrac{14}{32}[/tex]

[tex]\dfrac{14}{32}=\dfrac{7}{16}[/tex]

Therefore;

[tex]\dfrac{9}{16} -\dfrac{4}{32} =\dfrac{7}{16}[/tex]

The new length of the threaded section will be 9/16 - 4/32 = 7/16

The correct option that indicates the new length of the threaded section is C. 7/16

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The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.

It is not always possible to interview or survey an entire population. Therefore, in many research studies, a portion of the population that is expected to represent the population is drawn and surveyed instead. The portion that is drawn is called the sample, and the method used to draw the sample is called the sampling method. Broadly, there are two types of sampling methods. The probability sampling method is a method wherein all members of the population have an equal probability to be selected to be included in the sample. The non-probability sampling method is a method wherein not all members of the population have an equal probability to be selected to be included in the sample. Instead, members are recruited into the sample based on the researcher's subjective and personal judgment.

Simple Random Sampling Method:

Simple random sampling method, sometimes abbreviated as SRS, is the purest form of probability sampling. Figuratively, it is like putting the names of the entire population in a hat and drawing each member from the hat with a blindfold. Therefore, every member of the population has an equal chance of being included in the sample.

Two-stage Cluster Sampling Method:

In the first stage of a two-stage cluster sampling method, the population is first divided into subgroups called clusters. For instance, the population is divided into subgroups based on geographic location. Unlike strata in stratified sampling, clusters are heterogeneous and each cluster is supposed to represent the heterogeneity of the population. These clusters are also known as primary sampling units or PSUs. In the second stage, the simple random sampling method is used to draw individuals from each of the PSUs to be included in the study sample.

Hence, The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.

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