Write the statement "the sum of a number and 10.7 is at most −3.2" as an inequality.

−3.2 + b > 10.7
−3.2 + b < 10.7
b + 10.7 ≥ −3.2
b + 10.7 ≤ −3.2

The solution to the following system using substitution is (2,1).

What is system of equations ?
Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

[tex]$$\left[\begin{array}{c}y=-4 x+9 \\y=3 x-5\end{array}\right]$$[/tex]

Substitute y=3 x-5

[3 x-5=-4 x+9]

Isolate x for 3 x-5=-4 x+9: x=2

For y=3 x-5

Substitute x=2

[tex]y=3 \cdot 2-5[/tex]

Simplify

y=1

The solutions to the system of equations are:

y=1, x=2

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An n x 11 matrix can have a maximum of n different eigenvalues, whereas a 2 x 2 matrix can only have a maximum of two. Below, there is a detailed explanation of this.

a collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

The study of matrices is the main focus of the mathematical field known as matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics.

solution of a 2 x 2 matrix is in given form:

|A - λI| = 0

here,

A =  eigenvalue

I = identity matrix

now

|A - λI| = (a11 - λ)

(a22 - λ) - a12a21 = 0

the solutions of above equation are  2 x 2 matrix's eigenvalues.

just like this, a matrix of size n by n may have up to n different eigenvalues as its characteristic equation is a polynomial of nth degree with up to n roots (i.e. n eigenvalues). all due to the equation form: |A - I| = 0, where A is an eigen and I is an identity matrix.

by expanding the determinant:

|A - I| =  (-1)

having coefficients c1, c2,..., cn, having sum = zero.

which is nth degree polynomial equation consisting of n possible solutions, that are basically n x n matrix's eigenvalues .

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In the given equation y = 3x + 12, x is the independent variable and y is the dependent variable.

A mathematical connection in which the values of one or more independent variables uniquely determine the values of a dependent variable.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equation is y = 3x + 12. Here in the equation, the value of the y variable is dependent on the value of x. Then the x variable is independent and the y variable is dependent and depends upon the x variable.

Therefore, in the given equation y = 3x + 12, x is the independent variable and y is the dependent variable.

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a) [tex]f(-4)[/tex] is equal to the output when [tex]x=-4[/tex]. Therefore, [tex]f(-4)=-7[/tex].

b) [tex]f(-3)=-11[/tex]

c) [tex]f(3)=-3[/tex]

d) [tex]f(4)=-1[/tex]

On solving the provided question, by substitution method we got that y=1.43 and x=o.65

To solve systems of linear equations, use the algebraic technique of substitution. The name of the technique implies that it involves substituting the values of variables from one equation into another.

x=cakes , y=donuts

3x+6y=$10.14 ------ eqt.1

4x+4y=$8.32 ------ eqt.2

solve eqt.1 for "y"

y=1.43

x=o.65

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The correct question is

Ellie and Mary went to the Stef bakery. Ellie bought 3 cakes and 6 filled donuts for ​$10.14. Mary bought 4 of each for ​$8.32. What is the price of each type The price of a  is The price

The system of equations to model this situation is given by;

x + y = 461

3x + 4y = 1624

The school sold 220 students tickets and 241 adult tickets.

let

Number of students tickets = x

Number of adults tickets = y

x + y = 461

3x + 4y = 1624

From (1)

x = 461 - y

Substitute into (2)

3x + 4y = 1624

3(461 - y) + 4y = 1624

1383 - 3y + 4y = 1624

- 3y + 4y = 1624 - 1383

y = 241

Substitute into (1)

x + y = 461

x + 241 = 461

x = 461 - 241

x = 220

In conclusion 220 students tickets and 241 adults tickets were sold.

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[tex](2x^2 + 5x + 7) + ( - 1,022 - 7x + 1)\\\\2x^2 + 5x + 7 - 1,022 - 7x + 1\\\\2x^2 + 5x + 7 - 1,022 - 7x + 1\\\\2x^2-2x-1,014[/tex]

Answer:

wednesday: 4

thursday: 32

Step-by-step explanation:

Answer:

[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball &4\% & 17\%& 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&78\%&22\%& 100\%\\\cline{1-4}\end{array}[/tex]

Step-by-step explanation:

Create a blank frequency table:

[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & & &\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & &\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]

If 79% of the participants played pickleball, then 21% of the participants do not play pickleball.

Input these percentages into the table:

[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & & & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & & 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]

Of those who play pickleball, 6% are female.

Therefore, of those who play pickleball, 94% must be male.

The total percentage of those who play pickleball is 79%, so find 6% and 94% of 79%:

[tex]\begin{aligned}\textsf{Plays pickleball (female)}&=6\% \; \sf of \; 79\%\\&=0.06 \times 0.79\\&=0.0474\\&=5\%\; \sf (nearest\;percent)\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Plays pickleball (male)}&=94\% \; \sf of \; 79\%\\&=0.94 \times 0.79\\&=0.7426\\&=74\%\; \sf (nearest\;percent)\end{aligned}[/tex]

Input the found percentages into the table:

[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & & 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]

Of those who do not play pickleball, 21% are male.

Therefore, of those who do not play pickleball, 79% must be female.

The total percentage of those who do not play pickleball is 21%, so find 21% and 79% of 21%:

[tex]\begin{aligned}\textsf{Does not play pickleball (male)}&=21\% \; \sf of \; 21\%\\&=0.21 \times 0.21 \\&=0.0441\\&=4\%\; \sf (nearest\;percent)\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Does not play pickleball (female)}&=79\% \; \sf of \; 21\%\\&=0.79 \times 0.21\\&=0.1659\\&=17\%\; \sf (nearest\;percent)\end{aligned}[/tex]

Input the found percentages into the table and calculate the column totals:

[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball &4\% & 17\%& 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&78\%&22\%& 100\%\\\cline{1-4}\end{array}[/tex]

Answer:

c

Step-by-step explanation:

i took the test :)

The speed of a cyclist rode 3.75 miles in 0.3 hours is 0.36 hours.

Given that, a cyclist rode 3.75 miles in 0.3 hours.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

A) We know that, speed =Distance/Time

Now, speed =3.75/0.3

= 12.5 miles per hour

B) Here, distance =4.5 miles and rate =12.5 miles per hour

Now, 12.5 =4.5/Time

⇒ Time =4.5/12.5

⇒ Time =0.36 hour

Therefore, the speed of a cyclist rode 3.75 miles in 0.3 hours is 0.36 hours.

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Then the enrollment change rate from 2010 to 2020 is -52.2%.

Here ,

Formulate 860 - 1510 / 1510 based on the given condition.

We have calculate the difference or sum = -650/1245

By converting a fraction to a decimal we get, = -0.52208

we have to multiply a number by its numerator and denominator by 100,

We get,

= -0.52208*100/100

-52.208/100 is the product or quotient.

Hence ,

In 2010, a school had 1510 students enrolled. In 2020, there will be 860 students enrolled. Then the enrollment change rate from 2010 to 2020 is -52.2%.

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The next time Maria will do both workouts on the same day is 15 days

Find the lowest common multiple (LCM) for both weight days and long-run days

3 = 3 , 6, 9, 12, 15, 18, 21

5 = 5, 10, 15, 20, 25, 30

The lowest common multiple (LCM) for both weight days and long-run days is 15

Therefore, Maria will do both workout again in 15 days time.

Complete question:

The chart shows Maria's workout schedule. Today she worked out with weights and then had a long run. When is the next time Maria will do both workouts on the same day? Weights every 3 days and long run every 5 days

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S = 25x + 250 is the equation models the food truck's average sales in dollars, S, in terms of the price for taco, x.

Equation is a declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws. also see equation system.

Given

A food truck vendor averages 150 tacos sold when the price per taco is $1.

A study shows that the average number of tacos sold will increase by 25

tacos for every $1 that the price per taco is lowered.

The calculation needed to determine which equation best represents the food truck's average sales in dollars, s, in terms of the price per taco, x, is as follows:

S = 25x + 250

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The correct option using linear equations is [tex]y\leq 2.85x[/tex].

What are linear equations?

A linear equation is one with variables of power 1, such as ax+b = 0, where x is the variable and a and b are fundamental values. Equations are claims that two mathematical expressions comprising one or more variables are equal. The term "linear equation" refers to an equation where the greatest power of the variable is one.

Since the budget is y, the total amount spent on fuel must be less than or equal to the budget. Since it is $2.85 per gallon, the correct equation would be [tex]y\leq 2.85x[/tex].

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490

472 <490<500

it fits the criteria

Answer:

x= 1.7

y= -1.9

Step-by-step explanation:

I will be using substitution method

in the first equation i will isolate y

3x-y=7

   +y +y

3x=7+y

-7. -7

3x-7=y

now since y is equal to 3x-7 we can put 3x-7 where y is in the second equation

4x+2(3x-7)=3

4x+6x-14=3

combine like terms

10x-14=3

   +14 +14

10x=17

/10. /10

x= 1.7

now we fill in x in any equation to find y

i will put it into the first one

3(1.7)-y=7

5.1-y=7

-5.1.  -5.1

-y=1.9

/-1.  /-1

y= -1.9

hopes this helps please mark brainliest

The right response is (b), as it increases the minimum sample size required to ensure a given margin of error.

When a tiny sample of data from a relatively large population is estimated, this is what is meant by the term "margin of error" .  The standard deviation, sample size, and desired confidence level are often the factors that control the margin of error.

calculation

Let's take a look at the values in the supplied statement to discover the missing term.

the population's standard deviation is where

m stands for "Margin of Error," and Z stands for "Empirical Value of Z-Score" at a specific confidence level.

As a result, the recommended minimum sample size for a particular degree of confidence is

⇒ (Z×σ)²/m²

The minimal sample size is directly correlated with the population's standard deviation, as shown by the calculation above.

Therefore, when the population "standard deviation" increased, the minimal sample size needed would also "rise."

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Answer: None of these

Step-by-step explanation:

The slope of the graph of [tex]f[/tex] is [tex]\frac{-224-64}{-2-1}=96[/tex].

Using point-slope form,

[tex]f(x)-64=96(x-1)\\\\f(x)-64=96x-96\\\\f(x)=96x-32[/tex]

Therefore, none of the options are correct. This can be confirmed by an online calculator.

Answer:

If Gonga's health insurance deductible is $5,500 and her medical bills for the year total $50,000, she will be required to pay the first $5,500 of her medical bills out of pocket.

Step-by-step explanation:

This means that she will be required to pay a total of $5,500 out of pocket on her annual medical bills. After she has paid this amount, her health insurance will cover the remaining costs of her medical bills up to the limit of her policy.

Answer:

$5,500

Step-by-step explanation:

You can mail small things weighing 70 pounds or less to any location in the US for a set price using USPS Small Flat Rate boxes. The cost of a USPS Small Flat Rate package is only $8.45.

The United States Postal Service (USPS), often known as the Post Office, U.S. Mail, or Postal Service, is a separate executive branch agency that is in charge of delivering postal service across the United States, including its associated states and insular territories.

It is one of the few governmental organizations that the US Constitution expressly grants authority to. 516,636 career employees and 136,531 non-career employees work for the USPS as of 2021.

The first postmaster general of the United States Postal Service, Benjamin Franklin, was appointed in 1775 during the Second Continental Congress. He also held a comparable role for the colonies of the Kingdom of Great Britain.

With the passing of the Postal Service Act in 1792, the Post Office Department was established.

Hence, A USPS Small Flat Rate box only costs $8.45.

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Answer:

2x+3

Step-by-step explanation:

Combine like terms.

7x-2x-3x=2x

Then add 3 to expression

Answer:

2x+3

Step-by-step explanation:

we know that we would have to add up all the commen variables first to give the most simplified answer

first take the -2x and add it with the -3x. you get -5x.

than take the -5x and add it to the 7x. you will grt 2x

lastly add them up and you get 2x+3

The smallest number of bags the groundskeeper must buy to cover the field is 165 bags.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr²

A groundskeeper needs grass seed to cover a circular field, 290 feet in diameter. A store sells 50 pound bags of grass seed. One pound of grass seed covers about 400 square feet of field.

The smallest number of bags the groundskeeper must buy to cover the field.

Diameter of the field = 290 feet

Radius = 145 feet

Area of the circular field = πr²

= 3.14 ×145²

= 66018.5ft²

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Answer:

340

Step-by-step explanation:

550 - 210 = 340

Answer:

1/14 xy (x² + 8y)

Step-by-step explanation:

common factor of the number = 1/14

common factor of letter part = xy

x³ : x = x²

y : y = 1

1/14 xy (x²

x : x = 1

y² : y = y

1/14 xy (x² + 8y)

Answer:

Step-by-step explanation:

The actual length of the explanation is 6 meters.

Answer:x=8

Step-by-step explanation:

3x/2-5=7

Move all terms not containing x to the right side of the equation by adding 5 to both sides

3x/2-5+5=7+5

3x/2=12

Multiply both sides of the equation by 2/3 to isolate x.

3x/2*2/3=12*2/3

x=24/3

x=8

Answer: x= 8

Step-by-step explanation:

3x/2-5=7

3x/2 = 12

3x = 24

x= 8

If you can, please give me a Brainliest, thank you!

As per the concept of compound interest, it take 62.915 years for the account to earn $7500

Compound interest:

The general formula to calculate the compound interest is written as,

A = P(1 + r/n)^nt

where

A = Accrued amount (principal + interest)

P = Principal amount

r = Annual nominal interest rate as a decimal

n = number of compounding periods per unit of time

t = time in decimal years;

Given,

Compounding frequency = Quarterly

Interest rate = 1.75%

Opening balance = $2500

Final amount = $7500

Now, we have to calculate the time time for the person to achieve the final amount,

First, convert R as a percent to r as a decimal

r = R/100

r = 1.75/100

r = 0.0175 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(7,500.00/2,500.00) / ( 4 × [ln(1 + 0.0175/4)] )

t = ln(7,500.00/2,500.00) / ( 4 × [ln(1 + 0.004375)] )

t = 62.915 years

Therefore, the  time required to get a total amount of $7,500.00 with compounded interest on a principal of $2,500.00 at an interest rate of 1.75% per year and compounded 4 times per year is 62.915 years.

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Answer:

is there a graph available????

Step-by-step explanation:

Therefore , large of a sample would be required in order to estimate the mean per capita income will be $3,838.

You can assess the degree to which the distribution of your data conforms to that predicted underneath the null hypothesis of the statistical test you are just using by utilizing a test statistic. The data distribution, which is determined by the confidence interval and deviation from the central tendency of each observation, represents the frequency of each observation.

Here,

First step is to find z 80% confidence level

At 80% confidence level the z will be:

α/2 = 1 - 80% = 1 - 0.80 = 0.20

α/2= 0.20 / 2 = 0.01

Zα/2= Z0.01= 1.28 from z table

Now let calculate the Sample size using this formula

Sample size = n= [( Z[tex]\alpha[/tex]/2* σ ) / E]^2

Let plug in the formula

n = (1.28*12.1/0.25)^2

n= 3,838.05

n=3,838.(Approximately)

Therefore , large of a sample would be required in order to estimate the mean per capita income will be $3,838.

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It takes 43 hours to reach final depth of -132 feet with rate of change 72 feet per day.

Depending on the context, several phrases may be used to describe rate of change. For instance, acceleration/deceleration is the rate of change with respect to speed or velocity. The slope of the line of best fit determines the pace of change in statistics and regression modeling. It is the population growth rate. Rate of change is frequently referred to as momentum in the financial markets.

The formula [tex]R=\frac{D}{T}[/tex], or rate of change equals the distance traveled divided by the time required to do so, can be used to approach rate of change problems in general. The term "distance" can be changed to another depending on the context of the issue, such as change in worth or price.

Given,

Rate of change=72 feet per day =3 feet per hour.

Final depth=132feet;

Time taken= [tex]\frac{Final}{Rate}=\frac{132}{3} =43hours\\[/tex].

It takes 43 hours to reach final depth of -132 feet with rate of change 72 feet per day.

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