f(x) = x^2 + 1. g(x) =. 5 - x

(F+ g)(x)

The area of the figure in the first, second, and third cases will be 76 square ft, 120 square cm, and 87.5 square in, respectively.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.

The area of the trapezoid will be calculated as,

A = 1/2(sum of parallel sides) x height

8. The area of the figure is calculated as,

A = 1/2 (6 + 6 + 7) x 8

A = 76 square ft

9. The area of the figure is calculated as,

A = 1/2 (8 + 4) x 4 + 8 x 12

A = 24 + 96

A = 120 square cm

10. The area of the figure is calculated as,

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

A = 37.5 + 50

A = 87.5 square in

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The scientific notation of the given number will be equal to 6.48 × 10⁻⁷. Hence, option C is correct.

A way to express numbers that are either too large or too little to be conveniently stated in decimal form is through scientific notation. It is also known as "scientific form" in Britain because researchers, mathematicians, and engineers frequently use it for intricate calculations involving large numbers.

As per the given information in the question,

The given number is,

0.000000648

As we move towards the right of the given point then the power will be in negative form.

So, it can also be written as,

6.48 × 10⁻⁷

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the answer is C:

6.48 × 10−7

The expression that is equivalent to −6(b − 7) is: B. -6b + 42.

Expressions that are equivalent to each other will give the same value when simplified and solved in their simplest forms.

Simply put, two expressions will be equivalent if they have the same number of terms or they will give the same quantity when you plug in the values of all the variables that are given in the expressions.

Given the expression, -6(b - 7), the steps below shows how we can simplify to determine the expression that is equivalent to it

-6(b - 7) [given]

Open the parentheses by using the distributive property of equality, which involves multiplying each of the terms within the parentheses by the term outside of the parentheses:

-6(b) -6(-7) [distributive property]

-6b + 42

-6b + 42 is the equivalent expression of -6(b - 7).

Thus, the answer is: B. -6b + 42.

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A. The equation that represents the balance is, 2x + 3 = 15.

B. Each box contains, x = 6 apples.

Given the problem above, to write an equation that would represent the balance, we would assume both sides of the balance are separated by the equal sign, "=".

Therefore, let the unknown number of apples in each box be be represented as x.

A. Apples in the two boxes would be 2x, the total apples on the left of the balance would be expressed as:

2x + 3

On the right, we have 15 apples, therefore, the equation that represents the balance is: 2x + 3 = 15

B. Solve to find x, the number of apples in each box:

2x + 3 = 15

2x + 3 - 3 = 15 - 3

2x = 12

x = 12/2

x = 6

This means that there were 6 apples in each box.

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Using the function f(x) = 7+ 4x, -13 is the value of f(-5).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

We might create a function with a set of persons as the domain X and a set of numbers as the codomain. For instance, if the codomain Y is the collection of whole integers, then define the function c so that its output, c(x), equals the number of offspring of every given x.

Four main categories may be used to classify different sorts of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.

Given that,

f(x) = 7 + 4x

now, putting the value of f(-5), we get -

f(-5) = 7 + 4(-5)

or, f(-5) = -13

Using the function f(x) = 7+ 4x, -13 is the value of f(-5).

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The probability that the next respondent questioned would say they plan to vote is 0.59.

What is probability?

The ratio of the number of favorable outcomes to the total number of outcomes of an event is defined as probability.

We know that the probability of an occurrence =the number of favorable outcomes divided by the total number of events.

Given that, 315 respondents stated they planned to vote, while 217 said they did not.

Now, the probability of voting is:

P(voting)=315(315+217)

= 315/532

= 0.59

As a result, the likelihood that the next respondent questioned would say they plan to vote is 0.59.

The probability that the next respondent questioned would say they plan to vote is 0.59.

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The expression that represent the area of the cabin for rectangular floor plan is 2w² + 5w.

What is the area of rectangular shape?

In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter.

Given that the length of a cabin is equal to 5 feet more than twice the width.

Assume that the width of the cabin be w.

Then the mathematical expression of twice the width is 2w.

Then the mathematical expression of 5 feet more than twice the width is 2w + 5.The length of the cabin is 2w + 5 feet.

The area of rectangular shape is product of length and width.

The area of the cabin is (2w + 5)w

Apply distributive property:

= 2w × w + 5 × w

= 2w² + 5w

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Answer:

Step-by-step explanation:

35/90 gets devided by 5

7/18

3/36 gets devided by 3

1/12

Answer:35/90 = 7/18

            3/36=1/12

Step-by-step explanation:

for 35/90 you divide both sides by 5 giving you 7/18 and 3/36 you divde both by 3 giving you 1/12.

Hope this helped

The three cut pieces should be 10 inches, 20 inches, and 40 inches  for the shortest, middle-sized and longest respectively

This is a word problem. We need to understand the sentence in order to translate it correctly.

To find the length of each of the three cut pieces, we can use the given information to set up a system of equations.

Let L, M and S be the length of the longest, middle-sized and shortest piece respectively

So we can set up the following equation:

L = 2M

S = M-10

L + M + S = 70

2M + M + (M - 10) +  = 70

We can combine like terms to get:

4M - 10 = 70

4M = 80

We can divide both sides by 4 to get:

M = 20

Therefore, the length of the middle-sized piece is 20 inches.

Since L = 2M

L =  2 × 20 inches = 40 inches.

Since S = M - 10

S = 20 - 10 = 10 inches.

Therefore, the three cut pieces should be 10 inches, 20 inches, and 40 inches for the shortest, middle-sized and longest respectively

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The parking cost is the function of the amount of time the car is parked and for 1 hour the cost of parking is $3 with a maximum amount of $12 for parking. The correct statements are C and D.

A function is a relationship between the dependent and independent variables. The independent variables are function inputs, while the dependent variables are function outputs. The value of a dependent variable is determined by the input.

Here in the graph, the cost of parking is varying with time. It means that the cost of parking is dependent on the time of parking but the maximum amount for parking is $12 for any number of hours of car parking.

Hence, the correct statements are C and D.

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Answer:

0.41 years

Step-by-step explanation:

940 hours is equivalent to 0.41 years. When rounded to the nearest hundredth, that would be 0.00 years. It is not possible to convert hours directly to years because they are different units of time measurement. Years are a measure of the time it takes for the Earth to orbit around the Sun, while hours are a measure of time within a day. To convert hours to years, you would need to know the number of hours in a year, which can vary depending on the number of days in the year and the number of hours in a day.

Answer:

Hi!

I think the answer you might be looking for is 0.11

I hope this helped you :)

Answer:

QT = 108 m

Step-by-step explanation:

the diagonals of a rectangle are congruent and bisect each other, so

QS = PR = 216 , then

QT = [tex]\frac{1}{2}[/tex] QS = [tex]\frac{1}{2}[/tex] × 216 = 108 m

Answer: 108

Step-by-step explanation:

diagonals of a rectangle are equal in length

∴ PR = QS = 216

Diagonals of a rectangle bisect each other

=> QT = QS = [tex]\frac{QS}{2} \\= > \frac{216}{2}\\ = 108[/tex]

The slope of the linear relationship is 15.

Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run"). The slope of a line tangent to a function's graph in differential calculus is determined by the derivative of that function and serves as a representation of the function's instantaneous rate of change with regard to changes in the independent variable. The slope of a tangent line in the graph of a position function, which plots the distance travelled by an object against the passage of time, corresponds to the object's instantaneous velocity.

Given

A linear relationship is given.

y₁ = -9

y₂ = 6

x₁ = 0

x₂ = 1

Slope:

m = y₂ - y₁/x₂ - x₁

m = 6 + 9/1 - 0

m = 15/1

m = 15

The slope of the linear relationship is 15.

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Answer:

Slope = 15

Step-by-step explanation:

Now we have to,

→ find the slope of linear relationship.

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Coordinates we use from table,

→ x1 = 0, y1 = -9

→ x2 = 1, y2 = 6

Then the required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (6 -(-9))/(1 - 0)

→ m = (6 + 9)/1

→ m = (15)/1

→ [ m = 15 ]

Hence, the required slope is 15.

There are 50 two-point questions and 10 five-point questions on the test.

What is a linear equation in two variables?

A linear equation in two variables is an equation that can be written in the form Ax + By = C, where A, B, and C are constants and x and y are variables. The graph of a linear equation in two variables is a straight line, and the equation represents a linear relationship between the variables.

To solve this problem, you can use the fact that the total number of points on the test is 150 and that some of the questions are worth two points and some are worth five points.

Let x represent the number of two-point questions on the test, and let y represent the number of five-point questions on the test.

We can set up the following system of equations to represent the given information:

2x + 5y = 150

x + y = 60

To solve this system, you can use the substitution method. First, solve the second equation for y:

y = 60 - x

Substitute this expression for y into the first equation:

2x + 5(60 - x) = 150

This simplifies to:

2x + 300 - 5x = 150

Combine like terms:

-3x = -150

Divide both sides by -3:

x = 50

Substitute this value for x into the second equation to find the value of y:

y = 60 - 50 = 10

Hence, there are 50 two-point questions and 10 five-point questions on the test.

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Perimeter of triangle is P= 18x+16v-2w.

How do triangles work?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a single point.

                      The triangle's three angles add up to a total of 180 degrees.

.

side lengths of a triangle are (9v-7w),(7v+10x),(8x+5w) centimetres.

 We know that perimeter of the triangle is sum of all the three sides.

So here perimeter p= addition of all sides of a triangle.

Therefore ,

      P = ( 9v - 7w) + (7v + 10x ) + ( 8x + 5w)

          = 9v - 7w + 7v + 10x + 8x + 8w

           = 18x + 16v - 2w

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The addends 4, _ 37 + 1,28_ is completed so there will be need to regroup to add.

the addends. 4, 837 + 1,287

the sum is 6124

Regrouping refers to rearranging numbers into groups according to place value to assist kids in handling greater numbers.

When performing operations like addition and subtraction on two-digit integers or bigger, regrouping is the process of forming groups of tens. Regrouping refers to the process of performing an operation by rearranging groups in place value.

Using regrouping for the addition problem

addend 4 8 3 7

addend  1 2 8 7

sum                 4

                    1      regrouped to tens column

addend 4 8 3 7

addend  1 2 8 7

sum              2 4

                1         regrouped to hundreds column

addend 4 8 3 7

addend  1 2 8 7

sum           1 2 4

             1              regrouped to thousands column

addend 4 8 3 7

addend  1 2 8 7

sum        6 1 2 4

the sum is 6124

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Presence: a statistical issue, refers to the finding that a systematic relationship exists between the two variables of interest in the population.

The above statement is False.

Presence refers to the finding that there is a systematic relationship between two variables in the population of interest.

Direction means knowing if the relationship is positive or negative.

Strength means knowing how long the relationship will last.

Systematic relationship is also known as Covariance. Covariance is a statistical term that refers to the systematic relationship between two random variables such that changes in the other reflect changes in one.

The relationship between probability and statistics usually falls into one of three categories: deterministic, random, or statistical. Statistical relationships are a hybrid of deterministic and random relationships.

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Answer:

• Statement of the given problem,

⚫ A man spends 70% of his income and saves Rs. 2550. What is his income?

According to above data,

⚫ the required income of the

given man

= 2550/(1 - 70/10)

☐ = 2550/0.30

= 8,500 (Rs) [Ans]

The proportion we get is 0.291 and that matches up with our first choice that we see.

A proportion simply means the amount or quantity of a thing present in another thing taken as whole.

The main purpose of stating stuff in proportions is to compare shares. If 2 people receive shares in a 1:1 proportion, it means they have exactly equal shares. If 2 people invest in something and one partner invests $3 for every $2 the other invested, the major partner would expect the profits to be divided 3:2 in their favor.

This issue informs us that a town's residents were polled by an elected official to see how satisfied they were with the town's services. Both homeowners and renters were included in the survey. The following charts show the percentage of respondents that are unsatisfied with city services. In order to calculate the percentage of surveys with low satisfaction, we only need to consider the third column to the right, which is labeled "low satisfaction," and the number we are interested in is the 1, which corresponds to the row labeled "total," because it represents the total number of survey respondents who have low satisfaction, whether or not they are home owners or renters. This number is 23 points.

But that only represents the whole population of those with low levels of satisfaction. We can find the total number of respondents in the cross section between the total column and the total row, giving us 110 points. We wish to multiply that total for the low level by the entire number of respondents. Therefore, if we want that proportion right away, we need divide 23 by 110 points. When we round off to four decimal places, the result is 0.291, which corresponds to our initial option that we see.

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Answer:

A - 0.2091

Step-by-step explanation:

I took it

The best option is to Convert it to a decimal and multiply is the best way to describe rate in simple interest formula. The correct option is A.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.

Simple Interest (S.I.) is a method for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.

Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount. The correct option is A.

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Answer:

f(20) = 10

Step-by-step explanation:

Answer:

6400

Step-by-step explanation:

We have 1 + 3 + 5 + ... + 155 + 157 + 159.

We can use Gauss's strategy.

Since we are adding 80 numbers, there are 40 pairs. Each pair adds up to 1 + 159 = 160. (Notice that 3 + 157, 5 + 155 = 160)

Thus, because there are 40 pairs and each pair adds up to 160, we have 160 * 40 = 6400.

I hope this helps!

The idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population is referred to as Alternative Hypothesis.

Alternative Hypothesis:

In statistical hypothesis testing, the alternative hypothesis is one of the statements proposed in the hypothesis test. In general, the purpose of a hypothesis test is to show that, given the conditions, there is sufficient evidence to support the reliability of the alternative hypothesis rather than the sole assertion in the test (the null hypothesis) . It is usually consistent with research hypotheses because it is generated from literature reviews, previous studies, etc. However, in some cases the research hypothesis is consistent with the null hypothesis.

In statistics, the alternative hypothesis is often denoted by Ha or H1. Hypotheses are formulated to compare them in statistical hypothesis testing. In the field of inferential statistics, two competing hypotheses can be compared for their explanatory and predictive power.

For scalar parameters, there are four main types of alternative hypotheses:

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Answer:

15 c m.

Step-by-step explanation:

120 divided by 8 =15

Answer: Mode: 180

Quartiles:

Q1 --> 149

Q2 --> 165.5

Q3 --> 178

Mean: 162.944....

Median: 165.5

Step-by-step explanation:

Answer:191

Step-by-step explanation:

65x2=130

130+61=191

Work is done by A in one day [tex]$=\frac{1}{15}$[/tex]

By B [tex]$=\frac{1}{12}$[/tex]

[tex]\mathrm{C}=\frac{1}{20}[/tex]

boards could be used for his project

Together in 1 Day [tex]\text { Together in } 1 \text { Day }=\frac{1}{15}+\frac{1}[/tex][tex]{12}+\frac{1}{20}=\frac{4+5+3}{60}=\frac{12}{60}=\frac{1}{5}[/tex]

2 days work [tex]$=\frac{2}{5}$[/tex]

Remaining work [tex]$=1-\frac{2}{5}=\frac{3}{5}$[/tex]

one day work of [tex]$\mathrm{A}, \mathrm{B} \Rightarrow \mathrm{A}+\mathrm{B}=\frac{1}{15}+\frac{1}{12}=\frac{4+5}{60}=\frac{9}{60}=\frac{3}{20}$[/tex]

[tex]$$\begin{aligned}& (A+B) \text { work for } t \text { days }=\frac{3}{20} t=\frac{3}{5} \\& t=4 \text { days }\end{aligned}$$[/tex]

A and B will complete the work in 4 days.

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