Write an expressionNick has x toy race cars. This is one third of what Bob has. How many toy race cars does Bob have?

Answer:

g = 118°

k = 98°

h = 62°

m = 82°

Step-by-step explanation:

g = 118° (opposite angles)

k = 98° (opposite angles)

h + 118° = 180°

h = 180° - 118°

h = 62°//

m + 98° = 180°

m = 180° - 98°

m = 82°//

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer: \(cosx =- \sqrt{ 1 - sin^2x}\)

Step-by-step explanation:

Generally speaking; \(cos^2x + sin^2x = 1\)

rearranging this gives us all sorts of cool things.

for now, we will use: \(cosx = \sqrt{ 1 - sin^2x}\)

This however, is general.

In the third quadrant, cosine is negative. So cosx in QIII will be:

\(cosx =- \sqrt{ 1 - sin^2x}\)

and thats the answer :)

Let's solve the equation for v to identify the expressions:

Therefore the equivalent expressions are D and E

Answer:

you will need a map scale

Part 1:

The PMT Function in Excel is used to calculate the repayment of a loan. The PMT Function calculates the amount of loan repayment.

The generic formula for PMT Function is as follows:

=PMT(rate,nper, pv,[fv],[type])

Now let us understand each of the components of the PMT Function:

rate: The interest rate for the loan

per: Total number of payments of the loan repayment.

PV: Present Value of  a series of Future Payments ie. the Principal of the Loan

VF: The future value of the loan or the cash balance that an individual wants to obtain after the loan is paid. This can be omitted, if omitted its value will be taken as zero ie the value of the loan in the future will be zero.

Type: The numbers 0 and 1 indicate when the payment of the loan is due. This is optional and can be omitted If it is 0 or omitted then payments are considered to be due at the end of the period(ie. end of month or quarter or end of year as the case may be). If it is  1 then payments are considered to be due at the beginning of the period((ie. beginning  of month or quarter or end of the year as the case may be)

Part 2:

The Excel IPMT Function can be used to calculate the interest portion of loan repayment for a given period.

The generic formula for Excel IPMT Function is as follows:

=IPMT(rate,per,nper,pv,fv,[type])

Now let us understand each of the components of the IPMT Function:

rate: The interest rate for the loan

per: The period for which the interest payment has to be determined and should range between 1 and per

per: Total number of payments of the loan

PV: Present Value of  a series of Future Payments ie. the Principal of the Loan

VF: The future value of the loan repayment or the cash balance that an individual wants to obtain after the loan is paid . This can be omitted, if omitted its value will be taken as zero ie the value of the loan in the future will be zero.

Type: The numbers 0 and 1 indicate when the loan repayment is due. This is optional and can be omitted If it is 0 or omitted then payments are considered to be due at the end of the period(ie. end of month or quarter or end of year as the case may be). If it is  1 then payments are considered to be due at the beginning of the period((ie. beginning of the month or quarter or end of the year as the case may be).

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Answer:

y = - x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (4, - 3) ← 2 points on the line

m = \(\frac{-3-1}{4-0}\) = \(\frac{-4}{4}\) = - 1

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = - x + 1 ← equation of line

Answer:

c would be your answer:)

Answer:

D. x=-2

Step-by-step explanation:

Pluggy chuggy those answer choices and -2 is the only one that works. The rest of the answer choices are extraneous. Therefore the answer is -2 and can not be infinitely many solutions since B and C do not work.

Hello!

3x + 4 = 1

3x + 4 - 4 = 1 - 4

3x = -3

3x/3 = -3/3

x = -1

The solution of the equation 3x + 4 = 1 is -1.

The answer is:

C) x = -1

Work/explanation:

To solve this equation, I subtract 4 from each side:

\(\sf{3x+4=1}\)

Subtract :

\(\sf{3x=-3}\)

Divide each side by 3:

\(\sf{x=-1}\)

Hence, C is correct.

f(x+1):-

f(-x)

LHS≠RHS

On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:

x = 1.49y

-1.49y + x = 0

-149y + 100x = 0

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The linear equation in the required form is: x - 1.49y = 0

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b

Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."

Using this information, we can write:

x = 1.49y

To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.

Subtracting 1.49y from both sides, we get:

x - 1.49y = 0

So the linear equation in the required form is:

x - 1.49y = 0

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The value of x is 58.51 degree.

We have,

Perpendicular= 8

Base = 4.9

Using trigonometry

tan x = Perpendicular/ Base

tan x = 8/4.9

tan x= 1.63265306122449

x = 58.51253064

Thus, the value of x is 58.51 degree.

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Answers to ratios are first one is option B, second one is option A and third one is option C.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

1. Ratio of smoothie size to mangos used for Kim = 8 : 1

Ratio of smoothie size to mangos used for Bri = 24 : 3

                                                                             = 8 × 3 : 1 × 3

                                                                             = 8 : 1

Ratio of smoothie size to mangos used for Angela = 32 : 4

                                                                                    = 8 × 4 : 1 × 4

                                                                                    = 8 : 1

So the ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

So the answer is option B.

2. Ratio of width to length of larger canvas = 4 : 6 = 2 : 3

Ratio of width to length of smaller canvas = 2 : 3

So the painting's width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

So the answer is option A.

3. Ratio of students who prefer free time at the beginning of the class to students who prefer free time at the end of the class is 12/19

Total students = 12 + 19 = 31

Out of 31 students, 12 students prefer free time at the beginning of the class and 19 students prefer free time at the end of the class.

So the answer is option C.

Hence the answers on ratios are done.

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Answer: 7725.5775

Step-by-step explanation:

d=27

r=d/2=27/2=13.5

the volume of the spherical balloon= 3.14*r^3

                                                       = 3.14*(13.5)^3

                                                       = 7725.5775

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We want to calculate the volume of the spherical shell of chocolate.

The chocolate shell is spherical with a thickness of 0.5cm

Volumes of spherical shells can be calculated with the formula;

The outer diameter is 8cm. The outer radius is therefore 4cm

The inner diameter is 8-2(0.5)=7cm. The inner radius is therefore 3.5cm

Therefore, we can find the volume of the chocolate shell as;

Therefore,

Answer:

In order to find the answer in years:

5 years and 6 month .

5 year is already in year .just the thing to do is convert 6 month into years..

:6÷12=0.5 years

so the answer is 5.5 years.

:5+0.5=5.5 years

Answer:

5.5 years or 5 1/2 years

Step-by-step explanation:

6 months = 1/2 of a year

Hope I helped!

The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.

The figures in the image are right triangles.

A)

angle D = 17 degree

Adjacent to angle D = 14 mm

Opposite to angle D = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( 17 ) = x/14

x = tan( 17 ) × 14

x = 4.3mm

B)

angle Z = 82 degree

Adjacent to angle Z = 43.1 m

Hypotenuse = x

Using trigonometric ratio,

cosine = adjacent / hypotenuse

cos( 82 ) = 43.1 / x

x = 43.1 / cos( 82 )

x = 309.7 m

Therefore, the measure of x is 309.7 meters.

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Answer: As we know that the formula of outlier is

IQR = Q3 - Q1

= 52 - 32

= 20

52 + 1.5(20) = 82...

so anything above 82 is an outlier

now

32 - 1.5(20) = 2.

..anything below 2 is an outlier

so...the 83 is outlier

so correct option is D

hope it helps

Step-by-step explanation:

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

$90

Step-by-step explanation:

Off course the school district will pay in salary by $90 less.

a) the expected number of smokers is 21.6, and

b) the standard deviation of the number of smokers is approximately 4.21.

a) To find the expected number of smokers, you need to multiply the probability of a student being a smoker (18% or

0.18) by the number of students surveyed (120). So, the expected number of smokers is:

Expected number of smokers = 0.18 × 120 = 21.6

b) To find the standard deviation of the number of smokers, you can use the formula for the standard deviation of a

binomial distribution, which is:

Standard deviation = √(n × p × (1 - p))

where n is the number of students surveyed, p is the probability of a student being a smoker, and (1 - p) is the

probability of a student not being a smoker. Plug in the values:

Standard deviation = √(120 × 0.18 × (1 - 0.18)) = √(120 × 0.18 × 0.82) ≈ 4.21

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The answer will be 0. 10 >  0. 01 . Option B

Given the values as;

Turn the values into proper fractions

a. 0. 10 = 10/ 100

Reduce to simpler terms

= 10/ 100

= 1/ 10

b. 0. 01 = 1/ 100

a = 1/ 100

b = 1/ 100

This means that both decimals are not of  equal proportion and thus a is greater than (>) b

Thus, the answer will be 0. 10 >  0. 01 . Option B

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Answer:

120,000 ft^3

Step-by-step explanation:

step 1: 20ft times 150ft is 3000ft.

step 2: 3000ft times 40ft^3 is 120,000ft^3

The inverse οf the given functiοn is  (5x+1)/2.

An inverse functiοn is a functiοn that undοes the resuIts οf anοther functiοn. A functiοn g is the inverse οf a functiοn f when x=g(y) and y=f(x). In οther wοrds, appIying f and then g is the same as dοing nοthing. In terms οf the cοnnectiοn between f and g, this can be written as g(f(x))=x.

Here, we have

Given: f(x) = (2x-1)/5

We have tο find the inverse οf the given functiοn.

f(x) = (2x-1)/5

y = (2x-1)/5

Interchange the variabIes.

x =  (2y-1)/5

SοIve fοr y

5x + 1 = 2y

y = (5x+1)/2

RepIace y with f⁻¹(x) tο shοw the finaI answer.

f⁻¹(x) = (5x+1)/2

Hence, the inverse οf the given functiοn is  (5x+1)/2.

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Answer:

\(5\frac{5}{8} \\\)

hope this is what you what.

9.3 ft³

use the rule:

\(\rightarrow \sf (\dfrac{V_1}{V_2} )= (\dfrac{h_1}{h_2} )^3\)

solve:

\(\rightarrow \sf (\dfrac{74\frac{2}{5} }{V_2} )= (\dfrac{10\frac{1}{3} }{5\frac{1}{6} } )^3\)

\(\rightarrow \sf (\dfrac{74\frac{2}{5} }{V_2} )= (2 )^3\)

\(\rightarrow \sf \dfrac{74\frac{2}{5} }{V_2} =8\)

\(\rightarrow \sf V_2 = \dfrac{74\frac{2}{5} }{8}\)

\(\rightarrow \sf V_2 = 9.3 \ ft^3\)

Answer:

Given:

\(\sf Height \ of \ Prism \ X = 10\frac13=\dfrac{(10 \times 3)+1}{3}=\dfrac{31}{3}\)

\(\sf Height \ of \ Prism \ Y = 5\frac16=\dfrac{(5 \times 6)+1}{6}=\dfrac{31}{6}\)

\(\sf Volume\ of \ Prism \ X = 74\frac25=\dfrac{(74 \times 5)+2}{5}=\dfrac{372}{5}\)

Prism X is a dilation of Prism Y.

⇒ Scale factor of dilation = height of Prism X ÷ height of Prism Y

                                          \(\sf =\dfrac{31}{3} \div \dfrac{31}{6}\)

                                          \(\sf =\dfrac{31}{3} \times \dfrac{6}{31}\)

                                          \(\sf =\dfrac63\)

                                          \(\sf =2\)

If Prism X is a dilation of Prism Y by scale factor 2, then Prism Y is a dilation of Prism X by scale factor \(\frac12\).

To find the volume of Prism Y, we simply need to multiply the volume of Prism X by the cube of scale factor \(\frac12\), since volume is measured in cubic units.

\(\sf \implies volume \ of \ Prism \ Y = volume \ of \ Prism \ X \times (scale \ factor)^3\)

                                    \(\sf = \dfrac{372}{5} \times \left(\dfrac12\right)^3\)

                                    \(\sf = \dfrac{372}{5} \times \dfrac18\)

                                    \(\sf =\dfrac{372}{40}\)

                                    \(\sf =\dfrac{93}{10}\)

                                    \(\sf = 9 \frac{3}{10} \ ft^3\)

Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

Answer:

a. The present value of these receivables is $42,123.64

b. The total value at the end of 10 years is $69,257.02

c. The present value of these payments is $10,059.37

Step-by-step explanation:

Let's consider the relationship between the circumference and the radius:

 ⇒ first, consider the equation for finding the circumference

      \(Circumference = 2\pi *radius\)

Let's consider the known information

Let's plug the known information to find the radius:

  \(Circumference = 2\pi *radius\\36\pi =2\pi *radius\\radius = 18\)

Thus the radius is 18 cm

Answer: 18 cm

Hope that helps!

The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.

To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.

The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k hits

n is the total number of trials (in this case, the player's 10 times at bat)

k is the number of successful trials (in this case, 4 hits)

p is the probability of success in a single trial (in this case, the player's batting average, 0.298)

(1 - p) is the probability of failure in a single trial

Plugging in the values:

P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Using the combination formula C(n, k) = n! / (k! * (n - k)!):

P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Calculating the values:

P(X = 4) ≈ 0.161

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