The sum of 3 and r is less than 7.What number sentence represents the statement?

Answers

Answer 1

The sum of 3 and r can be represented by "3 + r"

If this sum is less than 7, we can use the symbol "lesser than" (<) to compare the sum with the number 7, so our number sentence is:

[tex]3+r<7[/tex]


Related Questions

Hello, I need some assistance with the following question. Q1.

Answers

Given the expression f/g

Which is a rational expression.

The domain is all real numbers of (x) except the zeros of the denominators

The zeros of the denominators can be calculated using the equation g(x)=0

So, the answer will be as follows:

The domain of f/g consists of numbers (x) for which g(x) ≠ 0 that are in the domains of both f and g

ok my question is math algebra. consider the linear equation y-1=0 and grapthe two points

Answers

To find:

We need to find two points on the linear equation y-1=0 and to plot those points on graph.

Step by step solution:

We know that:

General coordinate of any two points on line y = 1:

= (x, 1)

So let us assume any two random points on the line:

= (1,1) and (2,1)

We will now mark them on the graph:

What are three ratios equivalent to 9/5?

Answers

The given ratio is 9/5

This ratio is already in the simplified form. To find equivalent ratios, we would multiply the numerator and denominator by constant numbers. We have

If we multiply by 2, it becomes

9 * 2/5 * 2 = 18/10

If we multiply by 3, it becomes

9 * 3/5 * 3 = 27/15

If we multiply by 4, it becomes

9 * 4/5 * 4 = 36/20

Thus, three equivalent ratios are

18/10, 27/15 and 36/20

What is the slope of the line that passes through (5,4) and (7,10)a.3b. -3 C. 2D.-2

Answers

To find a slope of a line we need two points, so we will do it as follows.

[tex]m=\frac{\Delta y}{\Delta x}=\frac{10-4}{7-5}=\frac{6}{2}=3[/tex]

Therefore it is (a) the slope is 3.

Answer:

a.3

Step-by-step explanation:

To find the slope, use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 10-4)/(7-5)

   = 6/2

   = 3

A manager measured the number of goods, y, that his company produced in a hours. The
company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45
goods.
Which equation, in point-slope form, correctly represents the goods produced by the company
after x hours?
Oy-45 = 5(x-9)
Oy+9= 5(x +45)
Oy 45= 5(x + 9)
Oy-9=5(x - 45)

Answers

Answer:

[tex]y-45=5(x-9)[/tex]

Step-by-step explanation:

Definition of the variables:

y = total number of goods produced.x = time in hours.

Given information:

The company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45 goods.

As the rate of change is constant and linear, the rate of change is the slope of the line.  Therefore, the slope is 5.

At hour 9 (x-value) the company had produced 45 (y-value) goods.  Therefore, this can be represented by the point (9, 45).

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and point into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-45=5(x-9)[/tex]

Therefore, the equation that correctly represents the goods produced by the company after x hours is:

[tex]\boxed{y-45=5(x-9)}[/tex]

find the are and perimeter

Answers

L: Length

W: Width

The perimeter of a rectangle is:

[tex]P=2W+2L[/tex][tex]\begin{gathered} P=2(3ft)+2(5ft) \\ P=6ft+10ft \\ P=16ft \end{gathered}[/tex]

The area of a rectangle is:

[tex]A=W\cdot L[/tex][tex]\begin{gathered} A=3ft\cdot5ft \\ A=15ft^2 \end{gathered}[/tex]

URGENT!!! help!!!!!!!!!!!!!

Answers

Triangles' resemblance is reflected by their congruence. If the matching sides and angles of two triangles match, the triangles are said to be congruent.

For triangles, there are five primary congruency rules: Side-Side-Side is an SSS criterion. The side-angle-side SAS criterion. Angle, Side, Angle is an ASA criterion. Angle-Angle-Side is an AAS criterion.

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

An isosceles triangle in geometry is one with at least two equal-length sides. It is sometimes stated as having exactly two equal-length sides and other times as having at least two equal-length sides, with the latter version adding the equilateral triangle as one of the possible configurations.

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The electronics company makes two types of switches. Type a takes 4 minutes to make and requires $3 worth of materials.Type b takes 5 minutes to make and requires $5 of materials. In the latest production bath, it took 32 hours to make these switches and the materials cost 1740. How many of each type of switch was made?

Answers



Let

x ------> number of switch type A

y -----> number of switch type B

so

Remember that

1 hour=60 min

32 hours=32*60=1,920 minutes

4x+5y=1,920 -------> equation 1

3x+5y=1,740 ------> equation 2

Solve the system of equations

Solve by graphing

using a graphing tool

see the attached figure

Solution is

x=180

y=240

therefore

the number of switch type A was 180the number of switch type B was 240

In the accompanying diagram, three vertices of parallelogram ORST are O(0,0), R(b,d), and T(a,0). What are the coordinates of S?A. (a, b)B. (a+b, d)C. (a+b, b)D. (a, d)

Answers

In a parallelogram, the opposite sides are parallel.

This means that RS is parallel to OT. So, the y value of S is the same as the y value of R, which is d, so y = d. Thus:

[tex]S=(x,y)=(x,d)[/tex]

Now, we need to find x.

Since the sides RO and ST are also parallel, the x distance from O to R is the same as the x distance from T to S.

The x distance from O to R is

[tex]b-0=b[/tex]

The x distance from T to S is

[tex]x-a[/tex]

Since these x distances are equal, then:

[tex]\begin{gathered} b=x-a \\ x=a+b \end{gathered}[/tex]

Then, the coordinates of S are:

[tex](a+b,d)[/tex]

Which corresponds to option B.

Eliza had $14 and Emma had $64 more than Eliza how much did Emma have?

Answers

Given

Eliza had $14

Emma had $64 more than Eliza

Find

how much did Emma have

Explanation

as we have given

Eliza has $14

so , Emma = $64 + $14 = $78

Final Answer

Therefore , the Emma had $78

Seventeen percent of people say they've seen a ghost or felt its presence. If 10 people are asked, what is the probability that at least two have seen a ghost or felt its presence?Round your answer to at least three decimals.

Answers

Answer: the probability that at least two have seen a ghost or felt its presence is 0.527

Explanation:

In this scenario, it is either a person asked has seen seen a ghost or felt its presence or they have not. These outcomes are independent of each other. Thus, it's a binomial distribution. We would apply the formula for calculating binomial probability which is expressed as

P(x) = nCx * p^x * q^(n - x)

where

p = probability of success

q = 1 - p = probability of failure

n = sample size

x = number of successes

From the information given, we are concerned with the people that say they've seen a ghost or felt its presence. Thus,

p = 17% = 17/100 = 0.17

q = 1 - 0.17 = 0.83

n = 10

x = 2

We want to find P(x ≥ 2)

P(x ≥ 2) = 1 - [P(x = 0) + P(x = 1)

P(x = 0) = 10C0 * 0,17^0 * 0.83^(10 - 0) = 0.1552

P(x = 1) = 10C1 * 0,17^1 * 0.83^(10 - 1) = 0.3178

P(x ≥ 2) = 1 - (0.1552 + 0.3178) = 1 - 0.473

P(x ≥ 2) = 0.527

the probability that at least two have seen a ghost or felt its presence is 0.527

A spinner can land on either red or blue You spin seven times and then roll a six sided die. Find the number of possible outcomes in the sample space?

Answers

If we spin the spinner once, we can get two possible outcomes (red or blue).

If we spin it twice, the outcomes can be (blue, blue), (blue, red), (red, blue), (red, red); this is, 4 different results.

Then, if we spin the spinner 7 times, there are 2^7=128 possible outcomes.

Finally, we can get any of the 128 possible outcomes from the spinner and rolling a 1; similarly, for rolling a 2, 3,..., 6.

Therefore, the number of possible outcomes of spinning the spinner seven times and rolling a die is

[tex]2^7\cdot6=128\cdot6=768[/tex]

There are 768 possible outcomes in the sample space.

determine the interview on which the function is concave upward and concave downward

Answers

We have to identify the intervals where the function is concave upwards and where is concave downward.

We can differentiate them in a graph as:

We then have only one interval where the function is concave upwards: between x = -1 and x = 4. We can identify other intervals where the function is concave downwards and interrupted by discontinuities.

Then, we can write all the intervals as:

[tex]\begin{gathered} (-\infty,-5)\longrightarrow\text{Concave downward.} \\ (-5,-1)\longrightarrow\text{Concave downward.} \\ (-1,4)\longrightarrow\text{Concave upward}. \\ (4,\infty)\longrightarrow\text{Concave downward.} \end{gathered}[/tex]

1. Evaluate the following expressions if a = 2. b = 3, x = 4, and y = 5.+3(27-»

Answers

When a=2, b=3, x=4, and y=5,

evaluate:

[tex]b^2+3(2x-y)[/tex]

Let's replace b, x and y by the appropriate values:

[tex](3)^2+3(2(4)-5)[/tex]

now let's solve what is inside the parenthesis:

[tex]9+3(8-5)[/tex]

again more solving inside the second parenthesis:

[tex]9+3(3)[/tex]

and again, first multiplying what is indicated. Recall that the rule PEMDAS for order of operations indicates that Parenthesis have to be solved first, then exponents, then multiplications and divisions, and the VERY LAST is additions and subtractions:

[tex]9+9=18[/tex]

You do the same type of replacement of variables wit numbers, and then use of the rules for order of operations to evaluate the rest.

Like:

[tex]ab+ya^3[/tex]

and then evaluate:

[tex]\frac{y+ab}{b+x}[/tex]

If y varies directly with x and y = 90 when 3 = 15, then what is y when = 4?y =+

Answers

Recall than a direct variation implies the following type of relationship between y and x:

y = k * x

where k is a constant value

Then you have (by dividing by x, the following:

y / x = k (the constant)

then, we are told that when y = 90 , x = 15, so we have:

90 / 15 = k

6 = k

so,now that we know what the constant k is (6), we can answer the question: What is y when x = 4?

so we write:

y = k * x

y = 6 * 4

y = 24

This is the value of y when x is 4 since the constant k is 6 as we found above.

Another example:

We need to find the variation relationship for a case that when y = 6, x = 12

We think the same way we did before, starting with the fact that a direct variation is of the form:

y = k * x

given the info that when x = 12, y = 6, we can find the constant k:

6 = k * 12

divide by 12 both sides:

6/12 = k

1/2 = k

So k is 1/2 (one half)

Then we can write the variation as:

y = (1/2) x

(the product of 1/2 times x)

A bus travels 8.4 miles eastand then 14.7 miles north.What is the angle of the bus'resultant vector?Hint: Draw a vector diagram.O[?]

Answers

A bus travels 8.4 miles east and then 14.7 miles north.

What is the angle of the bus resultant vector?

see the figure below to better understand the problem

The angle of the bus resultant vector R is equal to

tan(x)=14.7/8.4

mm

Which of the following are mathematical sentences? Check all that apply. A. 34 B. r + 7 = 4 C. 5g = 9 D. 4x E. 8r = 12 F. x = 1

Answers

The mathematical sentences that can be found in the sentence are:

B. r + 7 = 4 C. 5g = 9 D. 4x E. 8r = 12 F. x = 1

What are mathematical sentences?

A mathematical sentence  can be described as the statement that comprises the  two expressions nor more than two expression.

It should be noted that these two expressions  can make use of the  numbers as well as the variables and in some of the cases combination of them however the  mathematical sentence do encompass the symbols  which could be inform of equals, greater than, as well as  less than.

Therefore, the options that are examples of mathematical sentences are option B C D E F.

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The mathematical sentences which can be found in the sentence are;

B. r + 7 = 4, C. 5g = 9, D. 4x, E. 8r = 12 and F. x = 1

What are mathematical sentences?

A mathematical sentence can be described as a statement that comprises two expressions or more than two expressions.

Expression can be defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Remember that these two expressions can make use of the numbers as well as the variables and in some cases a combination of them however the mathematical sentence does encompass the symbols which could be in form of equals, greater than, as well as less than.

Hence, the options that are examples of mathematical sentences are ; B. r + 7 = 4, C. 5g = 9, D. 4x, E. 8r = 12 and F. x = 1

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justify proposes each step

Answers

the answer is associative property of multiplicaction

because

A*(B*C)=(A*B)*C

B>DGiven:. E is the midpoint of ADE is the midpoint of BCProve: ΔΑΕΒΑ ΔDECE is the midpoint of ADGiven

Answers

We are given a mid-point for segments AD and BC, we have the following:

segments AE and DE are congruent, that is:

[tex]AE\cong DE[/tex]

By definition of mid-point.

Segments BE and CE are congruent, that is:

[tex]BE\cong CE[/tex]

By definition of mid-point.

We also have that angles AEB and DEC are congruent, that is:

[tex]\angle AEB\cong\angle DEC[/tex]

By the vertical angles theorem, which states that when two lines intercept their vertical or opposite angles are equal or congruent.

Now we can conclude that triangles AEB and DEC are congruent, that is:

[tex]\Delta AEB\cong\Delta DEC[/tex]

Due to the Side-Angle-Side Theorem, which states that when two triangles have two congruent sides and the angle between the congruent sides also congruent, then the triangles are congruent.

Write an equation and solve to find the value of your variable. 7.3 less than -2 times a number is the same as 16 1/2. n=?

Answers

The equation is -2n - 7.3 = 16 1/2

The value of the variable n = -11.9

STEP - BY - STEP EXPLANATION

What to find?

• Write the equation of the given statement.

,

• The value of n.

Given:

find the value of your variable. 7.3 less than -2 times a number is the same as 16 1/2. n=?​

To solve follow the steps below:

Step 1

Translate the given statement into equation.

Let n be the number.

-2n - 7.3 = 16 1/2

Step 2

Convert 16 1/2 to decimal.

-2n - 7.3 = 16.5

Step 3

Add 7.3 to both-side of the equation.

-2n = 16.5 + 7.3

Step 4

Simplify the right-hand side of the equation.

-2n =23.8

Step 5

Divide both-side of the equation by -2.

[tex]\frac{\cancel{-2}n}{\cancel{-2}}=\frac{23.8}{-2}[/tex]

n = -11.9

Therefore, the value of the variable n = -11.9

Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible Through (15,5) and (5,15)

Answers

Given that the required linepasses through the points (15, 5)and (5, 15).

Find the slope of the line using teo-point formula.

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{15-5}{5-15} \\ =\frac{10}{-10} \\ =-1 \end{gathered}[/tex]

Substitute the value of m into theslope-intercept form y = mx+c.

[tex]y=-x+c[/tex]

Plug in the point (5, 15)to find c, the y-intercept.

[tex]\begin{gathered} 15=-5+c \\ c=20 \end{gathered}[/tex]

Thus, y = -x + 20, which is the required equation of line.

based on the data provided what was the rent expenses each month

Answers

From the table it can be observed that rate expense for a month is -$1,120.00. The negative value means that amount is reduced.

So rent expense is -$1,120.00, where negative sign is for decrease in amount.

MP and MN are tangents to the circle.What is the value of x?133M90940NxºР17286

Answers

To get x, we will use the equation below:

[tex]\frac{1}{2}\lbrack(360-x)-x\rbrack=94[/tex]

open the inner paremthesis

[tex]\frac{1}{2}\lbrack360-2x\rbrack=94[/tex]

open the parenthesis

180 - x = 94

collect like term

180 - 94 = x

86 = x

Graph the image of rectangular TUVW after a translation 5 units right and 4 units up.

Answers

Answer:

Explanations:

From the rectangle TUVW, the coordinates of the points are shown below:

T(-5, -5), U(-1, -5), V(-1, 4), and W(-5, 4)

If TUVW is translated 5 units right and 4 units up, the coordinates of the new rectangle are in the form (x+5, y+4):

T'(0, -1), U'(4, -1), V'(4, 8), and W'(0, 8)

Property valued at $56,000 is assessed at of itsvalue. If the yearly tax is calculated as $3 per $100 ofassessed value, what is the yearly tax on this property?A. $ 420B. $1.120C. $1,260D. $1,680E $2,240

Answers

Since the yearly tax is calculated as $3 per $100 of assessed value, which is 3/4 of $56,000 , the yearly tax on this property can be calculated as: $56,000*3/4*$3/$100 = $ 1260. The answer is option C.

4. A 5% tax is added onto a $75 online order. How much are the taxes?

Answers

We have the following:

We know that 100% is the value of the purchase of $ 75, therefore, if we add 5%, it would be 105%, that is equal to 1.05, so we multiply the value of 75 by 1.05, and we are left with the following

[tex]\begin{gathered} 75\cdot1.05=78.75 \\ 78.75-75=3.75 \end{gathered}[/tex]

Total value is $78.75 and taxes are 3.75

You have been tracking an adult female Australian flatback sea turtle who weighs 25 kg. How many kilocalories must she consume each day to maintain her body weight?

Answers

The kilocalories that she must consume each day to maintain her body weight is 6250 kilocalories.

How to calculate the value?

From the information, the person has been been tracking an adult female Australian flatback sea turtle who weighs 25 kg.

It should be noted that the requirements is 250kcal per kilograms.

Therefore, the calories will be:

= Weight × Required calories

= 250 × 25

= 6250 kcaloriies

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In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11. What is the probability that the mixture will test positive?

Answers

From the information available, the mixture will test negative if all 6 samples are negative.

The probability of each is independent of the other for all 6 samples.

The probability of a sample testing positive is 0.11. That means the probability of a sample testing negative would be

[tex]\begin{gathered} P\lbrack neg\rbrack=1-P\lbrack pos\rbrack \\ P\lbrack\text{neg\rbrack}=1-0.11 \\ P\lbrack\text{neg\rbrack}=0.89 \end{gathered}[/tex]

However, for all 6 samples, the probability of having a negative result would be a product of probabilities, that is;

[tex]\begin{gathered} P\lbrack tests\text{ negative}\rbrack=0.89\times0.89\times0.89\times0.89\times0.89\times0.89 \\ P\lbrack\text{tests negative}\rbrack=0.89^6 \\ P\lbrack\text{tests negative\rbrack}=0.4969 \end{gathered}[/tex]

Therefore if we have the probability of the mixture testing negative as

[tex]P_{\text{neg}}=0.4969[/tex]

The probability of the mixture testing positive would be;

[tex]\begin{gathered} P_{\text{pos}}=1-P_{\text{neg}} \\ P_{\text{pos}}=1-0.4969 \\ P_{\text{pos}}=0.5031 \end{gathered}[/tex]

ANSWER:

The probability that the mixture will test positive is 0.5031

Rounded to 2 decimal places,

[tex]P_{\text{pos}}=0.50[/tex]

Okay okay if you don’t need it then I’ll let you know what I am

Cynthia wants to buy a rug for a room that is 18ft wide and 28ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 264 square feet of carpeting. What dimensions should the rug have ?

Answers

SOLUTION

Let us use a diagram to illustrate the information, we have

Now, from the diagram, let the length of the uniform strip of floor around the rug be x, So, this means the length and width of the rug is

[tex]\begin{gathered} \text{length = 2}8-x-x=28-2x \\ \text{width = }18-x-x=18-2x \end{gathered}[/tex]

Now, since she can afford to buy a rug of 264 square feet for carpeting, this means that the area of the rug is 264, hence we have that

[tex]\begin{gathered} \text{area of rug = (2}8-2x)\times(18-2x) \\ 264=\text{(2}8-2x)(18-2x) \\ \text{(2}8-2x)(18-2x)=264 \end{gathered}[/tex]

Solving for x, we have

[tex]\begin{gathered} \text{(2}8-2x)(18-2x)=264 \\ 504-56x-36x+4x^2=264 \\ 504-92x+4x^2=264 \\ 4x^2-92x+504-264=0 \\ 4x^2-92x+240=0 \end{gathered}[/tex]

Dividing through by 4 we have

[tex]\begin{gathered} x^2-23x+60=0 \\ x^2-20x-3x+60=0 \\ x(x-20)-3(x-20)=0 \\ (x-3)(x-20)=0 \\ x=3\text{ or 20} \end{gathered}[/tex]

So from our calculation, we go for x = 3, because 20 is large look at this

[tex]\begin{gathered} \text{From the length which is (2}8-2x) \\ 28-2(20) \\ =28-40=-12 \end{gathered}[/tex]

length cannot be negative, so we go for x = 3.

Hence the dimensions of the rug becomes

[tex]\begin{gathered} \text{(2}8-2x) \\ =28-2(3) \\ =28-6=22 \\ \text{and } \\ 18-2x \\ 18-2(3) \\ 18-6=12 \end{gathered}[/tex]

So the dimension of the rug should be 22 x 12 feet

Hello! I need some assistance with this homework question, pleaseQ12

Answers

Answer:

A(-1,4) and B(2,0)

Step-by-step explanation:

The quadratic parabola equation is represented as;

[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex of the parabola} \end{gathered}[/tex]

Therefore, if the given vertex (2,-5) and the other given point (-1,-1), substitute into the equation and solve for the constant ''a'':

[tex]\begin{gathered} -1=a(-1-2)^2-5 \\ -1=9a-5 \\ 9a=4 \\ a=\frac{4}{9} \end{gathered}[/tex]

Hence, the equation for the parabola:

[tex]f(x)=\frac{4}{9}(x-2)^2-5[/tex]

Now, for the line since it is a horizontal line, the equation would be:

[tex]g(x)=5[/tex]

Then, for (f+g)(x):

[tex]\begin{gathered} (f+g)(x)=\frac{4}{9}(x-2)^2-5+5 \\ (f+g)(x)=\frac{4}{9}(x-2)^2 \end{gathered}[/tex]

Then, the graph for the composite function and the points that lie on the graph:

A(-1,4) and B(2,0)

Other Questions
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