The ratio of cats to dogs seen by a veterinarian on one day is 2 to 5. If the vet saw 40 dogs in one day how many cats did he see

Final answer:

The divisibility rule for 7 is more complex than the rules for 2, 3, 5, and 10 due to the lack of a simple pattern or quick digit check, requiring multiple steps and manipulations of the number.

Explanation:

The divisibility rule for 7 is more complicated than the rules for 2, 3, 5, and 10 because it does not follow a simple pattern or involve a quick check of a number's last digit or sum. The rules for divisibility by 2, 3, 5, and 10 are straightforward: a number is divisible by 2 if its last digit is even, by 3 if the sum of its digits is divisible by 3, by 5 if its last digit is 0 or 5, and by 10 if it ends in 0.

The rule for divisibility by 7 requires more steps and cannot be easily performed in one's head. The process typically involves subtracting or adding multiples of 7 from different segments of the number, which often makes it more difficult for students to use effectively without practice or further understanding of the method. Complicated rules for divisibility by 7 prove the point that while mathematical rules are universally valid, some rules are inherently more complex than others.

Odd numbers are those numbers that gives a fraction when divided by 2

Prime numbers are those that can be divided only by 1 and the number itself.

Odd numbers are therefore : 23, 25, 31 and 45

Prime numbers are therefore: 2, 23 and 31

Answer:

There are 20345.556... feet in 6.2 km.

Step-by-step explanation:

Given that, 1 mile = 1.609 km and  1 mile = 5280 ft.

That means we can say,  1.609 km = 5280 ft.

So, 1 km = [tex](\frac{5280}{1.609})ft = 3281.541... ft[/tex]

Now, for converting 6.2 km into feet, we will just multiply 6.2 by 3281.541... ft.

Thus, 6.2 km = [tex](6.2 \times 3281.541...)ft = 20345.556... ft[/tex]

So, there are 20345.556... feet in 6.2 km.

Answer:-1)The three sets of approximation of time will be

Time taken to fall tennis ball from height of 60 m =35.41014 s ≈35.410 s (to the nearest thousandth)

≈35.41s  (to the nearest hundredth)

≈35.5 seconds(to the nearest tenth)

2)Time by the ball to hit the ground =35.5 seconds

Step-by-step explanation:

Time taken to fall tennis ball from height of 60 feet =  0.25 √60 s

So,time taken to fall tennis ball from height of 1 foot =0.25√60 divided by 60=[tex]\frac{0.25\sqrt{60} }{60}s[/tex]

We know that 1 m = 0.3048 foot

⇒60 m =60×0.3048=18.288 feet

therefore, Time taken to fall tennis ball from height of 60 m = 18.288 ×time taken to fall tennis ball from height of 1 foot=[tex]\frac{0.25\sqrt{60} }{60}\cdot18.288=35.41014\ s[/tex]

∴Time taken to fall tennis ball from height of 60 m =35.41014 s ≈35.410 s (to the nearest thousandth)

≈35.41s  (to the nearest hundredth)

≈35.5 seconds(to the nearest tenth)

The time it will take for a tennis ball dropped from a height of 60 meters to reach the ground can be calculated using the equation t = 0.25 √h. Three sets of approximations were determined for heights of 30m, 45m and 60m, with the final time for the 60m drop being approximately 1.94 seconds.

The time it takes for the tennis ball to hit the ground can be calculated using the equation t = 0.25 √h, with 't' being time and 'h' being height. Inserting the given height of 60 meters into this equation will reveal how long it takes for the tennis ball to hit the ground.

From these calculations, it can be determined that the time it will take for the tennis ball dropped from a height of 60 meters to hit the ground is "approximately 1.94 seconds".

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Given function: h(t) = -16t^2 + 96t + 5, where t represents the time in minutes.

We need to find the interval for which the arrow is going up.

The arrow is going up would be the values of time t =0 when it start and when it went to highest point.

Given function is a quadratic function and it represents a parabolic shape.

The highest point on the parabola is a vertex point.

Therefore, we need to find the x-coordinate of the vertex.

We know, formula for x-coordinate of the vertex is

[tex]\frac{-b}{2a}[/tex]

For the given quadratic a= -16 and b=96.

Plugging values of a and b in formula, we get

[tex]\frac{-96}{2(-16)}=\frac{-96}{-32} = 3.[/tex]

Therefore, after 3 seconds arrow would be at maximum height.

Therefore, the interval for which the arrow is going up is [0,3].

The value of expression is,

x = - 5

Here;

The written expression is;

''Four times the difference of a number and 5 is the same as 5 increased by four times the number plus five times the number.''

We have to solve this expression.

What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

Now,

Let a number is 'x'.

Then, The mathematical expression is written as;

4* ( x - 5 ) = 5 + (4*x) + (5*x)

We can solve as;

4* ( x - 5 ) = 5 + (4*x) + (5*x)

4x - 20 = 5 + 4x + 5x

- 20 - 5 = 4x + 5x - 4x

- 25 = 5x

x = -5

Hence, The value of expression is,

x = - 5

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Answer:

A. DF

Step-by-step explanation:

The length of OB is the same as OE, and the angle that AC makes with OB is the same as the angle DF makes with OE.  This means the length of both chords, AC and DF, must be the same.

We can conclude that [tex]\boxed{\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}} }[/tex]. Option (A) is correct.

Further Explanation:

Given:

The options are as follows,

A. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{DF}}}.[/tex]

B. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{OB}}}.[/tex]

C. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{AB}}}.[/tex]

D. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{O}}}.[/tex]

Explanation:

The length of OE is [tex]{\text{OE}} = 7.12{\text{ units}}.[/tex]

The length of OB is [tex]{\text{OB}} = 7.12{\text{ units}}.[/tex]

The length of OB and OE is [tex]7.12{\text{ units}}.[/tex]

AC and FD are the chords of the circle.

OE and OB are the perpendicular bisector of the chords AC and FD respectively.

The length of the perpendicular bisectors of chords is [tex]7.12{\text{ units}.[/tex]

The given chords of the circle are equidistant from the center of the circle.

We can conclude that [tex]\boxed{\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}} }[/tex]. Option (A) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Circles

Keywords: congruent, fill, blank, conclude, DF, OB, AB, AC, chord, tangent, displacement, two chords, radius, center, circle, equidistant,  

x = 2 ± [tex]\frac{1}{2}[/tex]√10

express the equation in standard form : ax² + bx + c = 0 ( a ≠ 0 )

then x = ( - b ±√( b² - 4ac) ) / 2a

given 2x² = 8x - 3, then

2x² - 8x + 3 = 0 ( in standard form )

with a = 2, b = - 8, c = 3

x = (8 ±√(64 - 24) )/4 = (8 ±√40) / 4 = (8 ± 2√10) / 4

x = 2 ± [tex]\frac{1}{2}[/tex]√10

Answer:

A. 2/5

Step-by-step explanation:

3/5*2/4+2/5*1/4

6/20+2/20

8/20 = 2/5

Answer:

Option A

Step-by-step explanation:

Given that Sal has a small bag of candy containing three green candies and two red candies.

He ate two candies one after the other.

The probability that both candies were the same color has to be calculated.

The probability that both candies were the same color = P(both are red or both are green)

= P(both are red)+P(both are green)

Total no of ways to draw 2 candies out of 5 = 5C2 = 5(4)/2 = 10

No of ways of drawing 2 red candies = 2C2 =1

No of ways of drawing 2 green candies = 3C2 =3

Hence required prob =(1+3)/10 = 2/5

[tex]\frac{84}{21}=4[/tex]

Therefore you need 4 batches of cupcakes if you want every person to get one cupcake.

The definition of a rational number is that it can be written in form [tex]\frac{p}{q}[/tex]. If it cannot be written in that form then it is not a rational number (which makes it an irrational number)

Answer: irrational number

part/whole=0.65

78/whole=0.65

whole =78/0.65 =120 £

Answer:

The price before discount would be $120

Step-by-step explanation:

The actual price of the phone is 100%-35% = 65% of the original price of the phone.

So by rule of three

If 65% of the price is $78, the total price of the phone would be:

[tex]Total price = \frac{74}{0,65} \\\\Total price = 120[/tex]

A constant is a number that stays the same no matter what any outside variables are.  In this case, the variables are the number of hours of the event and the number of attendees.  However, it states in the problem that the event will be 5 hours so that becomes known; the only thing that might change is the number of attendees so you can eliminate any cost that will be affected by that.  You are left with Facility Rental, Musical Entertainment, and Cleaning Fee.  Furthermore, you can be sure that Musical Entertainment and Cleaning Fee must be included in the constant because they are described as "flat rates", which means they do not change.

The answer is D) It is the total cost for entertainment, facility rental, and cleaning.

Hope this helps!

The statement that best describes the constant in the expression

25n + 2,800 is:

It is the cost per person for food, linens, and food decorations.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Facility Rental = $150 per hour of the event

Linens = $2 per attendee

Food = $20 per attendee

Table Decorations = $3 per attendee

Musical Entertainment = $1,800

Cleaning Fee = $250

The total cost of the event.

= 25n + 2,800

Where n is the number of attendees.

Now,

25 is the total cost per attendee for food, linens, and table decorations.

Thus,

The constant in the expression is 25 which is the cost per attendee for food, linens, and table decorations.

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Area of a triangle is 1/2 x base x height.

base = 12

Height = x+6

Area = 1/2 * 12 * x+6

Area = 1/2 * 12x * 72

Area = 6x + 36

Perimeter is the sum of the 3 sides:

x-7 + 12 + 2x+5

3x -2 + 12

3x+10

The last choice is the correct answer.

Answer:

At least 6907 people.

Step-by-step explanation:

Population std deviation = sigma= 10.6

Since population std deviation is known, we can use normal probability table to get sample size from confidence interval.

The sample mean weight loss is within 0.25 lb of the true population mean.

Hence  margin of error < 0.25

Margin of error = z critical (std dev/n) where n = sample size

Z critical for 95% = 1.96

Hence 0.25 >1.96(10.6)/sq rt n

Simplify to get

sq rt n > 1.96(10.6)/0.25 = 83.104

Square both the sides to get

n > 83.104 square = 6906.27

i.e. sample size should be atleast 6907.

Answer:

C. |-9| = 9

Step-by-step explanation:

Distance is always non-negative. Distances in a negative direction are made positive by the use of the absolute value function. The distance from 0 to -9 is one such distance.

Remark

You could convert base two to base 10 and then convert base 10 to base 8. That's the long way. The procedure below is the short way.

Step One

Write the base 2 number in groups of 3 starting from the right and going left

11 100 111

Step Two

Convert the base 2 numbers in groups of 3 to base 8. The largest result will be a 7

11 = 2*1 + 1 = 2 + 1 = 3

100 = 1*2^2 = 4

111 = 1*2^2 + 1*2 + 1 = 7

Step Three

Read the answer going down.

347 is the answer

Answer

347(8) = C

Answer:

Option C)347(8) is correct. Below is the explanation for changing the base 2 number to the base 8

Step-by-step explanation:

Given:

      11100111(2)

To find:

      Number with base 8.

Let's convert the given base 2 number to a base 10 number or an integer. Then convert it to a base 8 number.

11100111(2) = 1* [tex]2^{7}[/tex]+1* [tex]2^{6}[/tex]+1*[tex]2^{5}[/tex] + 0*[tex]2^{4}[/tex] +0*[tex]2^{3}[/tex] +1* [tex]2^{2}[/tex]+1*[tex]2^{1}[/tex] +1*[tex]2^{0}[/tex]

Simplify it

                 =128 +64+32 +0+0+4+1+1

                 =231

Now, change this integer 231 to a base 8 number ( I have attached a file for this)

We get an answer of 347(8). Option C is correct!

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answer is equal to 2X44/5mile=17.6mile

Each section of a race is 25 mile.

The race has 4 sections.

Which expression tells how many miles long the entire race is?

Answer:

4×2/5

A small company plans to invest in a new advertising campaign.

There is a 20% chance that the company will lose $5,000 ,

50% chance of a break even, and a 30% chance of a $10,000 profit

So the expected value from the advertisement campaign is calculated as - 20% of 5000 + 0% of 5000 + 30% of 10,000

= -1000 + 0 + 3000

= 2000

The expected value from the advertisement campaign is $2000.

So the Company must go ahead with the campaign.

Answer : Option A

Hope it helps.

Thank you ..!!

Area = 117 m²      width = 9 m

Area (A) = length (L) x width (w)

  117      =      L          *      9

117 = 9L

[tex]\frac{117}{9} = \frac{9L}{9}[/tex]

13 = L

Answer: length = 9 m

Answer:

117/9=13

13*9=117

So, the length is 13 since L*W=area.

:)

The correct logical order for the statements I, II, and III in the proof is: I. Definition of a Straight Angle, III. Angle Addition Postulate, and II. Substitution Property of Equality. This order supports the conclusion that corresponding angles, created by the transversal intersecting parallel lines, are congruent.

To complete the two-column proof that demonstrates the congruence of the corresponding angles when segments UV and WZ are parallel and line ST intersects both at points Q and R respectively, we need to place statements and reasons I, II, and III in the most logical order. This should allow us to show

corresponding angles are congruent, which is the ultimate aim of the proof.

The correct order of statements and reasons to complete the proof is:

Definition of a Straight Angle (I): We know that the angle measure of a straight line is 180°, hence m∠SQT = 180°.

Angle Addition Postulate (III): Based on the postulate, we can express m∠SQV + m∠VQT as equal to the measure of angle SQT because the two angles combine to form the straight angle, therefore m∠SQV + m∠VQT = m∠SQT.

Substitution Property of Equality (II): By substituting the equal values established in statements I and III, we get m∠SQV + m∠VQT = 180°.

After arranging the statements and their corresponding reasons, the proof logically demonstrates that the congruent angle pairs are a result of transversal ST intersecting parallel lines UV and WZ.

M(n) denotes Aiden's fee (in dollars) for his n^th drive on a certain day.

Then:

M(8)<M(4) means that 8th drive was less expensive than 4th drive.

Answer:

All options are wrong.

Step-by-step explanation:

We have y > –3x + 3 and y > 2x – 2

Option A - (1,0)

          y > –3 x 1 + 3 = 0

         We have y = 0, which is not greater than 0.

         Option A is not correct.        

Option B - (–1,1)

          y > –3 x -1 + 3 = 6

         We have y = 1, which is not greater than 6.

         Option B is not correct.

Option C - (2,2)

          y > –3 x 2 + 3 = -3

         We have y = 2, which is greater than -3.

          y > 2 x 2 – 2  = 2

         We have y = 2, which is not greater than 2.

         Option C is not correct.  

Option D - (0,3)

          y > –3 x 0 + 3 = 3

         We have y = 3, which is not greater than 3.

         Option D is not correct.    

All options are wrong.

The fraction equivalent to -84/-90 in the least common terms is 14/15, as both the numerator and the denominator can be divided by the common factor 6, resulting in a simplified positive fraction.

To find which fraction is equivalent to -84/-90 in the least common terms, we need to simplify the fraction by canceling out any common factors in the numerator and the denominator. We observe that both numbers are divisible by 6. When we divide the numerator and the denominator by 6, we get:

-84 / -90 = (-84 / 6) \/ (-90 / 6) = 14 / 15

Since a negative divided by a negative results in a positive number, we eliminate the negative signs and get the fraction in its least common terms as 14/15.

The answer to this question is the product is 12i

Answer:  The required product is [tex]-11+62i.[/tex]

Step-by-step explanation:  We are given to find the product of the following two complex numbers :

[tex]z_1=6+5i,~~~z_2=4+7i.[/tex]

We will be using the following property :

[tex](a+b)(c+d)=a(c+d)+b(c+d).[/tex]

Also, we will use the fact that [tex]i=\sqrt{-1},~~i^2=-1.[/tex]

The product of the given complex numbers is

[tex]z_1z_2\\\\=(6+5i)(4+7i)\\\\=6(4+7i)+5i(4+7i)\\\\=24+42i+20i+35i^2\\\\=24+62i-35\\\\=-11+62i.[/tex]

Thus, the required product is [tex]-11+62i.[/tex]

First, let's simplify the expression: 7 - 5 + 3x - 1  ⇒   3x + 1  (slope=3, y-intercept = 1)

Next, let's understand what they are asking for:

no solutions means same slope but different y-intercepts

Answer: 3x + _______ (the blank can be anything except 1)

one solution means different slopes

Answer: ________x + _______ (the first blank can be anything except 3, the second blank can be anything)

infinitely many solutions means same slope and same y-intercept

Answer: 3x + 1

Answer:

1.3x+9

2.1x+4

3.3x+1

Step-by-step explanation:

To express the ratio of flour to butter from a recipe as a fraction in simplest form, start by setting it up as a fraction and then multiply by the reciprocal of the denominator. In this case, a recipe with 6 cups of flour and three-fourths cup of butter simplifies to a ratio of 8:1.

To find the ratio of the amount of flour to the amount of butter as a fraction in simplest form, we start by writing the amounts given in the recipe as a fraction. There are 6 cups of flour and three-fourths (3/4) cup of butter. The initial ratio is therefore:

6 cups of flour / (3/4) cup of butter

To simplify, we can multiply both the numerator (the top part of the fraction) and the denominator (the bottom part of the fraction) by the reciprocal of the denominator:

6 / (3/4) = 6 × (4/3) = 24/3 = 8

So, the simplest form of the ratio of flour to butter is 8:1.