The sum of Lisa's age and Myra's age is 40. In 10 years, Lisa will be 3
times as old as Myra. How old is each person now?

Answer:

Radius =21,  height = 45  
Lateral Surface Area = [tex]5937.61[/tex] cm²
Total Surface Area = [tex]8708.49[/tex]  cm²

Radius = 28, height =28
Lateral Surface Area =  [tex]4926.01[/tex] cm²

Total Surface Area  =  [tex]9852.03[/tex] cm²

Step-by-step explanation:

If r is the radius of a cylinder with height h

Lateral surface area

[tex]L = 2\pi rh[/tex]

Top and bottom surface area for each which is a circle is [tex]\pi r^2[/tex]

So total bottom and top surface area = [tex]2 \pi r^2[/tex]

Total surface area =

[tex]2\pi rh + 2\pi r^2 = 2\pi r(h + r)[/tex]

For r = 21, h = 45
[tex]L = 2 \pi \cdot 21 \cdot 45 = 1890 \pi = 5937.61 \;cm^2[/tex]

[tex]T = 2\pi \cdot 21 (21 + 45) = 2772 \pi = 8708.4948\;cm^2[/tex]

For r = 28, h = 28

[tex]L = 1568\pi = 4926.01 cm^2[/tex]

[tex]T = 3136\pi = 9852.03 \;cm^2[/tex]

Answer:

89%

Step-by-step explanation:

534/600*100

= (534*100)/600

= 53400/600

= 89

Basics of percentage you can use this for also other unknown percentages just replace the “ 534 “ and the “ 600 “

Answer:

89‰

Step-by-step explanation:

[tex]\frac{534}{600} X100 = 89[/tex]‰

Answer: blue

Step-by-step explanation:

or b

Therefore , the magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.

An ordered combination of numbers “ a ” and “ b that is stated as just a / b, where b not greater than zero, is referred to as a ratio. A ratio is the result of equating two ratios. If there were one boy and three girls, the ratio could be shown as 1:3.   1/4 are boys, and 3/4 are girls. A part is a number, a proportion of size, or a difference among two or more things.

Here,

Since: Marco To avoid your batter and bakery items acquiring a purple-blue tinge, wash freeze blueberries multiple times in water it until water becomes lighter in color.

The magic muffin ratio is 2:2:1:1, which equals 1-two cups and 2,8 cups.

With a paper towel, dry them off, and then delicately fold it into the batter. Maintaining the lightness of rapid breads is the aim of this process.

The magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.

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Answer:c

Step-by-step explanation:

Answer:

To find the value of x in this situation, you can set up a proportion using equivalent ratios. The equivalent ratios will show the relationship between the number of words Santiago can text and the time it takes him to text them.

74 words : 4 minutes :: 37 words : x minutes

To solve for x, you can cross-multiply and divide:

74 * x = 37 * 4

x = (37 * 4) / 74

This simplifies to:

x = 2 minutes.

Step-by-step explanation:

Answer:

The second graph is not a function of x

Step-by-step explanation:

Note : -

1st graph : f(x) = secant inverse x

3rd graph : f(x) = c (constant function)

4th graph : It is a function which is +ve

Using equations to solve the word problem, the first child withdrew $700, second child withdrew $1500, and third child withdrew $1250.

A word problem is a mathematical exercise that requires the student to read and understand a narrative description of a problem, identify the mathematical quantities involved, and then formulate and solve an equation to find the solution. Word problems often involve real-world scenarios such as shopping, money, and time.

Let's define our variables;

We can proceed to write linear equations with our variables

1/2x = 1/4y ...eq(i)

z = 500 + x ...eq(ii)

From equation (i)

x = 1/2y

z = 500 + 1/2 y

x = 750

x = 1/2(y)

750 = 0.5y

y = 750 * 2

y = 1500

z = 500 + x

z = 500 + 750

z = 1250

The first child took out $750, the second child took out $1500, and the third child took out $1250.

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The net force acting on a 14kg wagon that produces an acceleration of 1.5 m/s2 is 21N.

Force is an external agent that is capable of changing the state of rest or motion of a body. It has a magnitude and a direction. The direction towards which the force is applied is known as the direction of the force, and the application of force is the point where force is applied.

It is simply known as a push or a pull.

The Force can be measured using a spring balance. The SI unit of force is Newton(N).

Force = mass x acceleration

Force = m x a

where mass = 14kg

acceleration = 1.5m/s2

Force = 14 x 1.5

Force = 21N

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Answer:

417.335=x

Step-by-step explanation:

The first seven terms of the Fibonacci sequence are: 0, 1, 1, 2, 3, 5, 8, 105, 225.

Sequence is an ordered arrangement of elements, usually numbers or objects, which follows a specific pattern. It is a mathematical concept that is used in a variety of areas, such as computer science, data analysis, and number theory. A sequence can be finite, like the first 10 numbers in the counting sequence, or it can be infinite, such as the set of natural numbers. It is important to understand the concept of a sequence in order to be able to use it in various areas.

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding numbers, starting from 0 and 1.

The Fibonacci sequence is named after mathematician Leonardo Fibonacci, who introduced the sequence in his book Liber Abaci in 1202.

The sequence is also known as the Golden ratio, because the ratio of successive numbers in the sequence converges on the Golden ratio of 1.618. The first seven terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, and the fourth and sixth terms of the sequence are 105 and 225 respectively.

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Answer:

b. x = 62 degree, y = 118 degree

Step-by-step explanation:

x is the vertical angle to the 62-degree angle, so x = 62 degree

We see that the angle x add with the angle y equal to 180 degrees, so to find y, we take

180 - 62 = 118 degree.

So, the answer is b. x = 62 degree, y = 118 degree

The vertical velocity of the string at the origin at time t would be zero, as the origin is a fixed point.

The origin is a fixed point, so it does not move. This means that the vertical velocity of the string at the origin at time t would be zero.

The origin of the string is a fixed point, meaning that it does not move. This implies that the vertical velocity of the string at the origin at time t would be zero, as the origin does not move or change its position. Since the origin is a fixed point, the vertical velocity of the string at the origin at time t would remain constant, and would be equal to zero. Thus, the vertical velocity of the string at the origin at time t would be zero.

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The angles of the triangle are 20.75, 54.75, 104.5

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here: if the first angle is 34 more than the 2nd and the 3rd is 5 less than twice the first. Let the second angle be x then first angle is x+34 and the 3rd angle is 2x+63

Using the triangle sum property we get

x+x+34+2x+63= 180

4x=83

x=20.75

Hence, the angles of the triangle are 20.75, 54.75, 104.5

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The area of quadrilateral BEFD, by using Heron’s Formula, is 16.

To calculate the area of quadrilateral BEFD, we first need to calculate the area of the entire triangle ΔABC. This can be done by using Heron’s Formula, which states that the area of a triangle is equal to the square root of the semi-perimeter multiplied by the product of the sides of the triangle, minus the sum of the squares of the sides.

In this case, the semi-perimeter is (a + b + c)/2, where a, b, and c are the sides of the triangle. The sides of triangle ΔABC are 9, 10 and 11, respectively. Applying Heron’s Formula, we have:

Area of ΔABC = √(9 + 10 + 11)/2 * (9 * 10 * 11) - (9^2 + 10^2 + 11^2)

= √27 * 990 – 1230

= √990

= 31.6

Now, since we know the areas of the three triangles within ΔABC (4, 9, and 7), we can subtract the sum of those three from the total area of ΔABC to calculate the area of quadrilateral BEFD.

Area of BEFD = 31.6 – (4 + 9 + 7)

= 31.6 – 20

= 11.6

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Answer:

62.5%

Step-by-step explanation:

We know that Mike's whole drink is 16 ounces.

If he drinks 6 ounces, that means we are subtracting 6 from the total (16 ounces)

16 - 6 = 10

Now that we have 10 ounces left, we have to find out what percent that is out of the total (16 ounces)

To do this, we must create a fraction: 10/16

You can simplify this by dividing both sides by 2, getting us 5/8

Now, you can either use long division, or a calculator or know that 1/8 is .125, then multiply that by 5 to get .625

Now, the question is asking us for a percent, not a decimal, so we must convert .625 to a percent by multipling everything by 100. This just means moving every number to the right 2 (keep the decimal still)

Once done, you will get 62.5% left!

Four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term are -35/3, -140/3, - 560/3, -2240/3 and 7, -28, 112, - 448  

Four numbers forming a geometric sequence can be calculate as follows

these terms: a₁, a₂, a₃, a₄

a₁ = a₂ + 35

a₃ = a₄ + 560

Use the formula for the n-term:

a₂ = a₁r

a₃ = a₁r²

a₄ = a₁r³

replace

a₁ = a₁r + 35 ⇒ a₁(1 - r) = 35

a₁r² = a₁r³ + 560  ⇒ a₁(1 - r)r² = 560

Subtracting from the first equation to  the second:

r² = 560/35

r² = 16

r = √16

r = ± 4

Use the first equation to find the first term:

a₁( 1 ± 4) = 35

1. a₁ = 35/-3 = -35/3

2. a₁ = 35/5 = 7

We have two sequences:

r = 4

-35/3, -140/3, - 560/3, -2240/3

r = -4

7, -28, 112, - 448  

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An acute triangle's circumcenter may be found inside, on, or outside the triangle. Exactly midway down the hypotenuse is where a right triangle's circumcenter is located (longest side). Every time an obtuse triangle is formed, its circumcenter lies outside the triangle.

The circumcenter of a triangle is the point where three perpendicular bisectors of its sides meet. A triangle's circumcenter is defined as the point at which the perpendicular bisectors of its own sides cross.  In all other senses, the circumcenter is the point at which a triangle's sides intersect to form a bisector.

Thus, circumcenter is acute or obtuse is depend on the triangle's circumcenter.

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An acute triangle's circumcenter may be found inside, on, or outside the triangle. Exactly midway down the hypotenuse is where a right triangle's circumcenter is located (longest side). Every time an obtuse triangle is formed, its circumcenter lies outside the triangle.

What is a triangle's circumcenter?

The circumcenter of a triangle is the point where three perpendicular bisectors of its sides meet. A triangle's circumcenter is defined as the point at which the perpendicular bisectors of its own sides cross.  In all other senses, the circumcenter is the point at which a triangle's sides intersect to form a bisector.

Thus, the circumcenter is acute or obtuse is depend on the triangle's circumcenter.

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Answer:

1) 92,22,66

2) 106,13,61

3) 87,34, 59

4)20,74,86

Step-by-step explanation:

1) Let the unknown angle be x

92 + 22 + x= 180( Sum of angles in a triangle )

114+ x = 180

x= 180-114

   =66

2) 106+ 13 + x =180

119 +x = 180

x= 180-119

x= 61

3) 59+34 +x = 180

93+x = 180

x= 180-93

   =87

4) 86+74 +x=180

160 +x =180

x= 180-160

 =20

Answer:

the correct answer has to be c

The area of given figure will be sum of of triangles and rectangles included in it and area will be = 27.7 m^2.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

As area of rectangle=length*breadth

and area of triangle = 1/2*base*height

Therefore area of figure=1/2*1*5+2*5+1/2*2*2+1/2*2*3+1*3+1/2*1*2+3*2

=5/2+10+2+3+3+1+6

=55/2

area of figure=27.5 m^2

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The substitution reaction is defined as a reaction in which a small or functional part of one chemical compound is replaced by another group of chemical compound, or it is a reaction in which one atom or molecule of a substance gets replaced by another atom or molecule.

There are certain conditions which are to be followed while a substitution reaction,

The hydrolysis of alkyl bromide (R-Br) under basic circumstances is an example of a substitution process.  Example, R-Br + OH R -> OH + Br.

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the two different forms of mixed numbers can be represented are  [tex]4 \frac{2}{10}[/tex] and 42/10.

What is mixed fraction?

A mixed fraction is a fraction that is created by fusing a whole number with a fraction. A mixed fraction is a fraction that is created by fusing a whole number with a fraction. A mixed fraction is a form of fraction that consists of both a whole number part and a fractional part. A mixed fraction would be, for instance, 3 1/10. It is also known as a mixed number.

the mixed number: 4 and two-tenths

= [tex]4 \frac{2}{10}[/tex]

this can also be written as 4*10 +2

= 42/10

Hence the two different forms of mixed numbers can be represented are  [tex]4 \frac{2}{10}[/tex] and 42/10.

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The value of y for the given conditions is 82.2.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.

Given a phrase, y divided by 6.85=1.2

y ÷ 6.85 = 12

y/6.85 = 12

multiply both sides by 6.85

y/6.85(6.85) = 12 x 6.85

y = 82.2

Hence the value of y is 82.2.

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On solving the question we can say that the , plot the equation by points in the graph to get the line in the graph.

Equations with graphs as the unknowns are known as graph equations. The concept of isomorphism is one of the key issues in graph theory. When are two graphs identical, we inquire? Different graph equations may be used to express the aforementioned graphs.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized. A lot of specialists, such as air traffic controllers, architects, computer programmers, and carpenters, employ equations on a daily basis.

The equation are

y = 1/2x - 2

for y = 0 , x= 4

and for x = 0 , y = -2

y = -3/4 x +

for y = 0 , x= 4

and for x = 0 , y = 3

Plot the points in the graph to get the line in the graph.

Again for

y = -2x + 1

for y = 0 , x = -1/2

for x= 0 , y = 1

and y = 3x -4

for y = 0 , x = 4/3

and for, x =0 , y = -4

again plotting the points in the graph.

similarly for

y + 2x = 3

for y = 0 , x = 3/2

and x = 0 , y = 3

plotitng the point in the graph we get the solution.

and 2y - 3x = 1

for y = 0 , x = -1/3

and x = 0 , y = 1/2

Plotting the points in the graph we can get the solution.

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The length in centimeters of side OP is 8.

A triangle is a plane figure which is bounded by three straight sides, and has a sum of its internal angle to be 180^o.

Two or more triangles can be referred to as similar if the corresponding sides and measure of corresponding internal angles have some common properties on comparison.

Thus on comparing the corresponding sides of the two given similar triangles, we have;

JK/ ON = KL/ OP

2/ 4 = 4/ OP

2OP = 4*4

       = 16

OP = 16/ 2

     = 8

OP = 8 cm

Therefore, the length of side OP is 8 cm.

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8 less than 3 times a number is at most 30 can be written as 8 < 3N ≤ 30

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Since 8 less than 3 times a number is at most 30

Let the number be N

Thus, 8 less than 3 times a number is at most 30 can be written as:

8 < 3×N  ≤ 30

8 < 3N ≤ 30

Note: at most means less than or equal (≤)

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The correct statements on the graph of time and calories is:

When two numbers are multiplied or divided, there is a proportionate relationship. Although a linear equation frequently includes a proportional component in addition to some constant number, a linear relationship can also be proportional.

A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.

As shown in the graph, the straight line passed through the origin which means that it is a proportional relationship.

The constant of proportionality in this case is therefore:

= Calories at a minute / Minute

= 20 / 2 minutes

= 10 calories per minute

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The points represent that Wanda should sew 16 small gloves and 2 pairs of large gloves to maximize the profit.

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠), can take the place of the equal sign "=" in this expression.

Given  Wanda sews small and large gloves,

time for small gloves = 45 minutes

time for large gloves = 120 minutes

total time = 16 hours = 960 minutes

let x be the number of small gloves and y be the number of large gloves,

inequality equation is 45x + 90y ≤ 960

and cost of small gloves = $2

cost of large  gloves = $4

total amout = $40

equation 2x + 4y ≤ 40

and the points (16, 2)

the points explain they are the minimum quantity of small and large gloves to maximize the profit the number of small gloves should not be less than 16 and the number of large gloves should not be less than 2.

Hence points (16, 2) explain the values of x and y.

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the complete question is in image.

The probability that Sheila is late on any one day is 0.295 or 29.5%.

We can use the law of total probability to find the probability that Sheila is late on any one day.

The law of total probability states that for any event B, the probability of event B occurring can be calculated by summing the probability of event B occurring given that event A has occurred, multiplied by the probability of event A occurring. Symbolically, this can be represented as:

P(B) = P(B|A1) * P(A1) + P(B|A2) * P(A2) + ... + P(B|An) * P(An)

In this case, event B is Sheila being late, and events A1 and A2 are Sheila walking or cycling to school, respectively. The probabilities of these events occurring are:

P(A1) = 0.65 (the probability that Sheila walks to school)

P(A2) = 0.35 (the probability that Sheila cycles to school, since 1- 0.65)

P(B|A1) = 0.4 (the probability that Sheila is late given that she walks to school)

P(B|A2) = 0.1 (the probability that Sheila is late given that she cycles to school)

Plugging these values into the equation gives:

P(B) = P(B|A1) * P(A1) + P(B|A2) * P(A2) = 0.4 * 0.65 + 0.1 * 0.35 = 0.26 + 0.035 = 0.295

So the probability that Sheila is late on any one day is 0.295 or 29.5%.

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