.On 1st March 2001, the ratio of Freddie’s age to his mother’s age was 1:11
On 1st March 2018, the ratio of Freddie’s age to his mother’s age was 2:5
Write the ratio of Freddie’s age to his mother’s age on 1st March 2030

Answers

Answer 1

Answer:

[tex]Ratio =16 : 31[/tex]

Step-by-step explanation:

Let

x = Freddie's age and y = His mother's age

Given

2001:=  [tex]x : y = 1 : 11[/tex]

2018:= [tex]x +17: y + 17= 2 : 5[/tex]

Required

The ratio of their age in 2030

[tex]x : y = 1 : 11[/tex]

[tex]x +17: y + 17= 2 : 5[/tex]

Express as fractions

[tex]\frac{x}{y} = \frac{1}{11}[/tex] --- (1)

[tex]\frac{x+17}{y+17} = \frac{2}{5}[/tex] -- (2)

In (1), make y the subject

[tex]\frac{x}{y} = \frac{1}{11}[/tex]

[tex]y = 11x[/tex]

Substitute [tex]y = 11x[/tex] in (2)

[tex]\frac{x+17}{y+17} = \frac{2}{5}[/tex]

[tex]\frac{x+17}{11x+17} = \frac{2}{5}[/tex]

Cross Multiply

[tex]5(x +17) = 2(11x + 17)[/tex]

[tex]5x +85 = 22x + 34[/tex]

Collect like terms

[tex]22x - 5x = 85 - 34[/tex]

[tex]17x = 51[/tex]

[tex]x =3[/tex]

[tex]y = 11x[/tex]

[tex]y = 11*3[/tex]

[tex]y = 33[/tex]

This means that: In 2001, Freddie was 3 and his mother was 33

In 2030 (29 years after);

Freddie will be: 3 + 29 = 32

His mother will be: 33 + 29 = 62

So, the ratio is:

[tex]Ratio =32 : 62[/tex]

Divide by 2

[tex]Ratio =16 : 31[/tex]


Related Questions

2^x-4x=0 find the value of x in the equation

Answers

9514 1404 393

Answer:

  x ≈ 0.309906932381 or 4

Step-by-step explanation:

There are no algebraic methods of solving a mixed exponential and polynomial equation. The value of x can be found by guessing, or by other means such as trial and error or graphing.

Attached is a graph showing two solutions. x = 4 is the integer solution (2^4 = 4·4). The irrational solution is approximately x ≈ 0.309906932381. That precision is obtained by Newton's method iteration, easily done by a graphing calculator.

What is the correct answer?

Answers

Answer:

6 units to the right, 3 units down

Step-by-step explanation:

A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard deviation of .4 billion years. (Their ages are approximately normally distributed.) You think the mean age is actually greater, and that this would lend support to an alternative theory about how the clusters were formed. You use a computer to randomly select the coordinates of 50 stars from the catalog of known stars of the type you're studying and you estimate their ages. You find that the mean age of stars in your sample is 3.4 billion years.

Answers

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

Please find the complete question in the attached file.

Lets [tex]\mu[/tex] in trillions of years be the maximum likelihood age of galaxies in a certain type of star cluster.

Calculating the Hypotheses:

Null hypothesis value:[tex]H_o : \mu = 3.3[/tex]

Alternative hypothesis value: [tex]H_A : \mu > 3.3[/tex]

Rafael is training for a triathlon, which includes swimming, biking, and running. The graph shows the total hours he spent swimming over the first 4 weeks of his training. Swim Training 0 Is the relationship between the time spent swimming and the number of weeks proportional? Complete the statements. 30 27 The points ? a straight line that 24 21 ? 4 through the origin. 18 Time (h) 15 12 6 3 0 1 2 3 4 5 6 7 8 9 10 0​

Answers

Answer:

For people that are doing this lesson on I-Ready

The points Lie on a straight line that goes through the origin.

The graph shows a relationship that is Proportional.

Step-by-step explanation:

Answer:

Step-by-step explanation:

lie on

goes

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs seven times as much (per unit area) as glass, use Lagrange multipliers to find the dimensions of the aquarium that minimize the cost of the materials. (Enter the dimensions as a comma separated list; Note that the variable volume is a capital V and must be entered as such, using the shift rather than caps-lock key)

Answers

Answer:

[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex]     [tex]b = \sqrt[3]{\frac{2V}{7}}[/tex]       [tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]

Step-by-step explanation:

Represent the volume of the box with V and the dimensions with l, b and h.

The volume (V) is:

[tex]V = l * b * h[/tex]

Make h the subject of the formula

[tex]h = \frac{V}{lb}[/tex]

The surface area (S) of the aquarium is:

[tex]S = lb + 2(lh + bh)[/tex]

Where lb represents the area of the base (i.e. slate):

The cost (C) of the surface area is:

[tex]C = 7 * lb + 1 * 2(lh + bh)[/tex]

[tex]C = 7lb + 2(lh + bh)[/tex]

[tex]C = 7lb + 2h(l + b)[/tex]

Substitute [tex]\frac{V}{lb}[/tex] for h in the above equation

[tex]C = 7lb + 2*\frac{V}{lb}(l + b)[/tex]

[tex]C = 7lb + \frac{2V}{lb}(l + b)[/tex]

[tex]C = 7lb + \frac{2V}{b} + \frac{2V}{l}[/tex]

Differentiate with respect to l and with respect to b

[tex]C_l=7b - \frac{2V}{l^2}[/tex] [tex]=0[/tex]

[tex]C_b=7l - \frac{2V}{b^2}[/tex] [tex]=0[/tex]

To solve for b and l, we equate both equations and set l to b (to minimize the cost)

[tex]7b - \frac{2V}{l^2}=7l - \frac{2V}{b^2}[/tex]

[tex]7l - \frac{2V}{l^2}=7b - \frac{2V}{b^2}[/tex]

By comparison:

[tex]l =b[/tex]

[tex]C_l=7b - \frac{2V}{l^2}[/tex] [tex]=0[/tex] becomes

[tex]7l - \frac{2V}{l^2}=0[/tex]

[tex]7l = \frac{2V}{l^2}[/tex]

Cross Multiply

[tex]7l^3 = 2V[/tex]

Solve for l

[tex]l^3 = \frac{2V}{7}[/tex]

[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex]

Recall that: [tex]l =b[/tex]

[tex]b = \sqrt[3]{\frac{2V}{7}}[/tex]

Also recall that:

[tex]h = \frac{V}{lb}[/tex]

[tex]h = \frac{V}{\sqrt[3]{\frac{2V}{7}}*\sqrt[3]{\frac{2V}{7}}}[/tex]

[tex]h = \frac{V}{\sqrt[3]{\frac{4V^2}{49}}}[/tex]

Apply law of indices

[tex]h = \sqrt[3]{\frac{49V^3}{4V^2}}[/tex]

[tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]

The dimension that minimizes the cost of material of the aquarium is:

[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex]     [tex]b = \sqrt[3]{\frac{2V}{7}}[/tex]       [tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]

Write a polynomial function of least degree that has real coefficients, the following zeros: 1,5,3+i and a leading coefficient of 1

Answers

Answer:

no te entiendo

yo también la busco

A line contains the points (6,-4) and (0,-2). What is the equation of the line?

Answers

Answer:

The equation of the line is:

[tex]y = -\frac{1}{3}x - 2[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept, that is, the value of y when x = 0.

(0,-2)

This means that the y-intercept is -2, that is, [tex]b = -2[/tex]. So

[tex]y = mx - 2[/tex]

Finding the slope:

When we have two points, the slope is given by the change in y divided by the change in x.

We have points  (6,-4) and (0,-2).

Change in y: -2 - (-4) = -2 + 4 = 2

Change in x: 0 - 6 = -6

Slope: [tex]m = \frac{2}{-6} = -\frac{1}{3}[/tex]

So the equation of the line is:

[tex]y = -\frac{1}{3}x - 2[/tex]

How much will a shopper save on a TV that is on sale for 25% off the regular price of $399.99

Answers

Answer: $99.99

Step-by-step explanation:

$399.99 * .25 (discount) = $99.99

I need help graphing this question,

[tex]f(x)=\frac{1}{18}(x+5)^2-11[/tex]

Answers

Answer:

The graph is attached

First identify the leading coefficient. It is positive in our case, it means the graph opens upPlot vertex, f(x) = a(x - h)² + kVertex is (h, k), in our case it is (-5, -11)Find x and y-intercepts and plotTo find x- intercepts find x when y = 0To find the y-intercept find y when x = 0

Once all points are plotted, connect them and extend up (see attached)

Evaluate b2−16a+5 when a=1/2 and b=7.

Answers

Answer:

11

Step-by-step explanation:

7x2=14

16x1/2=8

14-8=6

6+5=11

The evaluation of the given equation when the a is 0.5 and b = 7 so it should be considered as the 46.

Evaluation of the given equation;

Since the equation is

[tex]b^2 - 16a + 5[/tex]

So,

[tex]= (7)^2 - 16(0.5) + 5[/tex]

= 49 - 8 + 5

= 46

Hence, The evaluation of the given equation when the a is 0.5 and b = 7 so it should be considered as the 46.

Learn more about an equation here: https://brainly.com/question/14170257

y/18.5 + 5 = 8 wha is w

Answers

Answer:

y or w is 55.5

55.5/18.5 = 3

3+5=8

Step-by-step explanation:

hope that helps...

Please help me with these math problems (3) . I really need help . Multiple choice don't comment random for points please

Answers

Answer:

Follow me please

Mark brainliest

Answer:

B

Step-by-step explanation:

How can you use tables, graphs and equations to compare functions

Answers

Answer:

A graph is a chart or drawing that shows the relationship between changing things.

- They are a diagram displaying the relationship between numbers or amounts.

- A graph is one of the easiest ways to compare numbers.

- A graph or chart is used to present facts in visual form.

- They are a drawing that displays the relative sizes of numerical quantities.

- Graphs can be used to illustrate many types of data.

- They should be used to make facts clearer and more understandable.

- it shows trends over time.

- Forceful -- Emphasizes main point

- Convincing -- proves a point, see and hear

- Compact way to convey information

- More interesting than just talk or print

- Quick way for the audience to visualize what you are saying -- numbers trends up or down

- To bring facts to life

- To show and compare relationships

- To show and compare changes

- They are much easier to understand then a large

table of numbers

- without

the need to understand what each and every number in a table means.

They help you visually see the difference between two or more values.

Hope this helps!

Which line segment is a chord of o C in the diagram below?
O A. AB
O B. DE
O C. BD
O D. AC​

Answers

Answer:

A. AB

Step-by-step explanation:

line segment AB is a chord.

About 20,000 fewer babies were born in
California in 1996 than in 1995. In 1995,
about 560,000 babies were born. Which
equation can be used to predict the
number of babies y (in thousands), born x
years after 1995?

Answers

Answer:

The answer is B

Step-by-step explanation:

Your substracting the 20,000 from the 560,000

I Need help ASAP will mark the brainliest

Answers

Answer:

EG and QM

Step-by-step explanation:

SAS or side angle side

so to start evaluate what u have already

EF =QN means that the two sides are congruent

then <MQN = <GEF

the angle Q is = to angle E

so fid the next two sides that fit the pattern or EG and QM

6500 divide by 100. step by step​

Answers

Answer:

6500 / 100 = 65

Step-by-step explanation:

if you are dividing a number that has zeros by 10/100/1000... you can cancel out the zeros to find the answer.

find the area of this shape plz i really need this done asap plz help with no fake answers questions 50 points

Answers

Answer:

Green: 8

Red: 9

Bright Green: 4

Light Green: 12

Peach: 4

Step-by-step explanation:

Green: 1/2(4)(3)=6

1/2

1 1/2

6+1/2+1 1/2=8

Red: 1.5+3+1.5+2+1=9

Bright Green: 12-1-3-4=4

Light Green: 3x4=12

Peach: 1+1+1+1=4

Answer:

1. 8

2. 9

3. 4

4. 12

5. 4

If you do this on paper and match up the sides you will get the same. I would show, but I can’t add photos here on my device. But Yeah, I have these for homework and I got em correct. Sooooo, have a great day ladies and gents and everyone else(sorry, I don’t know how to say for non-binary people)

Determine the missing side length:

Answers

Answer

35

Step-by-step explanation:

Using Pythagoras theorem since it's a right angle triangle,

The missing side, say h,is the hypotenuse

28²+21²= h²

784+441=h²

√1225=√h²

h=35

Find the amplitude and the period of the graphed function; please show work or steps.

Answers

Answers:

Amplitude = 2Period = 5pi/2

===========================================

Explanation:

The lowest point occurs when y = -2. The highest point occurs when y = 2.

The vertical distance between the highs and lows is 4 units (since 2-(-2) = 2+2 = 4). This cuts in half to get 4/2 = 2.

The amplitude is 2. It measures the vertical distance from the midline to either the peaks or valleys.

-----------------------------

Note that this curve has two lowest points and one highest point shown. What we'll do is shift the graph over to the right so that each of those lowest points snap to a grid point. The lowest point on the left will move to where x = -pi, while the lowest point on the right snaps to x = 3pi/2. We'll keep each point at the same y coordinate.

The horizontal distance from x = -pi to x = 3pi/2 is

(3pi/2) - (-pi) = 3pi/2 + 2pi/2 = 5pi/2

This represents the horizontal distance from the left valley point to the right valley point. This is one full period of the curve. After we arrive at the right valley point, we repeat the process of going up and coming back down in this exact same fashion. The process is repeated forever to generate the cosine curve. The curve repeats itself every 5pi/2 units along the x axis.

Side note: any phase shift of a curve will have the same period as the original curve. This is why we're allowed to shift left or right to help find the period.


11. The length of a rectangle is double its width, If its width is 15cm, What is its area. Show
your steps.​

Answers

Answer:

450 cm squared

Step-by-step explanation:

W=15

L=2W =30

A= LxW

A= 15X30

A=450

A pool can be filled by one pipe in 8 hours and by a second pipe in 3 hours. How long
will it take using both pipes to fill the pool?
It will take about hours to fill the pool using both pipes.
(Type an integer or decimal rounded to the nearest tenth.)

Answers

Answer:

x=2.4 hours or 2 hours and 24 minutes together

Step-by-step explanation:

The length of a swimming poollane
is 10 more than 2 times the width.
If the area is 300 square meters,
find the width of the lane. Write a
quadratic equation which can be
used to find x, the width of the
pool.

Answers

Answer:

x²+5x - 150 = 0

Step-by-step explanation:

Let the length be y and width be x

If the  length of a swimming pool is 10 more than 2 times the width, then;

y = 2x+10 ...1

Since the Area is 300m²

A = xy

300 = xy .... 2

Substitute 1 into 2

300 = x(2x+10)

300 = 2x²+10x

Rearrange

2x²+10x - 300 = 0

Divide through by 2

x²+5x - 150 = 0

This gives the required quadratic expression

the equation of a line that is perpendicular to y = 2x + 1 passes through the point (4,-3)

Answers

Step-by-step explanation:

perp. -1/2

y + 3 = -1/2(x - 4)

y + 3 = -1/2x + 2

y = -1/2x - 1

The weight of adult female panthers in one habitat area are normally distributed with a mean of 82 pounds and a standard deviation of 9.8 pounds. What percent of the panthers weigh less than 76 pounds?

Answers

Answer:

27.09% of the panthers weigh less than 76 pounds

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 82 pounds and a standard deviation of 9.8 pounds.

This means that [tex]\mu = 82, \sigma = 9.8[/tex]

What percent of the panthers weigh less than 76 pounds?

The proportion is the pvalue of Z when X = 76. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{76 - 82}{9.8}[/tex]

[tex]Z = -0.61[/tex]

[tex]Z = -0.61[/tex] has a pvalue of 0.2709

0.2709*100% = 27.09%

27.09% of the panthers weigh less than 76 pounds

x²-12x+a=(x+b)² find a and b​

Answers

Answer:

Step-by-step explanation:

x² - 12x + a = (x + b)²

x² - 12x + a = x² + 2xb + b²

-12 = 2b and a = b²

b = -6

a = b² = 36

The value of a is 36 and b = -6.

What is the quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of: ax² + bx + c = 0.

The given expression is;

[tex]\rm x^2-12x+a=(x+b)^2[/tex]

The solution of the equation is determined in the folllowing steps given below.

[tex]\rm x^2-12x+a=(x+b)^2\\\\x^2-12x+a=x^2+2xb+b^2\\\\2xb + b^2 = a-12x[/tex]

On comparing the equation

[tex]\rm 2b =-12\\\\b =\dfrac{-12}{2}\\\\b=-6[/tex]

The value of a is;

[tex]\rm a=b^2\\\\b=-6\\\\a=(-6)^2\\\\a=36[/tex]

Hence, the value of a is 36 and b = -6.

Learn more about equation here;

https://brainly.com/question/15339001

#SPJ2

The measures of two complementary angles have a ratio of 2:3. What is the measure of the larger angle?

The measure of the larger angle is
°.

Answers

Step-by-step explanation:

complementary angles add up to 90

x +2/3x = 90

5/3x = 90

5x = 270

x = 54

the other angle is 36

double checking

54 * 2 ÷ 3 = 36

99165+67894321-9872345​

Answers

Answer:

58121141

Step-by-step explanation:

99165+67894321= 67993486  

67993486-9872345= 58121141

Constructed line PQ is the _______________ of line segment CD.

Answers

Answer:

Perpendicular bisector

Step-by-step explanation:

Construction done:

1). An arc is drawn from point O which intersects line 'l' at two points C and D.

2). From the points C and D two equal arcs on both the sides of the line 'l' have been drawn intersecting each other at points P and Q.

3). Points P and Q have been joined with the help of a straightedge.

Hence constructed line PQ is the PERPENDICULAR BISECTOR of the line segment CD.

Please help me it’s due today at 11:59

Answers

Okay first I think you might’ve highlighted incorrectly. You want to make sure the angles match with each other. Next you set up a proportion and solve. I’ll draw this all out for you. I hope this helps! :))
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