the sum of the ages of a father and his son is 38 years. if the father is 22 years older than his son , find their present ages ​

Answer:

y= -5x-8

Step-by-step explanation:

Slope-intercept form equation: y=mx+b

b is where the line meets the y line. So it meets it at the number "-8". Then with the mx in the equation, you find that by doing rise over run. I got 5/-1, which goes to just plain old -5.

I hope this helps!!!

The component form of two vectors 2u - v is (10, 0), no magnitude in the second direction.

A vector is a quantity that has both magnitude and direction.

Given are two vectors u = (4, - 1) and v = (-2, - 2).

∴ The value of 2u - v in component form is 2(4, - 1) - (-2, - 2).

2u - v = (8, - 2) - (-2, - 2).

2u - v = (8+2, - 2+2).

2u - v = 10

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Therefore the solution to this question of proportion,  78% of what number is 42 is 53.84.

In general, the word "proportion" is used to describe a part, share, or amount that is compared to an entire. Two ratios are in proportion, according to the definition of proportion, when they are equal. Two ratios or fractions being equal is expressed by an equation or a statement.

Here,

If 78% of x (any number) equals 42, then we need to set this up as an equation in order to figure it out.

1) Writing down 78% as a fraction. Taking into account that we refer to a product when we say 78% of some amount (x).

78%=78/100 \s=>78x/100=42

2) Afterward, we can continue: 

100*78x/100=42*100

78x=4200

x=4200/78

x=53.84

Therefore the solution of 78% of what number is 42 is 53.84.

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The population standard deviation sd would be 0.543 .

Given :

a survey is carried out at uiuc to estimate the proportion of students who like to wear costumes on halloween. 1000 students participated in the survey. if you were to create a confidence interval with 98% confidence and a 4% margin of error .

we know that

margin of error = z * s / [tex]\sqrt{n}[/tex]

Z score at 98% = 2.326

0.04 = 2.326 * s / [tex]\sqrt{1000}[/tex]

0.04 * [tex]\sqrt{1000}[/tex] = 2.326 * s

1.264 = 2.326 * s

s = 1.264 / 2.326

s = 0.543

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Answer:

Step-by-step explanation:

y = 6x - 12

6x - 12 = y

6x = y + 12

x = (y + 12)/6

The equation of the first graph is

y > 2x - 4

The equation of the first graph is

y ≥ -x + 4

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m calculating using the points on the graph (0, -4) and  (2, 0)

m = (y₀ - y₁) / (x₀ - x₁)

m = (-4 - 0) / (0 - 2)

m = (-4) / (-2)

m = 2

c = y intercept, from the graph

c = -4

The equation of the line is y = 2x - 4

shading above the line is greater than and dotted lines means it does not have equal to

hence y > 2x - 4

for the second graph

the slope, m calculating using the points on the graph (0, 4) and  (4, 0)

m = (y₀ - y₁) / (x₀ - x₁)

m = (4 - 0) / (0 - 4)

m = (4) / (-4)

m = -1

c = y intercept, from the graph

c = 4

The equation of the line is y = -x + 4

shading above the line is greater than and solid lines means there is equal to in the inequality

hence y ≥ -x + 4

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a) Green is 0.3, Yellow is 0.1

b) There are 12 green pins in the bag

Given,

In the question:

There are some colored pins in a bag. The pins can be green, yellow, purple, or grey. A pin is going to be taken at random from the bag.

The table shows the probabilities of picking a purple or grey pin.

The table is not given in the question :

So, The table is :

Colors:          Green         Yellow      Purple        Grey

Probability:                                         0.35           0.25

To find the :

a)Complete the table.

There are 14 purple pins in the bag.

b)Work out how many green pins are in the bag.

Now, According to the question:

The probability is the ratio between the possible outcomes over the total outcomes:

The value of the probability of possible outcomes is greater than 0 and smaller than 1 (0 < P < 1)

The sum of the probabilities of all outcomes must equal 1.

A bag contains some green, yellow, purple and grey pins

∵ The probability of picking a purple pin P(purple) = 0.35

The probability of picking a grey pin P(grey) = 0.25

→ The total of all possible outcomes is 1

The sum of the probability of green and yellow pins = 1 - 0.35 - 0.25

The sum of the probability of green and yellow pins = 0.4

P(green) + P(yellow) = 0.4 ⇒ (1)

∵ The probability of picking a green pin is 3 times the probability

of picking a yellow pin

P(green) = 3 P(yellow) ⇒ (2)

→ Substitute (2) in (1)

3 P(yellow) + P(yellow) = 0.4

4 P(yellow) = 0.4

→ Divide both sides by 4

P(yellow) = 0.1

The probability of picking a yellow pin is 0.1

→ Substitute P(yellow) in (20 by 0.1

P(green) = 3(0.1)

P(green) = 0.3

The probability of picking a green pin is 0.3

Green = 0.3, Yellow = 0.1

There are 14 purple pins in the bag

P(purple) = 0.35

0.35 of purple pins = 14

→ To find the total number of pins in the bag divide 14 by 0.35

The total number of pins = 14 ÷ 0.35

The total number of pins = 40 pins

P(green) = 0.3

The number of green pins = 0.3 × 40

The number of green pins = 12 pins

Hence, There are 12 green pins in the bag.

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Answer:

x=2 y=1

Step-by-step explanation:

Answer:

y=2x-3

Step-by-step explanation:

How many packages of cookies will be made?

15

Step-by-step explanation:

Sheila made 51 cookies… Sister make 27 cookies ( add them )

78…..

Brother ate 3 cookies..

78 - 3 =

75..

75/5 =

15

By solving the given equation  20 + 0.44x = 19 + 1.69x we get x=0.8.

When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. For instance, an equation in French is described as having one or more variables, whereas in English, an equation is any properly written formula that consists of two expressions linked by the equals sign.

Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved.

Given,

20 + 0.44x = 19 + 1.69x

20-19=1.69x-0.44x

1=1.25x

x=0.8

Therefore, by solving the given equation  20 + 0.44x = 19 + 1.69x we get x=0.8.

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The solution is the two percent changes are not the same, and the second percent change is greater

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage

Given data ,

Let the initial value of the pens = $ 4.09

Let the final value of the pens = $ 3.59

So , the percentage change is calculated by

Percentage decrease = ( ( final value - initial value ) / initial value ) x 100

Substituting the values in the equation , we get

Percentage decrease = ( ( 3.59 - 4.09 ) / 4.09 ) x 100

Percentage decrease = ( -0.5 / 4.09 ) x 100

Percentage decrease = -0.122249 %

Therefore , the approximate percentage decrease = -0.1 %

Now ,

The value of the pens is increased to = $ 4.09

So , the percentage change is calculated by

Percentage increase = ( ( final value - initial value ) / initial value ) x 100

Substituting the values in the equation , we get

Percentage increase = ( ( 4.09 - 3.59 ) / 3.59 ) x 100

Percentage increase = ( 0.5 / 3.59 ) x 100

Percentage increase = 0.13927 %

Therefore , the approximate percentage increase = 0.1 %

Hence , the two percent changes are not the same, and the second percent change is greater

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lower control threshold for the data is LCL = -0.007

The lower control limit on a control chart is the value below which any particular data point would be deemed to be out of statistical control owing to specific cause variation. It is represented by a line below the centerline.

The lower control limit formula: LCL = Pbar - [tex]3 \sqrt{p bar (1- p bar)/n}[/tex]

To date,

Size of sample = n

Sample size is 12 samples.

Televisions with defects = X

We have a sample defect = p

p chart week with n = 200

x = 4, 7, 5, 6, 8, 3, 12, 4, 4, 5, 6, 2.

P = x/n

p = 4/200 = 0.02

p = 7/200 = 0.035

p = 5/200 = 0.025

p = 6/200 = 0.03

p = 8/200 = 0.04

p = 3/200 = 0.015

p = 12/200 = 0.06

p = 4/200 = 0.02

p = 4/200 = 0.02

p = 5/200 = 0.025

p = 6/200 = 0.03

p = 2/200 = 0.01

total will be 0.33

p bar = 0.33/12

p bar = 0.0275

The lower control limit formula: LCL = Pbar - [tex]3 \sqrt{p bar (1- p bar)/n}[/tex]

LCL =  0.0275 - 3[tex]\sqrt{ 0.0275 (1- 0.0275/200}[/tex]

LCL = -0.007

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The value for n is n = the quantity 7 times c minus 25 all over negative p.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

−np − 3 = 7(c − 4)

Now, solving for n

-np - 3 = 7c - 28

-np = 7c - 28 + 3

-np = 7c -25

-n = 1/p( 7c- 25)

n= 1/ (-p) (7c- 25)

So, the value for n is n = the quantity 7 times c minus 25 all over negative p.

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Answer:12.9

Step-by-step explanation:

Therefore the required probability as a total number of the expected draw of blue tiles will be 16.

Probability = the number of possible paths to success / The total number of outcomes. That is a chance of getting an event

The formula for calculating an event's probability is the ratio of favorable outcomes to the total number of outcomes. Probabilities are always between 0 and 1. Probability = Number of Favorable Outcomes / Total Number of Outcomes is the general probability formula.

Given:

Number of red tiles = 14

Number of blue tiles = 20

Number of green tiles = 16

total number of tiles = 14+20+16=50

P(blue) = number of blue tiles / total number of tiles

            = 20/50

             =2/5

40 times the procedure is repeated

so, answer=(2/5)*40 = 16

Therefore the required probability as a total number of the expected draw of blue tiles will be 16.

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Answer:

3/48

Step-by-step explanation:

Answer:

ANS:- Y =4

Step-by-step explanation:

x =20 half x =10

y = 8 half y = 4

If the mass of dog is 45.5 lb then the mass in kilogram is  20.475 Kg .

In the question ,

it is given that ,

the mass of the dog is = 45.5 lb ,

we have to convert the given mass of dog into Kilogram .

For that we will need the conversion rate ,

the conversion rate to convert mass from lb to Kilogram is given as , 1 lb is = 0.45 kg ,

So , 45.5 lb in Kilogram will be equal to  = 45.5 × 0.45 ,

After multiplication ,

we get ,

mass = 20.475 Kg .

Therefore , the mass in Kilogram is 20.475 Kg .

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Answer: 9x = 288, 32 hours

Step-by-step explanation:

x can be the variable and it represents the hours he worked. 9 is the amount made each hour, so it is multiplied by x. 288 is the total made, so 9x=288.

9x = 288 Divide by 9 on both sides to isolate x
x = 32 hours. Kevin worked 32 hours this week

Answer:32

Step-by-step explanation: 32x9=288

Answer:

4 hours

Step-by-step :

If Sunny runs twice as fast as Moonbeam

Given the assumed data:

Sunny's speed = 12m/h

Moonbeam's speed= 6m/h

Therefore, if they run for 2 hours, Sunny would have covered 12 * 2 = 24 miles

While Moonbeam would have covered 6 *2 = 12 miles in the same 2 hours.

This given illustration shows that given that all parameters are equal, except the x2 speed of Sunny to that of Moonbeam, he would always be 2x faster than Moonbeam.

If they run for 4 hours, Sunny would have covered 12 * 4 = 48 miles

While Moonbeam would have covered 6 *4 = 24 miles in the same 4 hours.

The perimeter of the rectangle is 44cm

Given:

Area: [tex]Area = 105cm^{2}[/tex]

width: [tex]w= 7 cm[/tex]

To find the perimeter first we need to find the length of the rectangle.

We find it with the formula for the area of a rectangle:

[tex]Area = width*length[/tex]

so clearing for length:

[tex]length = \frac{area}{width}[/tex]

substituting known values:

[tex]length = \frac{105}{7} \\length = 15 cm[/tex]

And now we can calculate the perimeter:

[tex]perimeter = 2(width + length)\\\\perimeter = 2(7cm + 15cm)\\\\perimeter = 44cm[/tex]

Hence , the perimeter of the rectangle is 44cm

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Answer:

9 workers

Step-by-step explanation:

15 workers = 48 hrs build

x workers = 30 hrs build

cross multiply

15 × 30 = x × 48

450 = 48x

x =

[tex] \frac{450}{48} [/tex]

x = 9.37

so it will take approximately 9 workers to build a wall for 30hrs

i hope this helped

Answer:1/2

Step-by-step explanation:

3/4+(-1/2)-(-1/4)

3/4-1/2+1/4

1-1/2=1/2

Explanation is there for your question

The time taken by the horizon to develop is calculated with the half-life which is 675 years.

Organic matter particles have more negatively charged particles, which hold on the positively charged particles.

The organic matter in the soil affects the water holding capacity of the soil. Thus is if there are more organic matter, this means that the organic matter is more. Thus the farmer has to add more organic matter.

In order to reduce the the acidity, the farmers add Calcium oxide, Calsium hydroxide and so on.

The horizon s formed after years of sediment formation. Thus the process can take years.

This is the half-life of the soil and with the formula of half-life we get 225 * 3 = 675 years.

Therefore, the time taken by the horizon to develop is 675 years.

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Answer:

1

Step-by-step explanation:

→ Complete the square

( x - 2)² - 4 + ( y - 1 )² - 1 = 16

→ Simplify

( x - 2 )² + ( y - 1 )² = 21

→ Find centre

( 2 , 1 )

The system of equations y = (1/3)x + 7 and y = -2x³ + 5x² + x - 2 will have 1 solution thus option (B) is correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In other words, the equation must be constrained with some constraints.

As per the given equations,

y = (-1/3)x + 7 and y = -2x³ + 5x² + x - 2

The graph of both equations has been plotted below,

The number of points where both curves cut each other = 1

Thus, the number of solutions = 1

Hence "The system of equations y = (1/3)x + 7 and y = -2x³ + 5x² + x - 2 will have 1 solution".

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Answer:

1 solution

Step-by-step explanation:

Plato/Edmentum

Answer:

x=1

Step-by-step explanation:

because x has to be same in all number