sarah gets pocket money every week from the age of 5 until her 21st birthday and is given a choice of 2 options options .
option 1:get the same number of pounds each week as her age.
option 2 : get 5 pounds a week aged 5 and increasing by 15% a year.
which option should Sara choose ?

please help

Answer:

X = -4

Step-by-step explanation:

25^(x+3) = 1/5

5^2^(x+3) = 5^(-2)

5^(2x+6) = 5^(-2)

2x+6 = -2

2x = -8

x = -4

Answer:

x = -7/2

or can be written,

x = -3.5

Step-by-step explanation:

25 is a power if 5 and so is 1/5. If you can write both sides as 5 to "some" power. Then the equation is just getting those two exponents equal. See image.

 Using logarithms is a nice shortcut. But then you need need a calculator. See image.

The missing number so that the equation has no solution is -3 5/6.

A linear equation is an equation that has a single variable that is raised to the power of one. When shown on a graph, a linear equation is a straight line that slopes either upwards or downwards.

If the equation has no solution, it means that the value of the left hand equation and the value of the right hand equation are equal.

In order to determine the solution, take the following steps:

x + 19 = 2x - 4 - 7x

Combine similar terms together: 19 + 4 = 2x - 7x - x

Add similar terms together: 23 = -6x

Divide both sides of the equation by -6: x = 23 / - 6

x = -3 5/6

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The 99% confidence interval is ( 255.157, 262.843 ).

The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.

According to the given question,

n = number of pregnant women who are smokers

n   =   115

μ = average pregnancy length for the sample

μ   =   259

σ = standard deviation

σ   =   16

At a 99% confidence level,

α   =   0.01

z(α/2)   =   2.576

The confidence interval is

CI    =   μ ± z(α/2).(σ/√n)

      =   259 ± (2.576)(16/√115)

      =   259 ± (2.576)(16/10.724)

      =   259 ± (2.576)(1.492)

      =   259 ± 3.843

      =   ( 259 - 3.843, 259 + 3.843)

CI   =   ( 255.157, 262.843 )

Therefore, the 99% confidence interval to estimate the length of pregnancy for women who smoke is ( 255.157, 262.843 ).

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The complete question is

Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 115 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 259 days. From a large body of research, it is known that the length of human pregnancy has a standard deviation of 16 days. The researchers assume that smoking does not affect the variability in pregnancy length.

Find the 99% confidence interval to estimate the length of pregnancy for women who smoke.

Note: The critical z-value to use is 2.576

Percentage change expresses the ratio of the change in the amount of an initial quantity to the initial quantity as a percentage.

Mathematically, the formula for percentage change, C, can be presented as follows;

[tex]C = \dfrac{x_{2} - x_{1} }{ x_{1} } \times 100[/tex]

Where:C = The percentage change

[tex]x_{1} [/tex] = The original value

[tex]x_{2} [/tex] =The new value

Graphically, percentage change can be presented as follows;

When the number of fruits that drops from a three each month, changes from 10 to 8, the percentage change is therefore;

[tex] C = \dfrac{10-8}{10} = 20\% [/tex]The percentage change is 20%

Initial number of fruits that drops monthly from the tree;

##########

The new number of fruits that drops from the tree on the specified month;

########

The difference in the number of fruits that drops from the tree is 2, which corresponds to the 20 % calculated for the percentage change.

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The measure of side P to the nearest degree is 79 degrees.

Given:

ΔOPQ ,

O = 700 cm,

P = 840cm

Q = 620cm.

To find:

The measure of angle P.

According to the Law of Cosines:

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. The law of cosines states:

                                   [tex]cos A = b^{2} +c^{2} - a^{2} / 2bc[/tex]

Using Law of Cosines ΔOPQ, we get,

           cos P = o² +q²- p² / 2oq

       ⇒ cos P = (700)² + (620)² -(840)² /2×700×620

       ⇒ Cos P = 490000 + 384400 - 705600 / 868000

       ⇒ Cos P = 168800/868000

on further simplification, we get,

Cos P = 0.19447

P = Cos⁻¹ (0.19447)

P = 78.786236

P = 79.

∴ the measure of angle P is 79 degrees.

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Therefore, the measure of angle P is 79 degrees.

The following are the answers:

23. The cost for 7 lessons is $82, and the cost of 11 lessons is $122, we have;

The total cost of lessons is;  f(x) = y = 10·x + 12 and one lesson costs $22

24. The equation of population of Laredo, Texas is :

p = 92500t/17 + 123000

25. The linear equation to represent the temperature T at an elevation of x, where x is in thousands of feet is T = -(2000/3)x + (4228/3).

26. The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;

⇒ R = 4c

Given:

23. Lydia wants  to purchase guitar lessons.

7 lessons = $82

11 lessons = $122

we are asked to determine the linear equation which finds the total cost C for d lessons.

The general equation for the total cost of lessons is;

Let a represent the cost of 7 guitar lessons, and let b represent the cost of 9 guitar lessons, given that the cost increases linearly with the number of lessons, we have;

The cost increase per lesson = The slope of the linear function representing the total cost of a guitar lesson

Therefore,

slope = b-a/11-7 = b-a/4

Expressing the equation in slope and intercept form, we get:

(y-a) = b-a/4 . (x-7)

y = b-a/4 . x-7 × b-a/4 + a = b-a/4 . x + 11.a-7.b/4

y = b-a/4 . x + 11.a-7.b/4 = 1/4.((b-a).x+11.a-7.b

where a=$82 and b=$122 we ahve:

y = 1/4 . (122-82) . x+1/4 . (11×82-7×122) = 10x+12

The total cost of a lesson is:

y = 10×1+12

= 22

24. Given:

t = the number of years after 1990.

So, for 1990, t = 0. So the coordinate is (0, 123000).

For 2007, t = 17. So the coordinate is (17, 215500).

using point slope formula:

m = 215500-123000/17-0

m = 92500/17

⇒ p = 92500t/17 + 213000

25. The equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at

x = 0.

We know the slope is (y₂ - y₁)/(x₂ - x₁).

∴ Here the temperature is y and the height is x.

And the points are (6000, 76) and (12000, 49)

So, slope =(12000 - 6000)/(49 - 76).

Slope = (6000/-27).

Slope = -(2000/9).

Now we have to determine the y-intercept by putting any of the points in y = mx + b.

So, 76 = -(2000/9)×6000 + b.

76 = -(12000/9) + b.

76 = -(4000/3) + b.

b = 4000/3 + 76.

b = 4228/3.

∴ y = -(2000/3)x + (4228/3) or T = -(2000/3)x + (4228/3).

26. The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

he friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale.

On first day, they collect = $60

On second day, they collect = $88

Now,

We have to find the equation as;

⇒ R = mc + b

We need to find the value of m and b.

Since, The first point = (15, 60)

The second point = (22, 88)

Hence, Slope (m) = (88 - 60) / (22 - 15)

m = 28 / 7

m = 4

And, To find b substitute R = 60 , c = 15 and m = 4 in above equation,

⇒ R = mc + b

⇒ 60 = 4 x 15 + b

⇒ b = 0

Thus, Substitute m = 4 and b = 0 in equation (i) we get;

⇒ R = mc + b

⇒ R = 4c + 0

⇒ R = 4c

Therefore, The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;

⇒ R = 4c

Hence we get the required answers.

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The value of sin θ of the given right angle triangle using trigonometric ratios is; A: 5/13

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). They are based on the angles formed from the ratio of sides of a right angle triangle. Thus;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

From the given image, we see that;

Hypotenuse = 13

Adjacent = 12

Opposite = 5

Thus;

tan θ = 5/12

θ = tan⁻¹(5/12)

sin θ = 5/13

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The fraction of the teacups that are either indigo or teal in Cassie's Tea Shop are 1/2.

The fraction of teacups in Cassie’s Tea Shop which will either be indigo or teal can be found by adding the fractions of the tea cups which are indigo, to those which are teal.

Fraction of teacups which are indigo = 1/12

Fraction of teacups which are teal = 5/12

The fraction of teacups which are indigo or teal is:

= 1 / 12 + 5 / 12

= 6 / 12

In the simplest form, this is:

= (6 / 6) / (12 / 6)

= 1 / 2

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Answer: The answer to this problem is 1/2.

Step-by-step explanation:

The first thing you do is to add 1/12 and 5/12 together.

1/2 + 5/12 = 6/12

Then you simplify 6/12 to get the answer.

6/12 = 1/2

6/6 = 1

12/6 = 2

This is how you get the answer!

Answer:

26

Step-by-step explanation:

you are given 45° and 90° so you know the third angle will also be 45° because the sum of all angles always is 180°
with all 3 angles you apply the sine law
a / sin( α ) = b / sin( β ) = c / sin( γ )
then you'll see that a = 26

The given equation, -x + 3(1 + x) = 3(x +2), solved for x, is x = -3

From the question, we are to solve the given equation.

The given equation is

-x + 3(1 + x) = 3(x +2)

To solve this equation, we will determine the value of the variable in the equation.

The variable in the equation is x.

Thus, we will solve for x in the equation.

-x + 3(1 + x) = 3(x +2)

Clear the parentheses by applying the distributive property

-x + 3 + 3x = 3x + 6

Collect like terms

-x + 3x - 3x = 6 - 3

-x = 3

Multiply both sides of the equation by -1

-1 × -x = -1 × 3

x = -3

Hence, the value of x is -3

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According to the distance-speed-time formula, the equation that could be used to solve this formula is 60/x+10 - 60/x = 1/2

Distance-speed-time

Basically, the formula for speed is speed = distance ÷ time.

In order to work out what the units are for speed, you need to know the units for distance and time.

Given,

Jackie travels 60 km to work. Since she began taking a new route (still 60 km to work) she gets there 30 minutes sooner because she can drive 10 km/hour faster.

Here we need to find the equations could you use to solve the problem.

Let us consider x be the speed of Jackie.

Therefore, the time has been calculated as,

Time1 = 60/ x

Now, the speed is increased as 10, then it can be written as,

=> x + 10

Therefore, the new time Time2 is calculated as,

=> Time2 = 60 / x + 10

So, the equation is obtained by calculating the difference of the times,

So, the equation is,

=> Time 2 - Time1

=> 60/x+10 - 60/x

Now, we know in this one she gets there 30 minutes sooner,

So, it can be written as,

=> 60/x+10 - 60/x = 30/60

=> 60/x+10 - 60/x = 1/2

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Answer:

8 hours

Step-by-step explanation:

2 cars will be $400 since 2x200=400

500-400=120

He made $120 from hours alone so now we divide by 15

120/15=8

He worked 8 hours

Hopes this helps please mark brainliest

4y = -3x-12 the equation of a line perpendicular to y= 4/3 ​x−1 that passes through the point (-4,-8).

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis.

The slope of parallel lines is the same. The slopes of perpendicular lines are opposing reciprocals. To put it another way, if m=a/b, then m⊥= -b/a.

y= 4/3 x - 1

Slope = 4/3

Equation of line perpendicular to this line

y= -( 3/4) x+b

As slope is -1/m

Now as line passes through (-4,-8)

Plug it in

-8 = (-3/4)(-4) +b

-8= 3+ b

Gives b = -12

So the equation of line will be

y = (-3/4) x -12

or 4y = -3x-12

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Side-Side-Side can be used to prove this pair of triangles is congruent.

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent. When two or more triangles are taken that are similar to one another, their corresponding sides and angles are also similar to one another.

According to this question,

Two respective sides of triangles are equal.

One side is common between these two triangles.

Therefore, the third side of the triangles is equal as well.

As all respective sides of the triangles are equal, we can say that the triangles are congruent by Side-Side-Side.

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Researchers developed a blood test which is quite fair. It gives a positive reaction of 97% people who have that disease and 5% who don't have that disease.

Therefore, the Probability of Type I error if the new blood test is used is 0.025.

H₀ : "the individual does not have the disease"

(a) Probability of Type I error of rejecting  when  is true =

Probability of concluding the individual has the disease when in fact the individual does not have the disease = 0.025 because the blood test erroneously gives a positive reaction in 2.5% of the people who do not have the disease.

(b) Probability of Type II error = Probability of fail to reject  when  is true= Probability of concluding the individual does not have the disease when in fact he has the disease = 0.05 because the blood test gives a positive reaction in 97% of the people who have the disease, this implies that the test gives a negative reaction in 5% of the people who have the disease.

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The arithmetic sequence that has the given features is presented as follows:

[tex]a_n = 2 + 3(n - 1)[/tex]

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and called common difference d.

The nth term of an arithmetic sequence is obtained by the following rule:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the sequence.

The sum of the first n terms is presented as follows:

[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]

The sum of the first nine terms is of 126, hence:

[tex]S_9 = 126[/tex]

[tex]\frac{9(a_1 + a_9)}{2} = 126[/tex]

[tex]4.5(a_1 + a_9) = 126[/tex]

The ninth term is written as follows:

[tex]a_9 = a_1 + 8d[/tex]

Hence:

[tex]4.5(a_1 + a_1 + 8d) = 126[/tex]

[tex]9a_1 + 36d = 126[/tex]

[tex]a_1 + 4d = 14[/tex]

The sum of the second nine terms is of 369, hence:

[tex]S_{18} = 126 + 369[/tex]

[tex]S_{18} = 495[/tex]

Then:

[tex]\frac{18(a_1 + a_{18})}{2} = 495[/tex]

[tex]a_{1} + a_{18} = 55[/tex]

The 18th term is:

[tex]a_{18} = a_1 + 17d[/tex]

Hence:

[tex]2a_1 + 17d = 55[/tex]

From the first equation, it is found that:

[tex]a_1 = 14 - 4d[/tex]

Hence the common difference is obtained as follows:

2(14 - 4d) + 17d = 55

28 - 8d + 17d = 55

9d = 27

d = 3.

Hence the first term is of:

[tex]a_1 = 14 - 4(3) = 2[/tex]

Thus the definition of the sequence is:

[tex]a_n = 2 + 3(n - 1)[/tex]

The problem asks for the definition of the arithmetic sequence.

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Answer:

Your answer should be x = 2

Step-by-step explanation:

149 + 13(2) + 5 = 180.

Hope this helps.

Answer:

x=2

Step-by-step explanation:

You add 149 and 5, which is 154. Then you take the total which is 180, and subtract it by 154. So 180-154=26 Then you take and do 26/13 which is 2.

149+13(2)+5=180

149+26+5=180

Definitely 2.

Hope this helps!!!

Answer: x+x+y.y.y = 2x+y^3 ( y cube)

Step-by-step explanation:

Answer:

2x+y^3

Step-by-step explanation:

x's are added while y's are multiplied

The interpolations;

(a) 81st

= NORM.INV(0.81;0;1)

0.878

(b) 19th

=NORM.INV(0.19;0;1)

-0.878

(c) 76th

=NORM.INV(0.76;0;1)

0.706

(d) 24th

=NORM.INV(0.24;0;1)

-0.706

(e) 11th

=NORM.INV(0.11;0;1)

-1.227

Given,

Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is a probability distribution that is symmetric around the mean.

"A numerical measurement used in statistics of a value's relationship to the mean (average) of a set of values, assessed in terms of standard deviations from the mean," according to Wikipedia, is the Z-score.

For this case we can find the percentiles with the Norm.inv function in Excel and we got:

(a) 81st

= NORM.INV(0.81;0;1)

0.878

(b) 19th

=NORM.INV(0.19;0;1)

-0.878

(c) 76th

=NORM.INV(0.76;0;1)

0.706

(d) 24th

=NORM.INV(0.24;0;1)

-0.706

(e) 11th

=NORM.INV(0.11;0;1)

-1.227

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Answer:

im not sure if this helps but you can write it with letter like this y = mx + b

Step-by-step explanation:

Equation of the line passing through the given points is y = -1/5(x) + 29/5.

Given points:

(-1,6) and (-2,11)

slope m = 11 - 6 / -2 - (-1)

= 5/-2+1

= 5/-1

m = -1/5.

substitute m and (-1,6) in y=mx+c.

y = mx + c

6 = -1/5(-1) + c

6 = 1/5 + c

c = 6 - 1/5

= 30 - 1 / 5

c = 29/5.

y = mx + c

y = -1/5(x) + 29/5.

Therefore equation of the line passing through the given points is y = -1/5(x) + 29/5.

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The total Cost of the equipment is $2,27,700. In which the following included, excluded and expensed as incurred are

Invoicing costs - included in the price

Electrical work required for installation - Included in the price

Delivery costs - included in the price

Sales tax - included in the price

Repair costs - not included or excluded

A machine used by a company to produce products and services is known as a machine tool. It is a vital long-term asset as it speeds up the production process such as transportation, computers and other equipment. These costs will include the costs that were necessary to start opening the plant property. There are equipment costs.

We have given the following details ,

Total Cost DR Machinary DR Expense

Invoice cost $190,000 $190,000

electric work

and $20,000 $20,000

installation cost

delivery cost। $4,000 $4,000

sales tax $13,700 $13,700

repair cost $1,850 $1,850

total $22,9550 $22,7700 $ 1,850

Accordingly, all the mentioned costs except for the repair of the part will be included in the cost of the machinery.

Included in price Excluded

invoice repair cost

electric and installation

delivery

sales tax

Hence , the total equipment cost is $22,7700.

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Answer:

Urban

Step-by-step explanation:

Regarding the objective function C = 3x + 4y, the minimum and the maximum value are given as follows:

The objective function is defined as follows:

C = 3x + 4y.

The extremas of the function, that is, the minimum and the maximum values, can be obtained at either of these following points:

These extreme values are the numeric values at these points.

In this problem, there is only a single curve, hence the vertices are given as follows:

(0,0), (0,4) and (4,0).

Then the numeric values of the objective function are these points are given as follows:

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The expression that represents the total number of illustrations in Julio's sketch pad after his museum visit is given as follows:

Total number = 20 + x.

The expression that represents the total number of illustrations in Julio's sketch pad after his museum visit is obtained adding the previous amount of illustrations to the number of illustrations that were added during the visit to the museum, hence:

Total number of illustrations = Previous number of illustrations + number of illustrations added during the visit.

In the context of this problem, the values of these parameters are given as follows:

Hence the expression is defined as follows:

Total = 20 + x.

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Answer:

Step-by-step explanation:

First, find the slope of 4x - 5y = 7

Simplify it down to a readable form:

5y = 4x - 7

y = (4x - 7)/5

y = 4/5 x - 7/5

slope = 4/5

slope perpendicular to 4/5 is its opposite reciprocal, which would be -5/4.

given the point (2,3), we can get the equation using point slope form for linear equations: y-k = m(x-h) for point (h,k).

now plug:

y-3 = (4/5)(x-2)

y-3 = (4/5)x - 8/5

Answer:

x = 5; m<1 = 69

Step-by-step explanation:

We know that the two angles with degrees 20x+11 and 25x-14 are vertical angles and are thus congruent or equal.  Therefore, we can set the two angles equal to each other to find x:

[tex]20x+11=25x-14\\20x+25=25x\\25=5x\\5=x[/tex]

If we plug in x into any of the two angles, we find the measure of both angles is 111.

The most probable relationship between angle 1 and the other two angles is supplementary, which means that the measure of angle 1 and any of the two angles beside it is 180.

To find m<1, represented as x, we can use the equation:

[tex]180=20(5)+11+x\\180=111+x\\69=x[/tex]

Answer:

A square number is always nonnegative. So a quantity squared must be nonnegative.