Jack and Susie want to save to buy a trampoline for their children. They each open a savings account that earns 1.5% a year. Jack opens his account with $1,000, and Susie opens her account with $800.

x = number of years

The following functions represent the value of the savings accounts in x years:

Jack’s savings account: f(x) = 1000(1.015)x

Susie’s savings account: g(x) = 800(1.015)x

Which function represents the total amount Jack and Susie will save in x years?

200(1.015)x
1800(1.015)x
1800(1.015)2x
1800(1.030)x

The simplified form of the ratio of Marcela's balance to Ronnie's is [tex]\frac{50 + 9n}{29 -6n}[/tex]

From the question, we are to express the ratio of Marcela's balance to Ronnie's as a rational function

From the given information,

Marcela's balance = 250 + 45n

and

Ronnie's balance = 145 - 30n

Thus,

The ratio of Marcela's balance to Ronnie's is

[tex]\frac{250 + 45n}{145 -30n}[/tex]

Simplifying

[tex]\frac{250 + 45n}{145 -30n}[/tex]

[tex]\frac{5(50 + 9n)}{5(29 -6n)}[/tex]

[tex]= \frac{50 + 9n}{29 -6n}[/tex]

Hence, the simplified form of the ratio of Marcela's balance to Ronnie's is [tex]\frac{50 + 9n}{29 -6n}[/tex]

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If the sample size is n=40 ,mean of 20 and a standard deviation then the sampling distribution is normally distributed.

Given sample size is 40, sample mean is 20, sample standard deviation is 5.

We have to find whether the distribution is normally distributed or not.

Normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off simultaneously towards either extreme. It may be one tailed or two tailed also.

Yes the given distribution whose sample size is 40, sample mean of 20 and sample standard deviation of 5 is normally distributed as the sample size is greater than 30.

Signs of normal distribution are:

Hence the sampling distribution is normally distributed.

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The grid that is shaded red and blue in ratio 1 : 2 is grid (c)

The complete question is in the image

The ratio is given as:

Red : Blue = 1 : 2

There are 12 squares in each grid.

This means that:

Red : Blue = 12 * 1/(1 + 2) : 12 * 2/(1 + 2)

Evaluate

Red : Blue = 4 : 8

The grid that has 4 red and 8 blue is (c)

Hence, the grid that is shaded red and blue in ratio 1 : 2 is grid (c)

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Answer: 112

Step-by-step explanation:

area of the parallelogram is base times height

Answer:

Step-by-step explanation:

***I hope this helps and the explanation is helpful!***

Step-by-step explanation:

5 x 0.7 = 3.5

Using a system of equations, it is found that there are 5 dimes and 9 quarters in his pocket.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

He has a total of 14 coins, hence:

x + y = 14 -> y = 14 - x.

They are worth $2.75, hence, considering the value of each coin(dimes $0.1 and quarters $0.25), we have that:

0.1x + 0.25y = 2.75

Since y = 14 - x:

0.1x + 0.25(14 - x) = 2.75

x = (0.25*14 - 2.75)/0.15.

x = 5.

y = 14 - x = 14 - 5 = 9.

There are 5 dimes and 9 quarters in his pocket.

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The height of the mat off the ground is 5 / √3 feet

The right angle triangle has an adjacent side of 5 feet.

The hypotenuse and height of the right triangle is unknown.

Therefore,

tan 30 = opposite/adjacent

tan 30 = h / 5

h = 5 tan 30

h = 5 × 0.57735026919

h = 2.88675134595

h = 2.89 feet

Therefore, it can be written in surd form as follows:

height = 5 × 1 / √3

height = 5 / √3

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Answer:

its B my good sir

Step-by-step explanation:

Answer:

[tex]\displaystyle{y-1=5(x+6)}[/tex]

Step-by-step explanation:

A point-slope form is written in the equation of  [tex]\displaystyle{y-y_1=m(x-x_1)}[/tex]. Where [tex]\displaystyle{(x_1,y_1)}[/tex] is a coordinate point and [tex]\displaystyle{m}[/tex] is slope.

The definition of parallel is to both lines have same slope. The given line equation has slope of 5. Therefore, we can write the equation in point-slope form as:

[tex]\displaystyle{y-y_1=5(x-x_1)}[/tex]

Next, we are also given the point p(-6,1). Substitute [tex]\displaystyle{x_1}[/tex] = -6 and [tex]\displaystyle{y_1}[/tex] = 1 in:

[tex]\displaystyle{y-1=5[x-(-6)]}\\\\\displaystyle{y-1=5(x+6)}[/tex]

Hence, the line equation that’s parallel to y = 5x - 4 and passes through a point (-6,1) is y - 1 = 5(x + 6)

Answer:

y - 1 = 5 ( x + 6 )

Step-by-step explanation:

       Here,

          m ⇒ slope

    y = 5x - 4 ← equation of the old line

         Now it is clear to us that,

         m ⇒ slope of the line ⇒ 5

         c  ⇒ y-intercept ⇒ -4

                 That is, m = 5

                   y - y₁ = m ( x - x₁ ).

        m = slope

           ( -6 , 1 ) ⇔ ( x₁ , y₁ )

        Let us solve this now

         y - y₁ = m ( x - x₁ )

         y - 1 = 5 ( x - ( -6) )

         y - 1 = 5 ( x + 6 )

                y - 1 = 5 ( x + 6 )

Answer:

y=3x+3

Step-by-step explanation:

So generally you'll have a linear equation in the form of slope-intercept which looks like: y=mx+b, where m is the slope, and b is the y-intercept. the y-intercept, is the value of y, when x=0, which is going to be the constant b, because mx will be 0, because m * 0 = 0. m is the slope because as x increases by 1, the y-value increases by m, which in definition is the slope, how much a function increases as x increases by 1. So if you look at the table when x goes from -1 to 0, the y value goes from 0 to 3 or an increase in 3, and the same happens when x goes from 0 to 1. So the slope is 3, and the y-intercept as mentioned before is the value of y when x=0, which in this case is 3, which can be determined by looking at the table (look at y when x=0, it's 3). So this gives you the formula y=3x+3

Answer:

a and c

Step-by-step explanation:

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

y = 1/3x - 4/3

Only the slope matters in this problem. If the original equation has a slope of 1/3, you need to use the reciprocal and negate it. So the perpendicular slope would be -3.

 a. y 2 = –3(x – 4)

b. y − 5 = 3(x 11)

c. y = -3x – five-thirds

d. y = one-thirdx – 2 3x y = 7

So a and c are perpendicular to y - 1 = 1/3(x - 2)

Answer:

30°

Step-by-step explanation:

x + 90 = 2 × 60 ( angle at center = 2 × angle at circumference.)

x +90 = 120

x = 120-90

x = 30°

Answer:

5. 68 degrees :)

6. 55 degrees :)

Step-by-step explanation:

5.

A flat line is 180 degrees so we subtract to find x :)

Lets do that now :)

180 - 112 = 68

x = 68 degrees

6.

X will be the same as 55 degrees.

All lines are tipped the same what so that is why it is 55 degrees :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

x<40

Step-by-step explanation:

x+10<50

x+10-10<50-10

x<40

Trigonometric substitution may useful when integrating the integrals root of a sum or difference of two squares.

In arithmetic, trigonometric substitution is the substitution of trigonometric features for other expressions. In calculus, trigonometric substitution is a way of comparing integrals.

Moreover, one can also use trigonometric identities to simplify sure integrals containing radical expressions.

You can use trig substitution even when you do not have square roots. particularly, if you have an integrand that looks like an expression in the square roots proven inside the above table, then you can use trig substitution.

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The expression x³ - 64 can be rewritten using difference of cubes is; (x - 4)(x² + 4x + 16)

Difference of cubes can be rewritten in the form of;

a³ – b³ = (a – b)(a² + ab + b²)

So in this question, we are given;

x³ - 64 = x³ - (4)³

where a = x and b = 4

This gives us;

(x - 4)(x² + 4x + 4²)

⇒ (x - 4)(x² + 4x + 16)

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Answer:

5 (rounded)

Step-by-step explanation:

by using the Pythagorean theorem you can calculate b

[tex]a^{2} + b^{2} = c^{2}[/tex]

here we have a and c

first lets times it by themselves

16 + b^2 = 36

now lets isolate b^2

b^2 = 36-16

= 20

now we have to get rid of the exponent ^2

b = 4.47....

rounding it would be 5!

Hope that helps :>

Answer:

27 < AB < 81

Step-by-step explanation:

By the triangle inequality theorem,

If CB is the longest, AB + 27 > 54, meaning AB > 27.

If AB is the longest, 27 + 54 < AB, meaning 81 < AB.

Thus, 27 < AB < 81

The coordinate of the vertex is; (h, k) = (3, -5)

The final equation of the parabola is; y = 5(x - 3)² - 5

The vertex is the coordinate of the crest or trough of the curve. Now, in the given graph, we only have a Trough which is the lowest point of the graph.

The coordinate of the vertex is; (h, k) = (3, -5)

2) Since the general equation is;

y = a(x - h)² + k

We will have;

y = a(x - 3)² - 5

At x = 2, y = 0. Thus;

0 = a(2 - 3)² - 5

a - 5 = 0

a = 5

3) The final equation of the parabola is;

y = 5(x - 3)² - 5

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The ratio of corresponding sides of the triangle are not in the same proportion, hence they are not similar.

Two triangles are said to be similar if they have the same shape and angles. Also, the ratio of their corresponding sides are to be in the same proportion.

From the image shown, if the triangles are similar, hence:

AB / DE = AC / DF = BC / EF

Hence:

5.6 / 4 = 4.9 / 3.5 ≠ 2.4 / 1.5

1.4 = 1.4 ≠ 1.6

The ratio of corresponding sides of the triangle are not in the same proportion, hence they are not similar.

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Answer:

The answer would be 8.3*10^7.

Step-by-step explanation:

This is because the beginning factor in scientific notation (in this case it is 8.3) must be no less than one, and no more than ten. Once we figured that out, we simply count the number of decimal points from 3 to the final 0. Try it yourself. You will discover that the resulting answer is 7 decimal movements. Now, since we are using scientific notation, we will want to multiply by ten to the power of the number of decimal movements (in this case it is 7.) And that's all! The answer is 8.3*10^7. I hope this helped (:

The closest value will be 6.9 since the value is close to 49

The square root of a number can both be negative or positive. According to the question, we are to determine the square root of 47

The square root of 47 must be between the square root of 36 and square root of 64

√36 = 6

√64 = 8

This shows that the answer must be between 6 and 8. Hence the closest value will be 6.9 since the value is close to 49

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Answer: 6.9

Step-by-step explanation: just did the test

Answer:

<3 and <4

Step-by-step explanation:

From the diagram above,

Exterior angles are angles formed outside the triangle.

The angles are: <3 and <4

Answer:

848.23 mm²

Step-by-step explanation:

LA = πdh

LA = 3.14159 × 18 mm × 15 mm

LA = 848.23 mm²

Let [tex]a,b,c[/tex] be the randomly selected lengths. Without loss of generality, suppose [tex]a

[tex]P(A + B \ge C) = P(A + B - C \ge 0)[/tex]

where [tex]A,B,C[/tex] are independent random variables with the same uniform distribution on [0, 1].

By their mutual independence, we have

[tex]P(A=a,B=b,C=c) = P(A=a) \times P(B=b) \times P(C=c)[/tex]

so that the joint density function is

[tex]P(A=a,B=b,C=c) = \begin{cases}1 & \text{if }(a,b,c)\in[0,1]^3 \\ 0 & \text{otherwise}\end{cases}[/tex]

where [tex][0,1]^3=[0,1]\times[0,1]\times[0,1][/tex] is the cube with vertices at (0, 0, 0) and (1, 1, 1).

Consider the plane

[tex]a + b - c = 0[/tex]

with [tex](a,b,c)\in\Bbb R^3[/tex]. This plane passes through (0, 0, 0), (1, 0, 1), and (0, 1, 1), and thus splits up the cube into one tetrahedral region above the plane and the rest of the cube under it. (see attached plot)

The point (0, 0, 1) (the vertex of the cube above the plane) does not belong the region [tex]a+b-c\ge0[/tex], since [tex]0+0-1=-1<0[/tex]. So the probability we want is the volume of the bottom "half" of the cube. We could integrate the joint density over this set, but integrating over the complement is simpler since it's a tetrahedron.

Then we have

[tex]\displaystyle P(A+B-C\ge0) = 1 - P(A+B-C < 0) \\\\ ~~~~~~~~ = 1 - \int_0^1\int_0^{1-a}\int_{a+b}^1 P(A=a,B=b,C=c) \, dc\,db\,da \\\\ ~~~~~~~~ = 1 - \int_0^1 \int_0^{1-a} (1 - a - b) \, db \, da \\\\ ~~~~~~~~ = 1 - \int_0^1 \frac{(1-a)^2}2\,da \\\\ ~~~~~~~~ = 1 - \frac16 = \boxed{\frac56}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Your temporary equation: }[/tex]

[tex]\mathsf{5x + x = \ ?}[/tex]

[tex]\huge\textbf{We know: }[/tex]

[tex]\large\textbf{That ONE angle equals 90}^\circ\large\textbf{ and the whole entire angle is}\\\large\textbf{360}^\circ.[/tex]

[tex]\huge\textbf{Knowing that much information, we can}\\\\\huge\textbf{make the equation much easier to solve.}\\\\\\\huge\textbf{We will simplify the angle sides and it}\\\\\huge\textbf{should give you the answer behind the}\\\\\huge\textbf{the equal sign.}[/tex]

[tex]\mathbf{360^\circ - 90^\circ = \boxed{\mathbf{the\ mystery\ number\ behind\ the\ equal\ sign}}}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{the\ mystery\ number\ behind\ the\ equal\ sign = \boxed{\bf 270}}}}[/tex]

[tex]\huge\textbf{New equation:}[/tex]

[tex]\mathbf{5x + x = 270^\circ}[/tex]

[tex]\huge\textbf{COMBINE the LIKE TERMS:}[/tex]

[tex]\mathbf{(5x + x) = 270^\circ}[/tex]

[tex]\mathbf{5x + x = 270^\circ}[/tex]

[tex]\huge\textbf{Remember a variable by itself is}\\\\\huge\textbf{understood as an invisible 1.}[/tex]

[tex]\huge\textbf{Anyway, back to answering the equation}[/tex]

[tex]\mathbf{5x + x}[/tex]

[tex]\mathbf{= 5x + 1x}[/tex]

[tex]\mathbf{= 6x}[/tex]

[tex]\huge\textbf{New equation:}[/tex]

[tex]\mathbf{6x = 270^\circ}[/tex]

[tex]\huge\textbf{DIVIDE 6 to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{6x}{6}=\dfrac{270}{6}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{x = \dfrac{270}{6}}[/tex]

[tex]\mathbf{x = 45}[/tex]

[tex]\huge\textbf{Answer:}[/tex]

[tex]\huge\boxed{\mathsf{x = 45}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The probability of getting a tail on the coin and an even number on the number cube is 1/4.

option C is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The sample space for flipping a coin and rolling a cube dice.

S = (H, T) x (1, 2, 3, 4, 5, 6)

S = { (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5),

(T, 6) }

n(S) = 12

The number of outcomes of getting a tail and a number even number on the number cube.

= { (T, 2), (T, 4), (T, 6) }

= 3

The probability of getting tails on the coin and an even number on the number cube.

= 3/ 12

= 1/4

Thus,

The probability of getting a tail and an even number is 1/4.

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Answer:

13° , 29° , 138°

Step-by-step explanation:

let x be the smallest angle , then

2x + 3 is the middle angle and

2x + 3 + 109 is the largest angle

summing the 3 angles and equating to 180

x + 2x + 3 + 2x + 3 + 109 = 180 , that is

5x + 115 = 180 ( subtract 115 from 180 )

5x = 65 ( divide both sides by 5

x = 13

2x + 3 = 2(13) + 3 = 26 + 3 = 29

2x + 3 + 109 = 29 + 109 = 138

the 3 angles are 13° , 29° , 138°

Based on the data, table that shows a proportional relationship is the first table.

Data is said to be proportional if it increases or decreases at a constant rate.

The first table has proportional data because the height increases by 5 centimeters everyweek, which shows a constant rate.

Note: This question is incomplete; below I attach the missing section:

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