Find the amount A in an account (to the nearest cent) after 10 years if

dA
dt = rA, A(0) = 15,000 and A(8) = $22,377.37

Answer:

There Are 40 Bicycles And 23 Tricycles

Step-by-step explanation:

Let, x be bicycles and y be tricycles

Condition 1;

: x + y= 63

: x =63-y

Condition 2;

Number Of Tires=149

:2x + 3y =149 [2x=Two Tires Of Bicycle And

3y=Three Tires Of Tricycle]

:x = 149-3y/2

Combination 1 & 2;

63-y = 149-3y/2

126-2y = 149-3y

y=23

x = 63-23

=40

18,564 different groups of 6 children can be driven.

Here we are given 18 Children in total and we can fit Only 6 Children out of them.

The number of different groups of 6 children that can fit into the van ca be calculated with a simple formula

The formula used will be -

n! = n(n-1)(n-2)(n-3).......1

n!= (18 x 17 x 16 x 15 x 14 x 13) / (6 x 5 x 4 x 3 x 2)

  = 18,564

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Answer:

∠ABC = 98°

Step-by-step explanation:

an isosceles triangles base angles have the same angle measures

so both are 71

add them and then subtract that from 180 to find ∠ABD

180 - (71 + 71)

180 - 142 = 38

that is ∠ABD

to find ∠ABC you must add ∠DBC to ∠ABD

all angles of an equilateral triangle are equivalent

they are also 60 degrees

so add 60 to 38

38 + 60 = 98

that is your answer

The slope-intercept form of the equation of the line through the given point with the given slope is y=-4x+1.

The given coordinate point is (-1, 5) and slope=-4.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Substitute (x, y)=(-1, 5) and m=-4 in standard form of the slope intercept form, we get

5=-4×(-1)+c

⇒ c=5-4

⇒ c=1

Substitute m=-4 and c=1 in y=mx+c, we get

y=-4x+1

Therefore, the slope-intercept form of the equation of the line through the given point with the given slope is y=-4x+1.

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The number of leaves on a tree which is 2 yards tall and receives 9 hours of sunlight is 324 leaves.

z = k × y × x

Where,

If y = 10 yards, x = 3 hours, z = 540 leaves

z = k × y × x

540 = k × 10 × 3

540 = 30k

k = 540/30

k = 18

Then, find z when y = 2 yards and x = 9 hours

z = k × y × x

= 18 × 2 × 9

z = 324 leaves.

In conclusion, given the constant of proportionality, the number of leaves on the tree is 324 leaves.

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The solutions of the given system of Equations are (5/2, 41/2).

The set of values for each variable in a system of linear equations is referred to as the solution set.

The intersection or meeting points of the lines or planes used to illustrate the linear equations are also known as the solutions.

The elimination method is one way of resolving a system of linear equations. To obtain the equation in one variable using this technique, simply add or subtract the equations.

Here we have

y = 9x-2 --- (1)

y = 7x+3 --- (2)

From (1) and (2)

=>  9x - 2 = 7x + 3

=>  9x - 7x = 3 + 2

=> 2x = 5

=> x = 5/2

Substitute x = 5/2 in (1)  

=> y = 9(5/2) - 2  

=> y = (45/2) - 2

=> y = (45 - 4)/2

=> y = 41/2

Therefore,

The solutions of given system of Equations are (5/2, 41/2).

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The null hypothesis (H0) would be that the population mean number of hours married men in your area spend on child care per week is equal to the reported mean of 6.0 hours per week.

The population mean number is equal to the reported mean according to null hypothesis. The alternative hypothesis (HA) would be that the population mean differs from the reported mean.

H0: μ = 6.0 hours/week

HA: μ ≠ 6.0 hours/week

b. To find the sample mean, we need to add up all of the values in the sample and divide by the number of values. The sample mean is 6.34 hours/week.

To calculate the test statistic, we can use the formula:

t = (x' - μ0) / (s / √n)

where x' is the sample mean, μ0 is the hypothesized mean (in this case, 6.0 hours/week), s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (6.34 - 6.0) / (3.23 / √40) = 0.34 / (0.53 / 6.32) = 0.34 / 0.08 = 4.25

The p-value is the probability of getting a result as extreme as the one we observed, given that the null hypothesis is true. In this case, we would need to use a t-distribution table or a computer program to find the p-value, since the sample size is small and the population standard deviation is unknown.

c. If we select a level of significance of 0.05, then we can use the p-value to make a decision about the null hypothesis. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that the population mean differs from the reported mean. If the p-value is greater than 0.05, we do not have enough evidence to reject the null hypothesis and would conclude that the population mean is likely to be the same as the reported mean.

In this case, the p-value is greater than 0.207, so we do not have enough evidence to reject the null hypothesis. We would conclude that the population mean number of hours married men in your area spend on child care per week is likely to be the same as the reported mean of 6.0 hours per week.

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The equation of the line joining the points (2,-8) and (5,6) is y = 14 / 3 x - 52 / 3

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, the equation of the line passes through the points (2,-8) and (5,6). Let's find the slope.

m = 6 + 8 / 5 - 2

m = 14 / 3

Let's find the y-intercept using (5, 6).

y = 14 / 3 x + b

6 = 14 / 3 (5) + b

6 = 70 / 3 + b

b = 6 - 70 / 3

b =  18 - 70/ 3

b = -52 / 3

Therefore, the equation is y = 14 / 3 x - 52 / 3

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The population of the state in 2000 was 23.1 million and the population will be 28.3 million after 13.4 years.

The definition of an exponential function is given by the equation

y = aeᵇˣ, where bx is an exponent.

The given equation is [tex]A = 23.1e^{0.0152t}[/tex].

To find the population of the state in 2000, substitute t = 0 in the given equation:

[tex]A =23.1e^{0.0152(0)}\\\\A = 23.1[/tex]

Now, Substitute A = 28.3 into the given equation and solve for t:
[tex]28.3=23.1e^{0.0152t}\\\\e^{0.0152t}=1.2251\\\\0.0152t=\ln(1.2251)\\\\0.0152t=0.2030\\\\t=13.4[/tex]

Hence, the population of the state in 2000 was 23.1 million and the population will be 28.3 million after 13.4 years.

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Applying the property of exponents, the remainder that the number 10^2023 leaves after division by 13 is 9.

The remainder is the amount left over after a division operation.

An exponent is a number that indicates how many times a base number is used as a factor in a multiplication expression.

From the property of exponent:

We can rewrite 10^2023 as (10^13)^155 * 10^8:

10^2023 = (10^13)^155 * 10^8

We can then use the property of exponents to simplify:

10^2023 = (10^(13*155)) * 10^8

Since 10^13 is congruent to 1 mod 13, 10^(13*155) is congruent to 1 mod 13 as well. Therefore, 10^2023 is congruent to 10^8 mod 13.

We can find the remainder by calculating 10^8 mod 13:

10^8 = 100000000

After dividing 100000000 by 13, we get a remainder of 9.

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Therefore the solution to this question is expression a=3/5 & expression b=6/5  3a+b=3 , and  10a+5b=6+6=12 .

Probability is the study of how likely it is for an event to occur or for a statement to be true, with numerical explanations of probability being a key component. An event's probability is represented by a number between 0 and 1, where, broadly speaking, 0 indicates that the event is impossible and 1 indicates that it is certain to occur.

Here,

Naturally, the total probability for x∉[0,1] is 0 and since the total probability must be 1, we have

∫01a+bx2dx=1

The left-hand side is

[ax+b[tex]x^{3}[/tex]/3] x=1 & x=0 => a+b3

3a+b=3

In general, for continuous probability distributions we have

E(x)=∫P(x)xdx

(If you have a sufficiently advanced version of integration, the restriction to continuous distributions may be lifted.)

In this case, it's

E(x)=[a[tex]x^{2}[/tex]/2+b[tex]x^{4}[/tex]/4]x=1 & x=0 => a/2+b/4

So,

a/2+b/4=3/5

10a+5b=12

Being shrewd with matrix inversion or anything of the sort is pointless. Just get rid of b:

15a+5b=15

5a=3

a=3/5

b=3(1−a)=6/5

and indeed  3a+b=3 , and  10a+5b=6+6=12 .

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Answer:

Step-by-step explanation:

I know that in point-slope form, the equation is y - y1 = m(x - x1)

Fill in y1 and x1 with the points given in the multiple choices.

If you look at Letter A, it shows the point (0,9). If you fill that in the formula. You solve the equation:

y - 9 = -3/4(x - 0)

y - 9 = -3/4x

+9.     =.  +9

y = -3/4x + 9

Therefore your answer is letter A.

Answer:

$1471.49

Step-by-step explanation:

1571.13-80=1491.13

1491.13+456.82=1947.95

179.48+74.73+82.70+139.55=476.46

1947.95-476.46=1471.49

Step-by-step explanation:

-4y = 5x - 12

4y = -5x + 12

y = -5/4x + 3

Answer:

second

Step-by-step explanation:

2x+5>7

2x>2

x>1

therefore, second

The equation of Total Charges will be $1.95 + ($2.7 * x)

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.

Solution:

The equation of Total Charges will be

Let, the total distance in miles be x

Then,

Total Charges = $1.95 + ($2.7 * x)

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Answer:$441.05

Step-by-step explanation:

For this question you would multiply the amount of each DVD by the price and add them all up

like this:

11(27.95) +7(17.95)+1(7.95)=$441.05

The ratio shows how many times one value is contained in another value.

The ratio of office buildings to hotels will be 9 : 4.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of hotels to office buildings = 4 : 9

Now,

The ratio of office buildings to hotels will be 9 : 4.

Thus,

The ratio of office buildings to hotels will be 9 : 4.

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There is sufficient evidence to support the claim.

What is sufficient evidence ?

Sufficient evidence is admitted evidence that has enough overall weight, in terms of relevance and credibility, to legally justify a particular conclusion.

This is left tailed test .

The null and alternative hypothesis is ,

H0 :  mu= 34

Ha :mu < 34

Test statistic(t) = (x)

n= root (29.5 - 34) / 1.70

root 35

Test statistic = -15.66

P-value = 0

Alpha = 0.05

P-value <Alpha

Reject the null hypothesis .

There is sufficient evidence to support the claim.

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The coordinates of the turning point on the curve with the quadratic equation y = 9 + 18x - 3x² is (3,36).

What is a quadratic equation?

Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

It is given that:

The quadratic equation is:

y = 9 + 18x - 3x²

To find the turning point:

Graph the above quadratic equation;

From the graph:

The maximum point from where the graph starts to decrease is (3,36)

Thus, the coordinates of the turning point on the curve with the Quadratic equation y = 9 + 18x - 3x² is (3,36).

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The x-intercepts of the parabola are (x₁, y₁) = (6.67, 0) and (x₂, y₂) = (5.33, 0).

What is the equation of a parabola?

The general equation of a parabola is given by y = a(x – h)2 + k or x = a(y – k)2 +h. Here (h, k) denotes the vertex.

To write the equation of the given parabola in the desired form, we can complete the square.

The equation of a parabola with vertex at (h, k) and axis of symmetry x = h is given by:

y = a(x - h)^2 + k

where a is a nonzero constant.

In this case, the vertex is (6, -5) and the y-intercept is (0, 175), so the equation of the parabola is of the form:

y = a(x - 6)^2 - 5

Substituting the y-intercept, we have:

175 = a(0 - 6)^2 - 5

Solving for a, we find that a = 15/4.

Thus, the equation of the parabola is:

y = 15/4(x - 6)^2 - 5

To find the x-intercepts, we need to find the values of x such that y = 0. Substituting y = 0 into the equation of the parabola, we have:

0 = 15/4(x - 6)^2 - 5

Adding 5 to both sides, we have:

5 = 15/4(x - 6)^2

Dividing both sides by 15/4, we have:

4/15 = (x - 6)^2

Taking the square root of both sides, we have:

x - 6 = +/- 2/3

Thus, the x-intercepts are at x = 6 +/- 2/3.

Therefore, the x-intercepts of the parabola are (x₁, y₁) = (6 + 2/3, 0) and (x₂, y₂) = (6 - 2/3, 0).

Rounded to the nearest hundredth, the x-intercepts are (x₁, y₁) = (6.67, 0) and (x₂, y₂) = (5.33, 0).

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Profit is the money you have left after paying for business expenses.

The production of the products are given below with the profit as well:

a. Production of Product 1 = 50 units per week

b. Production of Product 2 = 0 units per week

c. Production of Product 3 = 145 units per week

d. Production of Product 4 = 10 units per week

e. Total Profit = $1250 per week

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Answer:

Step-by-step explanation:

A local manufacturing firm produces four different metal products, each of

which must be machined, polished and assembled. The specific time

requirements (in hours) for each product are as follows:

Machining,

hours

Polishing, hours Assembling,

hours

Product I 3 1 2

Product II 2 1 1

Product III 2 2 2

Product IV 4 3 1

Answer:

y = 2.5x

Step-by-step explanation:

When the relationship is proportional you can find the slope (or unit rate) by taking any point in the form y/x

20/8 = 2.5

30/12 = 2.5

This will work of every point n the line.

Rate percent is 10%

A coefficient that is a quotient of two values, where the denominator is written in percentage points and has the same units as the numerator when it is multiplied by a unit of time.

According to the given information

Sum of money ( principal ) P = 5000 rupees

Interest obtained in money = 1500 rupees

Time duration T = 3 years

According to the given information

I = P × T × [tex]\frac{R}{100}[/tex]

1500 = 500 × 3 × R/100

Rate percent is 10%

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Hello,

I hope you and your family are doing well!

A) To find the annual growth rate between 1991 and 2008, we can use the compound interest formula:

S = P(1 + r)

Where S is the final value of the house, P is the initial value of the house, and r is the annual growth rate.

Plugging in the values from the problem, we get:

165,000 = 95,000(1 + r)

Dividing both sides of the equation by 95,000 gives:

1.737 = 1 + r

Subtracting 1 from both sides of the equation gives:

0.737 = r

The annual growth rate between 1991 and 2008 is 0.737.

B) To express the growth rate in percentage form, we can multiply it by 100%:

0.737 * 100% = 73.7%

So the annual growth rate between 1991 and 2008 was 73.7%.

C) To find the value of the house in the year 2011, we can use the compound interest formula again, with the initial value of the house set to the final value in 2008:

S = P(1 + r)

Plugging in the values from the problem, we get:

S = 165,000(1 + 0.737)

Solving for S gives:

S = 165,000 * 1.737 = 285,195

So the value of the house in the year 2011 will be approximately $285,195. Rounded to the nearest thousand dollars, this is $285,000

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Happy Holidays!

Answer:

-9.661

Step-by-step explanation:

Adding a negative is the same as subtracting a positive and you started with a negative number so:

-6.05

-3.611

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

-9.661

Answer: -9.661

Step-by-step explanation:

A negative plus a negative will ALWAYS equal a negative. If you have an addition with two negatives, just add them normally and add the negative sign:
-6.05+(-3.611) = 6.05 + 3.611

6.05 + 3.611 = 9.661

Now add the negative sign:

9.661 = -9.661

Hope this helps!!

Answer:

35cm^2

Step-by-step explanation:

Things To Keep In Mind:

Height: 7 cm

Length: 10 cm

(L*H)/2=area of triangle

7*10=70

70/2=35

If there are any problems with this answer please feel free to tell me, thanks :)

The number of hours when Jai and Keilantra are the same distance from the stadium is 3 hours.

Jai is 254 miles away from the stadium. Jai is driving along the highway at a speed of 41 miles per hour. This will be:

254 - 41h

Keilantra is 293 miles away from the stadium. Keilantra is driving at speed of 54 miles per hour. This will be:

293 - 54h

The equations will be:

254 - 41h = 293 - 54h

54h - 41h = 293 - 254

13h = 39

Divide

h = 39/13

h = 3

The number of hours is 3 hours.

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Answer:

4x=4   or 4tims x =y

Step-by-step explanation:

1x4=4

3x4-=12

Answer: b

Step-by-step explanation:

3^2 + x^2 = 9^2

9 + x^2 = 81

x^2 = 72

x = sqrt(72)