If the circumference of a circle is 25 ft what is the diameter. Use 3.14

Answer:

10 feet

Step-by-step explanation:

Let's start by finding the current area of the deck:

Area = length x width = 20 ft x 10 ft = 200 sq ft

If Ian increases each dimension by the same amount, let's call this amount "x", then the new dimensions of the deck will be:

Length = 20 ft + x

Width = 10 ft + x

The new area of the deck will be:

New Area = (20 ft + x) x (10 ft + x)

We know that Ian wants the new area to be triple the original area of 200 sq ft, so:

New Area = 3 x 200 sq ft

New Area = 600 sq ft

Substituting this into the equation above and solving for "x", we get:

(20 ft + x) x (10 ft + x) = 600 sq ft

200 + 30x + x^2 = 600

x^2 + 30x - 400 = 0

(x + 40) (x - 10) = 0

We discard the negative solution, and we get:

x = 10 ft

Therefore, Ian should increase each dimension by 10 feet to triple the area of his deck.

To confirm, we can check the original area of the deck which is 20 ft x 10 ft = 200 sq ft.

If Ian increases each dimension by 10 feet, the new dimensions of the deck will be 30 ft x 20 ft. The new area of the deck will be 30 ft x 20 ft = 600 sq ft. This is triple the original area of the deck (200 sq ft), which is what we wanted to achieve.

Therefore, increasing each dimension by 10 feet will triple the area of the deck as required.

Ian should increase both the sides by 10 feet each.

This is a simple mathematics problems related to the topic of mensuration.

Firstly we calculate the current area of the deck:

Area of the deck (rectangle) = l x b

Area of the deck (rectangle) = 20 x 10

Area of the deck (rectangle) =  200 square feet

Since Ian wants to triple the area of the deck, the required area is 600 square feet.

We now look at pairs of numbers multiplying which will give us 600:

(1,600) (2,300) (3,200) (4,150) (5,120) (6,100) (8,75) (10,60) (12,50) (15,40) (20,30) (25,24)

Out of the above pairs only one pair fulfils Ian's criteria to increase the length and breadth of the deck by equal measure, i.e., (20,30). So, Ian should increase the length and breadth of his deck by 10 feet each.

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5.40 km is the distance Bokamoso ride on the way to school

What is speed, distance and time?

Speed is determined by dividing the distance travelled by the time taken to travel it. It gives the amount of time it took to travel a certain distance divided by the distance travelled.

Speed is inversely correlated with time and directly correlated with distance. As a result, distance equals speed times time, and time equals distance divided by speed; as speed rises, distance travelled will shorten, and vice versa.

Bokamosa rides at 16 km / hr

To get to school = 45 min

= 45 * 0.75 hour

= 0.3375 hr

Distance = Speed * Time

d = 16 * 0.3375

= 5.40 km

Hence, 5.40 km is the distance Bokamoso ride on the way to school.

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Answer:

x = 5

Step-by-step explanation:

given FH is a diameter , then

arc FH = 180°, that is

FG + GH = 180°

103° + GH = 180° ( subtract 103° from both sides )

GH = 77°

the central angle HIG is equal to the arc that subtends it GH , so

∠ HIG = 77°

∠ EIF and ∠ HIG are vertically opposite angles and are congruent , then

∠ EIF = 77°

the arc EF subtends the central angle EIF , so

EF = 77°

the sum of the 3 arcs = 180° , that is

HD + DE + EF = 180

15 + 18x - 2 + 77 = 180

18x + 90 = 180 ( subtract 90 from both sides )

18x = 90 ( divide both sides by 18 )

x = 5

then arc DE = 18x - 2 = 18(5) - 2 = 90 - 2 = 88°

Answer:

Step-by-step explanation:

answer 1,250

Check the picture below.

Make sure your calculator is in Degree mode.

[tex]\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}[/tex]

Answer:

The given quadratic equation is: 10x^2 + 7x + 3 = 0.

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 10, b = 7, and c = 3.

Substituting these values into the formula, we get:

x = (-7 ± sqrt(7^2 - 4(10)(3))) / 2(10)

x = (-7 ± sqrt(49 - 120)) / 20

x = (-7 ± sqrt(-71)) / 20

Since the square root of a negative number is not a real number, this quadratic equation does not have any real solutions. Therefore, none of the options (A), (B), (C), or (D) are correct.

The equation of the form y = c + b logₐX is y = -3 + 3 Log₃X

Recall that Slope-intercept form of a linear equation is where one side contains just “y”. It looks like y = mx + “b” where “m” and “b” are numbers. This form of the equation is very useful because the coefficient of "x" (the "m" value) is the slope of the line and the constant (the "b" value) is the y-intercept at (0, b)

The equation of the line is give as

y-y₁ = m(x-x₁) + c

Where m is the slope and c is the intercept

This implies that

y -3 = m(x -2)

But slope is given as  m = (y₂ - y₁)/(x₂-x₁)

m = (9-3)/ 4-2) = 6/2 = 3

Then, the equation is

y - 3 = 3x - 6

Collecting like terms we have

y = 3x -6+3

y = 3x -3

Writing this in the form y = c + b logₐX

y = -3 + 3 Log₃X

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The equation of the function in the form y = c + b log_a(x) is y = logₓ2

We can start by assuming that the equation is of the form y = c + b log_a(x), where c and b are constants and a is the base of the logarithm.

Using the point (2, 3), we get:

3 = c + b log_a(2)

Using the point (4, 9), we get:

9 = c + b log_a(4)

Simplifying the second equation using the logarithmic identity

loga(4) = 2 loga(2), we get:

3 +  2b loga(2) = 9

Substituting the first equation into this one, we get:

3 = 9 - 2b loga(2)

So, we have

-6 = - 2b loga(2)

Divide

bloga(2) = 3

So, we have

b = 3 / log_a(2)

Substituting this value of b into the first equation, we get:

3 = c + b log_a(2)

3 = c + 3 / log_a(2) * log_a(2)

So, we have

c = 0

Therefore, the equation of the curve is y = (2 / log_a(2)) log_a(x)

We can simplify this equation by using the logarithmic identity log_a(x^b) = b log_a(x):

y = 2 log_a(x) / log_a(2)

y = (2 / log(2)) log(x)

So the final equation is:

y = logₓ2

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Answer:

data given

interest rate 12%

amount to be received 15ooo

time9years

Step-by-step explanation:

from

A=p[1+r/100]^n

where

A is amount

p is principal

r is rate interest

n number of interist period

now,

15000=p[1+12/100]^8

15000/1.12^8 =p×1.12^8/1.12^8

p=6058.24

p=6058)

: .you should invest 6,058

The amount to be invested initially if you want to have fifteen thousand dollars after nine years is $3947.18.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

We are given that:

A=15000

r=0.12

t=9

We need to find P. You can do this by rearranging the formula:

P=ertA​

Then plug in the given values and use a calculator:

P=e0.12×915000​

P≈3947.18

Therefore, by the given interest rate the answer will be $3947.18.

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The correct choice is (4) x² = 34² +29² - 2(34)(29)*cos(56).

Trigonometry is one of the branches of mathematics that deals with the relationship between the sides of a triangle (a right-angled triangle) and its angles. There are six types of trigonometry.

We can use the laws of cosines and sines to solve this problem.

According to the law of cosines, we have:

cos(B) = (a² c² - b²) / 2ac

where a, b and c are the  lengths of opposite sides of angles A, B and C. In this case, we get that a = 34, b = x, and c = 29, and we know that angle C is 56 degrees . Because:

cos(B) = (34² 29² - x²) / (23429)

According to the Law of Sines, we have:

sin(B) / b = sin(C) / c

Substituting the given values ​​we get:

sin(B) / x = sin(56) / 29

Solving Sin(B) we get:

sin(B) = x * sin(56) / 29

Now we can use the identity sin²(B) cos²(B) = 1 to eliminate sin(B) and solve for x:

(x * sin(56) / 29)² cos²(B) = 1

Expanding and substituting  cos(B) from the previous expression, we get:

(x² * sin²(56) / 29²) ((34² 29² - x²) / (2(34)(29))²= 1

Simplifying and solving for x², we get:

x² = 34²+ 29² - 2(34)(29)*cos(56)

Therefore, the correct choice is (4) x² = 34² +29² - 2(34)(29)*cos(56).

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The volume of the rectangular prism is (867/20) cubic inches.

A volume is just the amount of space taken up by any three-dimensional solid. A cube, a cuboid, a cone, a cylinder, or a sphere are examples of solids. Volumes differ depending on the shape.

To find the volume of a rectangular prism, we need to multiply its length, width, and height. In this case, the length is 10 1/5 inches, the width is 4 1/4 inches, and the height is 2 inches. We can convert the mixed numbers to improper fractions and then multiply:

length = 10 1/5 inches = (51/5) inches

width = 4 1/4 inches = (17/4) inches

height = 2 inches

Volume = length x width x height

= (51/5) inches x (17/4) inches x 2 inches

= (867/20) cubic inches

Therefore, the volume of the rectangular prism is (867/20) cubic inches.

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Answer:

FV ≈ $5,673.56

Step-by-step explanation:

To calculate the total amount that Matt will have saved after 2 years of saving $225 per month at an annual interest rate of 5%, we can use the formula for the future value of an annuity:

FV = P * (((1 + r/12)^(n*12) - 1) / (r/12))

where:

FV is the future value of the annuity

P is the periodic payment (in this case, $225 per month)

r is the interest rate per year (in this case, 5%)

n is the number of years (in this case, 2)

Substituting the given values, we get:

FV = $225 * (((1 + 0.05/12)^(2*12) - 1) / (0.05/12))

Using a calculator, we get:

FV ≈ $5,673.56

Therefore, after 2 years of saving $225 per month at an annual interest rate of 5%, Matt will have saved approximately $5,673.56.

The given exponents term can be written in the form of [tex](a^{4})^{12}[/tex] .

What about exponents?

Exponents are a mathematical operation that involves multiplying a base number by itself a certain number of times. Exponents are often referred to as powers, and the base number is raised to a power, which is usually represented by a superscript number. For example, 2^3 means 2 raised to the power of 3, which is 2 x 2 x 2 = 8.

Exponents are commonly used in many areas of mathematics, including algebra, calculus, and geometry. They are used to represent very large or very small numbers, to simplify calculations, and to express repeated multiplication in a more compact form. Exponents can also be negative or fractional, allowing for the representation of roots and other mathematical concepts.

According to the given information:

In the given question [tex](a^{48} )[/tex] can be written as,

[tex](a^{4})^{12}[/tex] = [tex](a^{4})^{12} = a^{48}[/tex]

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To convert the expression, Y=x^2-64/16 into the polar form, we would have: r = 2 / √(sin^2θ + cos^2θ).

The polar form of a mathematical expression is a way of representing complex numbers using their magnitude and angle.

For a complex number z = a + bi, where a and b are real numbers, its polar form is given by z = r(cosθ + i sinθ), where r is the magnitude of z and θ is the angle that z makes with the positive real axis.  

So, for the given expression, the polar form can be converted this way:

r^2 sin^2θ = r cos^2θ - 4

r^2(sin^2θ + cos^2θ) = 4

r = 2 / √(sin^2θ + cos^2θ)

Therefore, the polar form is r = 2 / √(sin^2θ + cos^2θ).

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The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.

In statistics, the critical value is a value that is used to determine whether to reject the null hypothesis in a hypothesis test. It is based on the chosen level of significance, which is the maximum probability of making a Type I error (rejecting a true null hypothesis). The critical value is determined by the sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.

To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.

Using a t-distribution table with 21 degrees of freedom (n-1), we find that the critical value for a 99% confidence level is approximately 2.819.

Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).

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Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.

The standard deviation of statistics is a measurement of how much a group of data values deviate from their mean (average) value. While a significant standard deviation suggests that the pieces of information are dispersed throughout a broader range of values, a low standard deviation suggests that the data points are generally close to the mean.

given

a) If the sample's standard deviation is 3 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:

z = (30 - 15) / 3 = 5

b) The context of the data and the standard deviation will determine whether 30 inches is distant from a mean of 15 inches.

A departure of 15 inches from the mean, meanwhile, can be viewed as being significantly off the mean if the standard deviation is minimal.

c) If the underlying data's standard deviation is 10 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:

z = (30 - 15) / 10 = 1.5

Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.

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Therefore, the Left Riemann Sum for this function, interval, and number of subintervals is 50.

The top-left corner of these rectangles touched the y=f(x) curve. In other words, the value of f at the subinterval's left endpoint determined the height of the rectangle over that subinterval. This technique is called the left-endpoint estimate because of this.

With left endpoints and n = 5 subintervals, we may use the Left Riemann Sum formula to approximate the area under the curve of f(x) = x2 + 4 over the range [0, 5]:

Left Riemann Sum = ∑[i=1 to n] f(x_i-1) Δx

In this case, a = 0, b = 5, n = 5, and we will use the left endpoints, so:

Δx = (5 - 0)/5 = 1

Using the left endpoints, the subintervals and their left endpoints are:

[0,1],[1,2],[2,3],[3,4],[4,5]

[tex]so,\; x_0 = 0, x_1 = 1, x_2 = 2, x_3 = 3, x_4 = 4.[/tex]

Now we can calculate the Left Riemann Sum:

Left Riemann Sum= [tex]f(x_0)\Delta x + f(x_1)\Deltax + f(x_2)\Deltax + f(x_3)\Deltax + f(x_4)\Deltax[/tex]

= f(0)×1+f(1)×1+f(2)×1+f(3)×1 + f(4)×1

= 4+5+8+13+20

= 50

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The equation of the given line in the graph in slope intercept form is: y = 2x + 7

The general formula for the equation of a line in slope intercept form is:

y = mx + b

where:

m is slope

b is y-intercept

From the given graph, the y-intercept is b = 7

Let us pick two coordinates which are:

(-3.5, 0) and (0, 7)

Thus:

(y - 0)/(x + 3.5) = (7 - 0)/(0 + 3.5)

y = 2(x + 3.5)

y = 2x + 7

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f(x)=2x+7

domain: x = {2, 3, 5, 9}

Replace each x value and solve for y

x=2

f(2)= 2(2) + 7 = 4 + 7 = 11

x=3

f(3)= 2(3) + 7 = 6 + 7 = 13

x=5

f(5)= 2(5) + 7 = 10 + 7 = 17

x=9

f(9)= 2(9) + 7 = 18 + 7 = 25

We can find the range of the function by plugging in each value in the domain into the function and listing the output values:

When x = 2, f(2) = 2(2) + 7 = 11

When x = 3, f(3) = 2(3) + 7 = 13

When x = 5, f(5) = 2(5) + 7 = 17

When x = 9, f(9) = 2(9) + 7 = 25

Therefore, the range of the function for the given domain is y = {11, 13, 17, 25}.

Hence, the correct answer is B. y = {11, 13, 17, 25}.

The new triangle A'B'C' after the translation is A'(-3, 3), B'(4, -1), and C'(-2, 0).

A shape is translated when it is moved up, down, left or right without turning. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

To perform the given translation (x, y) → (x − 3, y - 4) on the triangle ABC with vertices A(0, 7), B(7, 3), and C(1, 4), we need to apply the same transformation to each vertex of the triangle and obtain their new coordinates.

For vertex A(0, 7), the transformation gives:

(x, y) → (x − 3, y - 4)

(0, 7) → (0 - 3, 7 - 4)

The new coordinates of A are (-3, 3).

For vertex B(7, 3), the transformation gives:

(x, y) → (x − 3, y - 4)

(7, 3) → (7 - 3, 3 - 4)

The new coordinates of B are (4, -1).

For vertex C(1, 4), the transformation gives:

(x, y) → (x − 3, y - 4)

(1, 4) → (1 - 3, 4 - 4)

The new coordinates of C are (-2, 0).

Therefore, the new triangle A'B'C' after the translation is A'(-3, 3), B'(4, -1), and C'(-2, 0).

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Answer:

Step-by-step explanation:

Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.

We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.

First, we differentiate the volume equation with respect to time t:

V = x^3

dV/dt = d(x^3)/dt

Using the chain rule:

dV/dt = 3x^2 * (dx/dt)

Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:

56 = 3 * (6)^2 * (dx/dt)

Solving for dx/dt:

56 = 108 * (dx/dt)

dx/dt = 56 / 108

dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)

So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.

Answer:

We can simplify the expression -8(2.5g-4.25)+5.25 by distributing the -8:

-8(2.5g-4.25)+5.25 = -20g + 34 + 5.25

Simplifying further, we can combine the constant terms:

-8(2.5g-4.25)+5.25 = -20g + 39.25

So the value of the constant term is 39.25.

Answer:

not sure if this is what you're looking for but..

Step-by-step explanation:

To find the factor pair of -15x^2 that adds to be 2x, we need to find two numbers that multiply to -15x^2 and add up to 2x. The first step is to factor out the greatest common factor (GCF) which is -x. This gives us:

-15x^2 + 2x = -x(15x - 2)

Now we need to find two numbers that multiply to -2 and add up to 15. The only pair of numbers that works is 1 and -15. Therefore, we can write:

-15x^2 + 2x = -x(15x - 2) = -x(1x - 15x)(-1)(-2)

So the factor pair of -15x^2 that adds up to 2x is (-1)(-2) which equals 2

Answer:-133.69

Step-by-step explanation:

5.96 x 106 -7.29 x 105

631.76 -7.29 x 105

631.76 - 765.45

= -133.69

The mean number of bedrooms in a house in this neighborhood will be: 3.824.

In order to find the mean number of bedrooms in a house in the Belmont Neighborhood, we need to calculate the weighted mean by multiplying each number of bedrooms by their respective frequency.

Next, we will add the products, and then divide by the total frequency. So we can start as follows:

(2 * 7) + (3 * 35) + (4 * 56) + (5 * 27) = 14 + 105 + 224 + 135 = 478

Total frequency = 7 + 35 + 56 + 27 = 125

Therefore, the mean number of bedrooms = 478 / 125  approximately 3.824

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Check the picture below.

so following the template below, a shift 2 units to the left, means C=2

[tex]G(x)=\sqrt{x+2}[/tex]

Answer:

Whats the question?

Step-by-step explanation:

The unit twenty-six point seven ounces in terms of milligrams is 756932.3  

To convert ounces (oz) to milligrams (mg), we can use the following conversion factor:

1 oz = 28,349.5 mg

Therefore, to convert 26.7 oz to mg, we can multiply 26.7 by the conversion factor as follows:

26.7 oz × 28,349.5 mg/oz = 756932.3  mg

So, there are approximately 756932.3 milligrams in 26.7 ounces of mass.

Comparing the calculated answer with the options given, we see that the answer is closest to 756,498.15 mg, which is not one of the options.

Therefore, we cannot choose any of the options given.

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Answer:

Step-by-step explanation:

We need to find a number which increased by 3.5 of itself equals 621.

Let that number be x.

x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.

x(1+3.5) = 621

x(4.5) = 621

x = 621/4.5

x = 138

Therefore the required number is 138.

Answer: 138

Step-by-step explanation:

We need to find a number which increased by 3.5 of itself equals 621.

Let that number be x.

x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.

x(1+3.5) = 621

x(4.5) = 621

x = 621/4.5

x = 138

Therefore the required number is 138.

Answer:

To simulate the probable outcomes of this event with a six-sided number cube, you can place the numbers 1-6 on the faces in the following order: 1, 4, 3, 2, 5, 6. Then roll the cube and use the following outcomes:

a) Correct: a roll of 6 Incorrect: a roll that is not 6

b) Correct: a roll of an even number Incorrect: a roll of an odd number

c) Correct: a roll of a number less than 3 Incorrect: a roll of a greater than or equal to 3

d) Correct: a roll of a number that is not divisible by 3 Incorrect: a roll of a number that is divisible by 3

Step-by-step explanation: