POSSIBLE POINTS: 10
Find the area of the composite figure below. Area of Triangle = bh, Area of Rectangle = lb Use Pythagorean formula to find the length () of the
Rectangle.
7 mm
10.4 mm
15.3 mm

Answer:

Step-by-step explanation:

(a)  

16

36

​

=

4

9

​

36:16=9:4

(b)  

144

324

​

=

4

9

​

324:144=9:4

(c)  

1125

125

​

=

1125

125

​

=

45

5

​

=

9

1

​

∴125:1125=1:9

6,000 mL is equal to 6 litres

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

We know that 6,000 mL  is equal to 6L

One litre is equal to 1000 ml

1 l = 1000 ml

6 l=6000 ml

Hence,  6,000 mL is equal to 6 litres

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Answer:

  total deposits: $35,100

Step-by-step explanation:

You have the value of an annuity earning 5% with payments of $65 a month for 45 years as $131,718.42. You want to know the total value of payments.

12 payments per year of $65 for 45 years will have a total value of ...

  12·65·45 = 35100

Total deposits will be $35,100.

The function that matches the above graph is Option C - F(x) = (1/2)^x - 3

Here are the properties of the function are given as follows

Domain - The domain of  the function is all real numbers, as there are no restrictions on the input value  x .

Range - the range of the function is (-3, infinity), as the output values approach but never reach - 3 as x approaches negative infinity, and the output values can be arbitrarily large as x approaches infinity.

x -intercept - The x-intercept of the function is (log(2, 3), 0), as F(log(2, 3)) = [( 1/2)^  (log(2, 3) ) ] - 3 = 0.

y-intercept - The y-intercept of the function is (0, -2.5), as F(0) = [(1/2)^0] - 3 = -2.5.

Asymptotes - The horizontal asymptote of the function is y = -3, as the output values approach but never reach -3 as x approaches infinity. There are no vertical asymptotes.

Decreasing function -  The function is a decreasing function, as the output values decrease as x increases.

Continuous function - The function is continuous for all real numbers.

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The p-value is a probability value for test that measures the strength of evidence against a null hypothesis.

It is a number between 0 and 1 and is typically compared to a significance level (such as 0.05) to determine whether to reject or fail to reject the null hypothesis.

However, a p-value cannot be calculated from a single number like -0.24 alone. A p-value is typically calculated using statistical tests, such as a t-test or ANOVA, which require more information about the data, such as the sample size, mean, and standard deviation.

Therefore, to find the p-value for a specific hypothesis test, you would need to perform a statistical test on the relevant data using appropriate statistical software or formula, and the resulting p-value will be specific to that test and the data analyzed.

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It takes A. 5 months to pay off (Mini) the highest interest card.

To determine the number of months it takes to pay off the credit card debt, we shall calculate the monthly payment to pay off the highest interest card first.

First, calculate interest accrued on each card per month:

Murk: (5.6/100)/12 * $675.49 = $2.98 per month

Mini: (9.85/100)/12 * $902.43 = $7.42 per month

Next, we determine the order in which to pay off the cards, which is highest interest card first, we can allocate the entire $375 to Mini and leave a minimum for interest accrued on Murk.

This should be a percentage of the balance.

Assuming it's 2% of the balance, which is $13.51.

So, in month 1, we will pay:

Mini: $375

Murk: $13.51

Leaving these balances:

Murk: $675.49 + $2.98 - $13.51 = $664.96

Mini: $902.43 - $375 + $7.42 = $534.85

In month 2:

Mini: $534.85 + $7.42 = $542.27

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $664.96 + $2.98 - $16.49 = $651.45

Mini: $542.27 - $375 + $7.42 = $174.69

month 3:

Mini: $174.69 + $7.42 = $182.11

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $651.45 + $2.98 - $16.49 = $638.94

Mini: $182.11 - $174.69 + $5.52 = $12.94

month4:

Mini: $12.94 + $7.42 = $20.36

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $638.94 + $2.98 - $16.49 = $625.43

Mini: $20.36 - $12.94 + $0.54 = $8.96

month 5:

Mini: $8.96 + $7.42 = $16.38

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $625.43 + $2.98 - $16.49 = $612.92

Mini: $16.38 - $8.96 = $7.42

So, Mini's balance is paid off here.

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Note:

And we can allocate the entire $375 budget to Murk.

This means we will pay off Murk in month 6:

Murk: $612.92 + $2.98 + $375 - $13.51 = $977.39

The probability that at least one of the three users is more careful is 0.936.

We need to find the probability that a single randomly selected Internet user is more careful, which is 0.60.

The probability that none of the three users are more careful is (0.40)^3 = 0.064.

Therefore, the probability that at least one of the three users is more careful is 1 - 0.064 = 0.936.

Rounding to three decimal places, the answer is 0.936.

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Answer: y= 1700 (1- .0325) ^15= 1700(.9675) ^15=1700(.60920660)= 1035.65 km Hope this helps!

Step-by-step explanation:To calculate the area of the forest after 5 years, we need to use the formula:

A = A0 * (1 - r/100)^t

PLEASE MARK BRAINLIST

The value of the expression 9 squared will be 81.

In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value will be:

= 9²

= 9 × 9.

= 81

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The requried insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.

The insurance premium of a bus is GH¢93.30 plus 15% of the insured value.

Let's first calculate 15% of¢250.00:

15% of GH¢250.00 = 0.15 x 250.00 = GH¢37.50

Now, we can add this amount to the base premium of GH¢93.30 to find the total insurance premium for the bus:

GH¢93.30 + GH¢37.50 = GH¢130.80

Therefore, the insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.

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The volume of the flower vase, can be found to be 2, 199 cm ³.

The volume of the flower vase can be found by subtracting the volume of the cone from the volume of the rectangular prism.

Volume of rectangular prism :
= Length x Width x Height

= 20 x 12 x 10

= 2, 400 cm ³

The volume of the cone is:

=  π x radius ² x height / 3

= π x 4 ² x 12 / 3

= 201. 06 cm ³

Volume of vase:

= 2, 400 -  201. 06

= 2198.94

= 2, 199 cm ³

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Answer:

v=-5

Step-by-step explanation:

Answer:

[tex]23 = 10v - 7 \\ 23 + 7 = 10v \\ 30 = 10v \\ v = 3 \\ \\ [/tex]

The value of the smaller of the two missing sides (the second leg) is,

⇒ 144 units

We have to given that;

The length of one of the legs of a right triangle is 17.

And, The lengths of the other two sides are consecutive integers.

Hence, Let the smallest of the other legs be x,

And, the hypotenuse be x + 1.

So, By using the Pythagorean theorem as;

⇒ 17² + x² = (x + 1)²

⇒ 289 + x² = x² + 1 + 2x

⇒ 2x = 288

⇒ x = 144

Thus, The value of the smaller of the two missing sides (the second leg) is,

⇒ 144 units

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The average rate of change for function f(x) = 1.85x² to the nearest tenth over the interval 10 ≤ x ≤ 20 is equal to 55.5 (Rounding to the nearest tenth).

Function models the cost of a square carpet

f(x) = 1.85x²

The average rate of change of a function f(x) over an interval [a, b] is,

Average rate of change = [f(b) - f(a)] / (b - a)

The average rate of change of f(x) over the interval 10 ≤ x ≤ 20.

Using the given function, we have,

f(10) = 1.85(10)²

       = 185

f(20) = 1.85(20)²

        = 740

Now calculate the average rate of change,

average rate of change

= [f(20) - f(10)] / (20 - 10)

= (740 - 185) / 10

= 55.5 (Rounding to the nearest tenth)

Therefore, the average rate of change of function f(x) over the interval 10 ≤ x ≤ 20 is approximately 55.5.

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The missing lengths and angles in the geometric systems are listed below:

Case 8: x = 60

Case 9: x = 48

Case 10: x = 5.535

Case 11: x = 5.665

Case 12: x = 9.103

Case 13: θ = 60°

Case 14: θ = 23.025°

In this problem we find two cases of geometric systems formed by triangles:

First case is analyzed by means of proportionality ratios and second case done by trigonometric functions:

Case 8

100 / x = x / 36

x² = 3600

x = 60

Case 9

x / 36 = 64 / x

x² = 36 · 64

x = 48

Case 10

x = 17 · sin 19°

x = 5.535

Case 11

x = 11 · cos 59°

x = 5.665

Case 12

x = 13 · tan 35°

x = 9.103

Case 13

cos θ = 7 / 14

cos θ = 1 / 2

θ = 60°

Case 14

tan θ = 17 / 40

θ = 23.025°

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Answer:

The problem describes rolling an unfair number cube which lands with 6, and asks for the number of outcomes where X=0, X=1, X=2, and X=3.

X can be 0, 1, 2, or 3 if X equals the number of times she rolls a 6 over the course of three tries.

We must count the instances where none of the three trials yields a six in order to determine the number of occurrences where X = 0. Since there is a 0.4 percent chance that the cube will fall on 6, there is a 0.6 percent chance that it won't. Therefore, there are 0.6 * 3 = 0.216, or 21.6%, of outcomes where X = 0.

To find the number of outcomes where X=1, we need to count the number of outcomes where exactly one of the three trials results in a 6. There are three ways to choose which trial will result in a 6, and each of the other two trials must not result in a 6. Therefore, the number of outcomes where X=1 is 3 × 0.4 × 0.6^2 = 0.432 or 43.2%.

We must count the outcomes where precisely two out of the three trials yield a six in order to determine the number of events where X=2. There are three options for selecting the two trials that will end in a 6, and the third trial cannot also end in a 6. The proportion of outcomes where X=2 is therefore 3 0.4 2 0.6 = 0.288 or 28.8%.

Finally, to find the number of outcomes where X=3, we need to count the number of outcomes where all three trials result in a 6. This occurs with probability 0.4^3 = 0.064 or 6.4%.

Therefore, the number of outcomes where X = 0 is 21.6%, X=1 is 43.2%, X=2 is 28.8%, and X=3 is 6.4%.

The  scale factor of the dilation is 30:1.

We have,

A superhero action figure has a volume of 1500 cm³.

The volume of the dilated figure is 45,000 cm³

Now, the scale factor should be

= 45000/ 1500

= 30 /1

Thus, the scale factor of the dilation is 30:1.

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Approximately, the amount of money, in cents, that Celine will save in 12 years is: B. 300

In this scenario, the years would be plotted on the x-axis (x-coordinate) of the scatter plot while the money (in cents) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the years and the money (in cents), an equation for the line of best fit is given by

y = 26.9x - 18.5

when x = 12, the amount of money, in cents, that Celine will save in 12 years is given by;

y = 26.9(12) - 18.5

y ≈ 300 cents.

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The frequencies based on the information are are 100, 40, and 6.

In the formula of the median, we have to calculate cumulative frequencies and have to use cumulative frequency of the interval previous to the median class. Also, in the formula of mode, frequencies are used and not the cumulative frequencies.

140 - y = 100

y = 40

substituting y and x in equation 1 is:

x + y + z = 146

100 + 40 + z = 146

z = 6

Therefore, the missing frequencies are 100, 40, and 6.

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The solution is,  the domain is: x ∈ (-∞, ∞).

Here, we have,

When we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here,

so the domain is:

x ∈ (-∞, ∞)

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complete question:

Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat

Answer:

2,600.

Step-by-step explanation:

Rounding 2,561 to the nearest hundred means rounding it to the nearest multiple of 100.

To do this, we need to look at the digit in the tens place, which is 6. Since 6 is greater than or equal to 5, we round up the digit in the hundreds place, which is 25, by 1.

Therefore, rounding 2,561 to the nearest hundred gives us 2,600.

Answer: the answer is 48 or b

Step-by-step explanation:

Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is given by:

A = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter, which is half the perimeter of the triangle:

s = (a + b + c) / 2

In this case, the side lengths are a = 9, b = 12, and c = 18. Therefore, the semiperimeter is:

s = (9 + 12 + 18) / 2 = 39 / 2

Using Heron's formula, we can now calculate the area of the triangle:

We can use unit conversion to find the value of $1 in Euros:

\begin{aligned}

£1 &= $1.41 \\

\frac{£1}{1.15} &= \frac{$1.41}{x} \\

x &= \frac{$1.41}{\frac{£1}{1.15}} \\

&= $1.7278

\end{aligned}

Therefore, $1 is equal to €1.7278.

Answer: There are 40 questions on Ethan's test.

Step-by-step explanation: To find what 32 is 80% of, you must first convert 80% to a decimal (.8).

Next, divide 32 by .8.

[tex]32/.8 = 40[/tex]

It will take the team 65 days to complete the maintenance of the entire sewage pipe

From the question, we have the following parameters that can be used in our computation:

Sewage pipe = 52 miles

Distance covered each day = 4/5 miles

Using the above as a guide, we have the following:

Number of days = Sewage pipe /Distance covered each day

Substitute the known values in the above equation, so, we have the following representation

Number of days = 52/(4/5)

Evaluate the quotient

Number of days = 65

Hence, the number of days is 65

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The lengths of the legs, the circumference and the radius of the circles are;

First part; The diameter = 18 units

The second leg = 9 units

Second part; The circumference = 34·π units

Third part; The radius is r = 36 cm

The radius of a circle is the distance from the center to the circumference.

First part;

cos(30°) = 9·√3 ÷ The diameter = (√3)/2

The diameter = (9·√3) ÷ ((√3)/2) = 18

The length of the other leg, using the relationship between special triangles is 18/2 = 9

Second part;

The lengths of the legs of the right triangle indicates that we get;

The square of the diameter, D² = 30² + 16² = 1156

The length of the diameter, D = √(1156) = 34

The formula for finding the circumference of a circle, C, based on the diameter can be presented as follows;

C = π × D

Therefore;

The circumference of the circle, C = π × 34

The circumference of the circle = 34·π units

Third part

The length of the 20° arc = 4·π cm

Therefore;

4·π = 2·π·r × 20/360

Where;

r = The radius of the circle

Therefore;

r = (360/20) × 4·π ÷ (2·π) = 36

The radius of the circle, r = 36 cm

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The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

Here, we have,

given that,

the expression is:

4x^2 - 4

now, we have to simplify this.

we know that ,

The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.

It is used to factorize the binomials of squares.

The a^2 - b^2 formula is given as:

a^2 - b^2 = (a - b) (a + b).

so, we have,

4x^2 - 4

= (2x)^2 - 2^2

= (2x -2 ) (2x+2)

Hence, The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

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The average rate of change for the given intervals are:

To compute the average rate of change for any given interval, determine the change between the function values at the endpoints and divide this value by the difference in independent variable values. it can be expressed as follows:

Average Rate of Change = (f(b) - f(a)) / (b - a)

The average rate of change for each point in the interval is determined form the graphs and used to solve for the average rate of change

(-5, -5) and (-4, 0):

Average Rate of Change = (0 - 0) / (-4 - (-5)) = 0 / 1 = 0

(-4, 0) and (-3, 3):

Average Rate of Change = (3 - 0) / (-3 - (-4)) = 3 / 1 = 3

(-4, 0) and (-1, 3):

Average Rate of Change = (3 - 0) / (-1 - (-4)) = 3 / 3 = 1

(-3, 0) and (-1, 0):

Average Rate of Change = (0 - 0) / (-1 - (-3)) = 0 / 2 = 0

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Based on Joey's debt-to-income ratio, the maximum monthly rent payment he can make and still maintain the DTI ratio would be; b. $898.

WE are given that Joey has a DTI ratio of 36% which means that his maximum debt payment should be 36% of his income.

This amount would be:

= DTI x monthly income

= 36% x 3,600

= $1,296

Maximum monthly rent can be found as:

= Maximum monthly debt payment - Car payment - Credit card payment

= 1,296 - 178 - 220

= $898

In conclusion, option B is correct.

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