Without using a calculator, match each expression to the correct point.
f
de
←++ ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
-5
-3
Point Expression
3
2
d
e
-4
f
-√8
-π
-2
-1
+
0

a. The tax paid would be:

$15,100 x 0.04 = $604

b. The car's total cost would be:

$15,100 + $604 = $15,704

The measure of other angles of the triangle in degrees are 90 and 50 degrees

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

Triangle = right triangle

Angle = 40 degrees

The sum of angles in a triangle is 90 degrees

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

40 + 90 + Other angle = 180

Evaluate

Other angle = 50

Hence, the other angle = 50 degrees

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Answer: with what?

Step-by-step explanation:

Explain what you need help with pls.

Answer:

Let m be the amount of money Caleb originally had. He spent 20% of it, so he now has 80% of his original amount.

10 = .80m

10 = $12.50

Answer:

Step-by-step explanation:

  opposite angles = congruent

so

10x = 7x + 33

3x = 33

x = 11

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

check

10 * 11 = 7 * 11 + 33

110 = 110

same value, the answer is good

Sue must earn an annual interest rate of 6.9% on the $20,000 in order to reach her goal of saving $50,000 in 10 years.

Amount If you wish to make an additional deposit to this account, you must first provide the amount you wish to deposit. Once the amount has been provided, you will be able to make the deposit. Please note that all deposits must be made in accordance with applicable laws and regulations.

In order to reach her goal of saving $50,000 in 10 years, Sue must earn an annual interest rate of 6.9%. This rate is calculated by using the formula A = P (1 + r)ⁿ, where A is the future amount, P is the present amount, r is the rate of interest, and n is the number of years.

In this case, Sue has a present amount of $20,000 and a future amount of $50,000. Therefore, the formula becomes $50,000 = $20,000 (1 + r)^10. Solving for r, the rate of interest is 6.9%. This means that Sue must earn an annual interest rate of 6.9% on the $20,000 in order to reach her goal of saving $50,000 in 10 years.

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Answer:

The measure of both of the smaller angles is 43°.

The measure of the larger angle is 94°.

Step-by-step explanation:

We can model the larger angle in relation to the smaller angle by representing each of the smaller angles (which are equal in measure) as a variable x and the larger angle as a variable y.

[tex]y = 2x + 8[/tex]

This shows that the larger angle is eight degrees more than twice (2 times) the smaller angles' measures.

We can now model the sum of all the triangle's angle measures because we know that a triangle's interior angle measures add to 180°.

[tex]2(\text{small}) + \text{large} = 180[/tex]

[tex]2x + y = 180[/tex]

What we have now is a system of equations which we can solve for using substitution. The first equation ([tex]y = 2x + 8[/tex]) is a definition of y in terms of x, so we can substitute that definition into the second equation and solve for x.

[tex]\begin{cases} y = 2x + 8 \\ 2x + y = 180\end{cases}[/tex]

[tex]2x + (2x + 8) = 180[/tex]

[tex]4x + 8 = 180[/tex]

[tex]4x = 172[/tex]

[tex]\boxed{x = 43\textdegree}[/tex]

So, the measure of each of the smaller angles is 43°.

Now, we can plug that x-value back into the first equation and solve for y.

[tex]y = 2(43) + 8[/tex]

[tex]y = 86 + 8[/tex]

[tex]\boxed{y = 94\°}[/tex]

So, the measure of the larger angle is 94°.

Answer: So, the value of the function f(x) = 2x + 3x^2 when x = 1/3 is 1.

Step-by-step explanation: To evaluate the function f(x) = 2x + 3x^2 at x = 1/3, we can substitute the value of x into the function. This gives us:

f(1/3) = 2(1/3) + 3(1/3)^2

Solving this expression following the order of operations, we first solve the exponent:

f(1/3) = 2(1/3) + 3(1/9)

Then we solve the multiplication:

f(1/3) = 2/3 + 3/9

= 6/9 + 3/9

= 9/9

= 1

So, the value of the function f(x) = 2x + 3x^2 when x = 1/3 is 1.

The margin of error, using a 95% confidence level is 0.026. The Option C.

The margin of error can be calculated using the formula which is "Margin of Error = Critical Value * Standard Deviation"

Given:

Sample proportion is 26%

Sample size is 1100

We can then calculate the Standard Deviation as follows:

= sqrt((p * (1 - p)) / n)

Plugging in the values, we get:

= sqrt((0.26 * (1 - 0.26)) / 1100)

= sqrt (0.00017490909)

= 0.01322497637

≈ 0.013

We must find Critical Value for a 95% confidence level. For a normal distribution, the Critical Value is approximately 1.96. Now, we can calculate the Margin of Error which is

= Critical Value * Standard Deviation

= 1.96 * 0.013

≈ 0.026

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The approximate amount of rotations it would take the monster truck to travel one mile is 1260 rotations.

Now, Based on the tire experiment, it will take fewer rotations for a monster truck with 6ft (which is 72 inches) tires to travel one mile compared to the other 3 tires from before.

This is because larger tires have a greater circumference, which means they are able to cover more distance with each rotation.

Hence, For calculate the approximate amount of rotations it would take the monster truck to travel one mile, we need to use the formula:

Number of rotations = Distance traveled / Circumference of the tire

Since the distance traveled is one mile, which is equal to 5280 feet, we need to convert the tire diameter from feet to inches, and then calculate the circumference:

Hence, We get;

Circumference = π x Diameter Circumference

                        = 3.14 x 72 Circumference

                        = 226.08 inches

Now, we can calculate the number of rotations:

Number of rotations = 5280 feet / (12 inches/foot x 226.08 inches/rotation)

Number of rotations = 5280 / 2712.96

Number of rotations ≈ 1.947 rotations

or ≈ 1260 rotations per mile

Therefore, the approximate amount of rotations it would take the monster truck to travel one mile is 1260 rotations.

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Sheena decorated 9 invitations on Saturday.

We are given the number of invitations made on Friday is 1/2 is a fraction. To find the number of invitations use the multiplication of fractions.

This can be done by multiplying the fraction by the total number of invitations. Similarly, we can find the number of invitations did Sheena decorate on Saturday.

Here we have

Sheena is making invitations for her birthday party. Sheena needs to make invitations for 54 of her friends.

On Friday you helped her make 1/2 of the invitations.

So the number of invitations made is:

=> 1/2 × 54 = 27 invitations

On Saturday, Sheena worked on decorating 1/3 of the invitations made on Friday, so the number of invitations she decorated is:

=> 1/3 × 27 = 9 invitations

Therefore,

Sheena decorated 9 invitations on Saturday.

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A. The percentage of students who passed the exam and completed the exam review is given as 55%.

B. The percentage of students who did not complete the exam review and passed the exam is given as 20%.

C. There is most probably an association between completing the exam review and passing the exam.

Part A:

The percentage of students who passed the exam and completed the exam review is given as 55%.

Part B:

The percentage of students who did not complete the exam review and passed the exam is given as 20%.

Part C:

The percentage of students who passed the exam and completed the exam review is 55%, while the percentage of students who passed the exam and did not complete the exam review is 20%.

These percentages are significantly different from each other, indicating that there is likely an association between completing the exam review and passing the exam.

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The total miles of run covered by Mark on Thursday is equal to  9 miles.

Mark ran 3 3/5 miles on Wednesday.

On Thursday, he ran 2 1/2 times as far as he did on Wednesday.

To find out how far he ran on Thursday,

We need to multiply his Wednesday distance by 2 1/2,

2 1/2 × 3 3/5

First, we need to convert both mixed numbers to improper fractions which is equal to,

2 1/2 = 5/2

3 3/5 = 18/5

Now, we can multiply,

5/2 × 18/5

= (5 × 18) / (2 × 5)

= 90/10 = 9

Therefore, the total miles Mark ran on Thursday is equal to  9 miles.

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In the Venn diagram , we can conclude that the statement is valid.

What is Venn diagram?

Venn diagrams are frequently used in mathematics, statistics, logic, teaching, linguistics, computer science, and business. They are also known as Set diagrams or Logic diagrams.

Here "Pen" and "Pencil". Since we know that every student brought a pen or a pencil, we know that there are no elements outside the 2 sets (these would be students who brought neither a pen or a pencil). Also, since every student brought a pencil or a pen, we also know that the overlap between the 2 sets is empty (this would be students who brought a pencil and a pen). So there are 2 areas remaining where students can be situated (1 and 2 in the picture).

We know that Marcie brought a pencil, so she is situated in area 2. This means she is outside the set "pen", and so she didn't bring a pen, and we can conclude that the statement is valid.

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The correct justification for the similarity between ∆MNO and ∆PQR is:

∆MNO was dilated by a scale factor of 3 from the origin, then rotated 90° clockwise about the origin to form ∆PQR.

To see why this is the case, we can apply the transformations to the vertices of ∆MNO and see if they match the vertices of ∆PQR.

First, we dilate ∆MNO by a scale factor of 3 from the origin:

M' = 3M = (3(3), 3(9)) = (9, 27)

N' = 3N = (3(9), 3(9)) = (27, 27)

O' = 3O = (3(12), 3(3)) = (36, 9)

Next, we rotate the dilated triangle 90° clockwise about the origin:

P' = (cos(90°)P - sin(90°)Q, sin(90°)P + cos(90°)Q)

= (0P - (-1)Q, 1P + 0Q) = (Qx + 1, Py)

Q' = (cos(90°)Q - sin(90°)P, sin(90°)Q + cos(90°)P)

= (0Q - (-3)P, 1Q + 0P) = (Px + 3, Qy)

R' = (cos(90°)R - sin(90°)S, sin(90°)R + cos(90°)S)

= (4R - 4S, -4R - 4S) = (4(R - S), -4(R + S))

Substituting the coordinates of the original vertices, we get:

P' = (-1 + 1, -3) = (0, -3)

Q' = (-3 + 1, -1) = (-2, -1)

R' = 4(-4 + 1, -1 + 3) = (-12, 8)

Comparing the coordinates of ∆PQR with those of the transformed ∆MNO, we can see that they match. Therefore, the similarity between ∆MNO and ∆PQR can be justified by dilating ∆MNO by a scale factor of 3 from the origin, then rotating it 90° clockwise about the origin to form ∆PQR.

It is given that cos(θ)=4/5 and 0 <0< 90, the value of sin(θ) would be 24/25. So, the correct answer is option b.  

To find sin(2θ) in terms of cos(θ), we will use double angle formula for sin which states that:

sin(2θ) = 2 sin(θ) cos(θ)

It is given that cos(θ) = 4/5,

Using the Pythagorean identity to find sin(θ):

[tex]sin^2[/tex](θ) + [tex]cos^{2}[/tex](θ) = 1

[tex]sin^2[/tex](θ) = 1 - [tex]cos^{2}[/tex](θ)

sin(θ) = [tex]\sqrt{(1 - (4/5)^2)}[/tex]

sin(θ) = 3/5

Substituting these values into double angle formula for sin:

sin(2θ) = 2 sin(θ) cos(θ)

sin(2θ) = 2 (3/5) (4/5)

sin(2θ) = 24/25

Therefore, the answer is (b) 24/25.

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Answer:

3.5 litres.

Step-by-step explanation:

We can use the unit rate method to find how much tea Ben drinks per hour.

First, we can convert 2/3 of an hour to an hour by multiplying it by 3/2:

2/3 hour * 3/2 = 1 hour

This tells us that the rate of drinking tea is constant, and Ben drinks 3 and 1/2 liters of tea per hour.

Therefore, Ben drinks 3.5 liters of tea per hour.

Answer:

A = $563.69

Step-by-step explanation:

First, convert R as a percentage to R as a decimal

r = R/100

r = 2/100

r = 0.02 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 500.00(1 + 0.02/12)^(12)(6)

A = 500.00(1 + 0.0016666666666667)^(72)

A = $563.69

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $500.00 at a rate of 2% per year compounded 12 times per year over 6 years is $563.69.

The surface area of solid B is calculated as:

13. 144π ft²       14. 85.3 ft²

Recall that the ratio of the surface areas of similar solids is equal to the square of the ratio of their linear measures.

Thus, we have the following:

13. Let the surface area of solid B be represented as x, therefore:

36π / x = 4² / 8²

x * 4² = 36π * 8²

16x = 2,304π

16x/16 = 2,304π/16 [division property of equality]

x = 144π ft²

14. Let the surface area of solid B be represented as x, therefore:

48 / x = 27² / 36²

Cross multiply:

x * 27² = 48 * 36²

729x = 62,208

729x/729 = 62,208/729 [division property of equality]

x = 85.3 ft²

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The density of the small rocks is 21 rocks per square feet.

To find the density of rocks per square feet, we need to take the quotient between the total number of rocks and the area covered.

We know that the patio has an area of 200 square feet, and the total number of rocks is 4200, then here we only need to take the quotient between these two values.

Density = (4200 rocks)/(200 ft²) =  21 rocks per ft²

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Complete question:

"Jen's patio has an area of 200 square feet. She is covering the area with 4200 small rocks.

What is the density of the rocks on the patio?"

The total number of different signals consisting of flags is 216

Given data ,

The number of different signals consisting of 9 flags that can be made using 3 white flags, 3 red flags, and 3 blue flags can be calculated using combinatorial principles.

There are 3 choices for the top flag (white, red, or blue), 2 choices for the second flag (since we've already used one color for the top flag), and 1 choice for the third flag.

Similarly, there are 3 choices for the fourth flag, 2 choices for the fifth flag, and 1 choice for the sixth flag. Finally, there are 3 choices for the seventh flag, 2 choices for the eighth flag, and 1 choice for the ninth flag.

Using the multiplication principle, we can multiply the number of choices at each step to get the total number of different signals:

3 × 2 × 1 × 3 × 2 × 1 × 3 × 2 × 1 = 3! × 3! × 3!

where "!" represents the factorial operation, which is the product of all positive integers up to a given number.

So, the total number of different signals consisting of 9 flags that can be made using 3 white flags, 3 red flags, and 3 blue flags is:

3! × 3! × 3! = 6 × 6 × 6 = 216

Hence , the number of signals is 216

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This is a binomial probability problem with n=11 (the number of drivers selected) and p=0.07 (the probability that a driver was involved in an accident).

To find the probability of getting 3 or more drivers who were involved in an accident, we need to find the probability of getting 3, 4, 5, ..., 11 drivers who were involved in an accident and then add those probabilities together.

We can use the binomial probability formula to calculate each of these individual probabilities:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the number of drivers who were involved in an accident, k is the number of drivers we want to calculate the probability for, and (n choose k) is the binomial coefficient, which is calculated as:

(n choose k) = n! / (k! * (n-k)!)

Using this formula, we can calculate the probability of getting exactly k drivers who were involved in an accident.

For k=3, we have:

P(X=3) = (11 choose 3) * 0.07^3 * 0.93^8 = 0.1038

For k=4, we have:

P(X=4) = (11 choose 4) * 0.07^4 * 0.93^7 = 0.0286

For k=5, we have:

P(X=5) = (11 choose 5) * 0.07^5 * 0.93^6 = 0.0052

For k=6, we have:

P(X=6) = (11 choose 6) * 0.07^6 * 0.93^5 = 0.0007

For k=7, 8, 9, 10, 11, we have:

P(X=7) = (11 choose 7) * 0.07^7 * 0.93^4 = 0.0001

P(X=8) = (11 choose 8) * 0.07^8 * 0.93^3 = 0.0000

P(X=9) = (11 choose 9) * 0.07^9 * 0.93^2 = 0.0000

P(X=10) = (11 choose 10) * 0.07^10 * 0.93^1 = 0.0000

P(X=11) = (11 choose 11) * 0.07^11 * 0.93^0 = 0.0000

To get the probability of getting 3 or more drivers who were involved in an accident, we need to add up the probabilities for k=3, 4, 5, ..., 11:

P(X>=3) = P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10) + P(X=11)

P(X>=3) = 0.1393

Therefore, the probability of getting 3 or more drivers who were involved in an accident out of 11 randomly selected drivers is 0.1393, or about 13.93%.

The domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.

Function is a process or a set of rules that take input values and produces an output. It is a mathematical expression that takes the inputs, performs an operation and produces an output. Functions are used to model real-world scenarios and to solve problems. It helps to simplify the code and makes it easier to understand and debug. Functions are also used to create reusable code that can be used in different applications.

A: Domain: (Negative infinity, infinity), Range: (Negative infinity, infinity)

B: Domain: (Negative infinity, 4), Range: (Negative infinity, 4)

C: Domain: (Negative infinity, 4], Range: (Negative infinity, 4]

D: Domain: [-3, 4], Range: [-7, 4]

Answer: D: Domain: [-3, 4], Range: [-7, 4]

The domain of f(x) is the set of all x-values for which the function is defined, which in this case is [-3, 4]. The range of f(x) is the set of all y-values for which the function is defined, which in this case is [-7, 4]. The value of f(-3) is -7, according to the graph.

To calculate the value of f(x) at any x-value, we can use the three equations given in the graph. For x ≤ -3, f(x) = x + 7. For -3 < x ≤ 0, f(x) = -x. For 0 < x < 4, f(x) =√x.

In conclusion, the domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.

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The domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.

What is function in math?

Function is a process or a set of rules that take input values and produces an output. It is a mathematical expression that takes the inputs, performs an operation and produces an output. Functions are used to model real-world scenarios and to solve problems. It helps to simplify the code and makes it easier to understand and debug. Functions are also used to create reusable code that can be used in different applications.

A: Domain: (Negative infinity, infinity), Range: (Negative infinity, infinity)

B: Domain: (Negative infinity, 4), Range: (Negative

infinity, 4)

C: Domain: (Negative infinity, 4], Range: (Negative infinity, 4]

D: Domain: [-3, 4], Range: [-7, 4]

Answer: D: Domain: [-3, 4], Range: [-7, 4]

The domain of f(x) is the set of all x-values for which the function is defined, which in this case is [-3, 4]. The range of f(x) is the set of all y-values for which the function is defined, which in this case is [-7, 4]. The value of f(-3) is -7, according to the graph.

To calculate the value of f(x) at any x-value, we can use the three equations given in the graph. For x ≤-3, f(x) = x+7. For -3 <x≤0, f(x)=-x. For O <x<4, f(x)=√x.

To calculate the value of f(x) at any x-value, we can use the three equations given in the graph. For x ≤-3, f(x) = x + 7. For -3 <x ≤ 0, f(x) = -x. For O <x<4, f(x)=√x.

In conclusion, the domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.

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If one of the rows in the matrix of a system of linear equations is a multiple of another row, the row-reduced form of the matrix will have a row of zeros.

One of the steps in the row reduction process is the elimination of a variable by subtracting a multiple of one row from another row. This operation will produce a row of zeros if one row is a multiple of another.

Hence, when one of the rows in the matrix of a system of linear equations is a multiple of another row, the row-reduced form of the matrix will have a row of zeros.

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The required probability of getting at least 3 sixes in 5 rolls of a fair die is 0.033.

The probability of getting exactly k sixes in n rolls of a fair die is given by the binomial distribution formula:

[tex]P(k) = (n C k) * p^k * (1-p)^{(n-k)}[/tex]

(n choose k) = n! / (k! * (n-k)!)

Using this formula, we can calculate the probability of getting exactly 3, 4, or 5 sixes in 5 rolls:

P(3) = (5 choose 3) * (1/6)³ * (5/6)² = 0.032

P(4) = (5 choose 4) * (1/6)⁴ * (5/6)¹ = 0.001

P(5) = (5 choose 5) * (1/6)⁵ * (5/6)⁰ = 0.00003

To get the probability of getting at least 3 sixes, we need to add up these probabilities:

P(at least 3 sixes) = P(3) + P(4) + P(5) = 0.032 + 0.001 + 0.00003 = 0.03303

Rounding to the nearest thousandth, the probability of getting at least 3 sixes in 5 rolls of a fair die is 0.033.

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Answer:

48

Step-by-step explanation:

480x0.1=48

The area of the blacktop in square meters is: 272m²

The formula for the area of a rectangle is:

A = l * w

where:

l is length

w is width

Thus:

A = 10m * 8m

A = 80m²

That’s the area of the first rectangle.

A = l x w

A = 24m x 8m

A = 192m²

That’s the area of the second rectangle.

Total area of composite shape = 192m² + 80m² = 272m²

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Answer:   -3 x y + x + 4.

Step-by-step explanation: