Find measure of angle HFJ
Look at picture for reference

Answer:

Step-by-step explanation:

A reflection over the y-axis and then a translation down 5 units.

Answer:

0.25

Step-by-step explanation:

scale factor=md/od

=0.5/2

0.25

Answer:

32)  7/12 ≈ 58.3%

33)  Min = 18
       Q1 = 26
       Median = 32
       Q3 = 47
       Max = 67

Step-by-step explanation:

To determine the probability of grabbing a lemon-lime or an orange-flavored bottle from the cooler, we need to calculate the number of favorable outcomes and the total number of possible outcomes.

In the given scenario, there are 4 lemon-lime flavored bottles and 3 orange-flavored bottles in the cooler, plus 5 fruit-punch flavored bottles. Therefore:

The probability of grabbing a lemon-lime or an orange-flavored bottle is:

\(\begin{aligned}\sf Probability &= \sf \dfrac{Favorable\;outcomes}{Total\; outcomes}\\\\&=\dfrac{7}{12}\\\\& \approx 58.3\%\end{aligned}\)

\(\hrulefill\)

The five-number summary is a statistical summary of a dataset that includes the minimum and maximum values, the median (middle value), and the first and third quartiles. It provides a concise overview of the distribution and central tendency of the data.

First, sort the given data in ascending order (this has already been done for us):

The minimum value is the smallest value in the data set.

\(\boxed{\sf Minimum \; value = 18}\)

The median is the middle value of the sorted data.

In this case, we have 8 data points, so the median is the average of the two middle values:

\(\boxed{\sf Median\;(Q_2)=\dfrac{28+36}{2}=32}\)

The first quartile is the median of the lower half of the data.

In this case, we have 4 data points in the lower half (18, 24, 28, 28), so the median is the average of the two middle values:

\(\boxed{\sf First \;Quartile\;(Q_1)=\dfrac{24+28}{2}=26}\)

The third quartile is the median of the upper half of the data.

In this case, we have 4 data points in the upper half (36, 44, 50, 67), so the median is the average of the two middle values:

\(\boxed{\sf Third\;Quartile\;(Q_3)=\dfrac{44+50}{2}=47}\)

The maximum value is the largest value in the data set.

\(\boxed{\sf Maximum\; value = 67}\)

Therefore, the five-number summary for the given data set is:

To construct the box and whisker graph (attached):

The events are mutually exclusive because a bottle cannot be both lemon-lime and orange-flavored simultaneously , the scenario involves mutually exclusive events.

The five-number summary is as follows:

Minimum: 18

Q1: 26

Median: 36

Q3: 47

Maximum: 67

The scenario states that there are 12 bottles of sports drinks in a cooler: 4 lemon-lime flavored, 3 orange-flavored, and 5 fruit-punch flavored. You grab a bottle, and it is either lemon-lime or orange flavored. To determine if this scenario involves mutually exclusive events, we need to assess whether the two events (grabbing a lemon-lime flavored bottle and grabbing an orange-flavored bottle) can occur at the same time or not.

In this case, the events are mutually exclusive because a bottle cannot be both lemon-lime and orange-flavored simultaneously. Therefore, the scenario involves mutually exclusive events.

To find the five-number summary (minimum, first quartile, median, third quartile, and maximum) for the given data and draw a box and whisker plot, we need to arrange the data in ascending order first:

18, 24, 28, 28, 36, 44, 50, 67

Arranging the data in ascending order: 18, 24, 28, 28, 36, 44, 50, 67

The minimum value is 18.

The first quartile (Q1) is the median of the lower half of the data: (24 + 28) / 2 = 26.

The median is the middle value of the data set: 36.

The third quartile (Q3) is the median of the upper half of the data: (44 + 50) / 2 = 47.

The maximum value is 67.

The five-number summary is as follows:

Minimum: 18

Q1: 26

Median: 36

Q3: 47

Maximum: 67

To draw a box and whisker plot, you can use the five-number summary to create a visual representation of the data distribution. However, since I can't draw graphs here, you can create a box and whisker plot yourself. Draw a number line and place a box that spans from Q1 to Q3, with a line inside representing the median. Add "whiskers" extending from the box to the minimum and maximum values.

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Answer:

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

Given sequence:

If t(n) = 200, we can try to find the value of n:

There is no integer solution, since 32 < 40 < 64 or 2⁵ < 40 < 2⁶, the value of n should be between 5 and 6.

The sequence should include integer numbers, so there is no solution.

Given function:

Solve for x if f(x) is 200:

Answer:

1.  No

\(\textsf{2.} \quad x=\dfrac{\ln 40}{\ln 2} \approx5.32\;(\sf 2\;d.p.)\)

Step-by-step explanation:

Given sequence:

\(t(n)=5 \cdot 2^n\)

To determine if the sequence has a term with a value of 200, substitute t(n)=200 into the equation and solve for n:

\(\implies 5 \cdot 2^n=200\)

\(\implies 2^n=40\)

\(\implies \ln 2^n=\ln 40\)

\(\implies n\ln 2=\ln 40\)

\(\implies n=\dfrac{\ln 40}{\ln 2}\)

\(\implies n=5.3219280...\)

In a sequence, n is a positive integer.  Therefore, it is not possible for the sequence to have a term with the value of 200, as when t(n)=200, n is not a positive integer.

Given function:

\(f(x)=5 \cdot 2^x\)

To determine if the function has an output of 200, substitute f(x)=200 into the function and solve for x:

\(\implies 5 \cdot 2^x=200\)

\(\implies 2^x=40\)

\(\implies \ln 2^x=\ln 40\)

\(\implies x=\dfrac{\ln 40}{\ln 2}\)

\(\implies x=5.3219280...\)

Therefore, it is possible for the function to have an output of 200 when:

\(x=\dfrac{\ln 40}{\ln 2}\)

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

7/20

Step-by-step explanation:

Hope this help and have a great day!!!

Answer:

7/ 20 LOL

Step-by-step explanation:

$3,244.21 can be withdrawn each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

where:

PV is the present value of the annuity

PMT is the payment amount per period

r is the interest rate per period

n is the total number of periods

In this case, we want to withdraw a fixed amount each month for 25 years, which represents 12 ×25 = 300 periods.

The interest rate per period is 7% / 12 = 0.5833%.

Let's assume that you want to withdraw a fixed amount each month, and you want the withdrawals to last for 25 years. To calculate the amount you can withdraw each month,

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

500,000 = PMT × [1 - (1 + 0.005833)⁻³⁰⁰] / 0.005833

Solving for PMT, we get:

PMT = PV × r / [1 - (1 + r)⁻ⁿ]

PMT = 500,000 × 0.005833 / [1 - (1 + 0.005833)⁻³⁰⁰]

PMT = $3,244.21

Therefore, you can withdraw $3,244.21 each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.

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Answer:

  D. No, because EFGH is a parallelogram but it’s diagonals are not congruent

Step-by-step explanation:

The differences between the end points of the diagonals are ...

  F -H = (1, 1) -(2, -5) = (1 -2, 1 -(-5)) = (-1, 6)

  G -E = (4, -2) -(-1, -2) = (4 -(-1), -2 -(-2)) = (5, 0)

The length of FH is more than 6, the length of GE is exactly 5. The diagonals are different length, so the figure cannot be a rectangle.

__

The midpoints of the diagonals will be in the same place if the sum of their end points is the same. (Dividing each sum by 2 gives the midpoint of that segment.)

  F+H = (1, 1) +(2, -5) = (3, -4)

  G+E = (4, -2) +(-1, -2) = (3, -4)

The diagonals bisect each other (have the same midpoint), so the figure is a parallelogram.

EFGH is a parallelogram, but not a rectangle: its diagonals are not congruent.

Answer:

×=64

I HOPE IT CAN HELP:(

The number of years it would take is approximately equal to 53 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

By substituting given parameters, we have the following:

96627 = 11211(1 + 0.0418)^t

8.61894567835 = (1.0418)^t

By taking the ln of both sides, we have:

Time, t = ln(8.61894567835)/ln(1.0418)

Time, t = 52.60 ≈ 53 years.

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Answer:

  $1741.44

Step-by-step explanation:

The discounted amount is 100% -10% = 90% of the original. The amount of the discount is 10% of the original, or 1/9 of the discounted amount:

  10% = 90% × 1/9

The discount was ...

  $15,673/9 = 1,741.44

_____

Check

The original is the sum of the discounted amount and the discount:

  original price = $15,673.00 +1,741.44 = $17, 414.44

10% of that value is 1,741.44, as shown above.

Answer:

x > -5

Step-by-step explanation:

-12x < 60

To solve the equation for x, we want x to be by itself on one side.  Let's start by dividing both sides by -12:

-12x/-12 < 60/-12

When dividing or multiplying by a negative number, we have to turn around the inequality sign, so now we have:

x > 60/-12

And 60/-12 = -5, so:

x > -5

Answer:

its c for my test

Step-by-step explanation:

i looked it up on maathway and its says -3 so slope is forst

Answer:

The range of values from one job is between $50 and $650.

Step-by-step explanation:

An electrician charges y amount to work x hours on a job. The electrician charges a $50 service fee and $30 per hour.

This means that his earnings in a job can be modeled by the following function:

\(y = 30x + 50\)

The electrician works maximum of 20 hours on any job. What is the range of values for one job?

Minimum, he works 0 hours, and earns:

\(y(0) = 30(0) + 50 = 50\)

Maximum, he works 20 hours, and earns:

\(y(20) = 30(20) + 50 = 650\)

The range of values from one job is between $50 and $650.

Answer: 5.0526

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 38 on the left side and the dividend 192 on the right side like this:

 3 8 ⟌ 1 9 2

Step 2:

The divisor (38) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:

       0    

 3 8 ⟌ 1 9 2

Step 3:

Multiply the divisor by the result in the previous step (38 x 0 = 0) and write that answer below the dividend.

       0    

 3 8 ⟌ 1 9 2

      0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.

       0    

 3 8 ⟌ 1 9 2

     - 0    

       1    

Step 5:

Move down the 2nd digit of the dividend (9) like this:

       0    

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

Step 6:

The divisor (38) goes into the bottom number (19), 0 time(s). Therefore, put 0 on top:

       0 0  

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

Step 7:

Multiply the divisor by the result in the previous step (38 x 0 = 0) and write that answer at the bottom:

       0 0  

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

         0  

Step 8:

Subtract the result in the previous step from the number written above it. (19 - 0 = 19) and write the answer at the bottom.

       0 0  

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

     -   0  

       1 9  

Step 9:

Move down the last digit of the dividend (2) like this:

       0 0  

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

     -   0  

       1 9 2

Step 10:

The divisor (38) goes into the bottom number (192), 5 time(s). Therefore put 5 on top:

       0 0 5

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

     -   0  

       1 9 2

Step 11:

Multiply the divisor by the result in the previous step (38 x 5 = 190) and write the answer at the bottom:

       0 0 5

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

     -   0  

       1 9 2

       1 9 0

Step 12:

Subtract the result in the previous step from the number written above it. (192 - 190 = 2) and write the answer at the bottom.

       0 0 5

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

     -   0  

       1 9 2

     - 1 9 0

           2

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 192 divided by 38 calculated using Long Division is: 5.0526

Answer:

f(x) = 4(1.095)^x.

Step-by-step explanation:

The function f(x) = 4(1+0.1/0.5)^0.5x can be simplified using the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction).

First, we can simplify 0.1/0.5 to get 0.2.

Next, we can simplify (1 + 0.2) to get 1.2.

Then, we can simplify (1.2)^0.5 to get approximately 1.095.

Finally, we can multiply 4 by 1.095^x to get the simplified function:

The required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

An arrangement of numbers in which the numbers are arranged from smallest to greatest numbers is called ascending order.

Given that, some numbers, 3√2, √3 − 1, √19 + 1, 6, 2√10 ÷ 5 and √14.

We need to order them from least to greatest,

3√2 = 4.24

√3 − 1 = 0.73

√19 + 1 = 5.35

6

2√10 ÷ 5 = 1.26

√14 = 3.74

The order from least to greatest is :-

0.73, 1.26, 3.74, 4.24, 5.35 and 6

i.e.

√3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

Hence, the required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

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Answer:

5

Step-by-step explanation:

The answer is 5 I just used google.

Answer:

5.52

Step-by-step explanation:

Answer:

A (0, -3) translated to the right 4 units.

Step-by-step explanation:

If you go right 4, you get (4, -3)

============================================================

Explanation:

Ignore the portions that are 12 and 13 units long.

The base of triangle ABC is 8 units long. The height is 5 units. The base and height are always perpendicular.

The area is base*height/2 = 8*5/2 = 40/2 = 20 square units

---------

Side note:

You could find the area of triangle ABD, where D is at the 90 degree angle location, and then subtract off the area of triangle ACD. This is a slightly longer approach compared to the first section above.

The worst month for the team in terms of results was October, with a total of three losses in five matches.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


The team won only one match and drew one, resulting in a total of five points. This was the lowest points total of any month during the season, a stark contrast to the other months where the team achieved much higher totals. The team's form during October was a far cry from their form during the rest of the season, with only one win in five matches. This poor form contributed to the team's overall lack of success during the season and led to their eventual relegation from the top division.

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Answer:

Average cost per litre of diesel = rs 8.00

Step-by-step explanation:

Amount spent on diesel each year = rs 4000

Price of a litre of diesel in the first year = rs 7.50

Price of a litre of diesel in the second year = rs 8.00

Price of a litre of diesel in the third year = rs 8.50

Average cost per litre of diesel = \(\frac{p_{1} + p_{2} + p_{3} }{n}\)

where n is the number of years.

Average cost per litre of diesel  =  \(\frac{7.5 + 8.00 + 8.50}{3}\)

                                                     = \(\frac{24}{3}\)

                                                     = 8

Average cost per litre of diesel is rs 8.00

So that he buys an average of 500 (i.e \(\frac{4000}{8}\)) litres every year.

Answer:

9

Step-by-step explanation:

The GCF between 54 and 27 is nine.

The length of a pendulum that makes one full swing in 1.9 seconds is 3 feet.

As per the given data, the given formula is:

\($T=2 \pi \sqrt{\left(\frac{L}{32}\right)}\) gives the time it takes in seconds.

Where,

T is the time it takes for a pendulum to make one full swing back and forth (in seconds).

L is the length of the pendulum, in feet.

Here we need to find the length of a pendulum that makes one full swing in 1.9 seconds to the nearest foot.

Substitute the given parameters into the formula will give;

\($1.9=2 \pi \sqrt{\left(\frac{L}{32}\right)}\)

Now divide both sides by 2π.

\($ \frac{1.9}{2 \pi}=\sqrt{\left(\frac{L}{32}\right)} \\\)

\($ 0.3024=\sqrt{\left(\frac{L}{32}\right)}\)

Then taking square on both sides.

\($ (0.3024)^2=\frac{L}{32} \\\)

0.09144576 = \($\frac{L}{32}\)

Later multiply both sides by 32.

2.9262 = L

The approximate value of the length of a pendulum:

L ≈ 3

Therefore, the length of a pendulum is about 3 feet.

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Answer:

C. 20 feet

Step-by-step explanation:

Let x = width

Let y = length

If the length is at least 10 feet longer than the width:

⇒ x + 10 ≤ y

⇒ x ≤ y - 10

If the perimeter is to be no more than 100 ft:

⇒ 2x + 2y ≤ 100

⇒ x + y ≤ 50

⇒ x ≤ 50 - y

Equate the equations for x and solve for y:

⇒ y - 10 = 50 - y

⇒ 2y = 60

⇒ y = 30

Substitute found value of y into one of the inequalities for x:

⇒ x ≤ 30 - 10

⇒ x ≤ 20

Therefore, the maximum possible width of the fence is 20 feet.

Each silver bead costs $0.50, and each green bead costs $1.

Let's assume the cost of each silver bead is 's' dollars, and the cost of each green bead is 'g' dollars.

According to the given information, the necklace requires 25 silver beads and 15 green beads, and the bracelet requires 10 silver beads and 5 green beads.

The total cost of the necklace beads is $27.50, and the total cost of the bracelet beads is $10.

Using this information, we can set up the following system of equations:

25s + 15g = 27.50 (Equation 1)

10s + 5g = 10 (Equation 2)

We can solve this system of equations using any appropriate method, such as substitution or elimination.

Let's use the elimination method to solve the system:

Multiplying Equation 2 by 3, we get:

30s + 15g = 30 (Equation 3)

Subtracting Equation 3 from Equation 1:

25s + 15g - (30s + 15g) = 27.50 - 30

-5s = -2.50

s = 0.50

Now, substituting the value of s into Equation 2:

10(0.50) + 5g = 10

5 + 5g = 10

5g = 5

g = 1

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...

SOLUTION

Given the figure below;

The radius of the inscribed circle is DE;

The radius of the circumscribed circle is CD;

Answer:

B.

Step-by-step explanation:

4² + 12² = c²

16 + 144 = c²

160 = c²

√160

:)

Answer:

\(c=\sqrt{160}\)

Step-by-step explanation:

Pythagorean theory formula:-

\(a^2+b^2=c^2\)

Where..

a= 4, b= 12, c= x

\(4^2+12^2=x^2\)

\(16+144=x^2\)

\(160=x^2\)

\(\sqrt{160}=\sqrt{x^2}\)

\(x=\sqrt{160}\)