solve for y. triangle PQR is congruent to triangle DEF, PQ= 15, QR= 10, RP=8, and EF = 6y +4

Answer:

B

Step-by-step explanation:

imagine math

After 4 years, with an initial deposit of $6,000 at a 1.5% annual interest rate compounded monthly, Isabel will have approximately $6,370.07 in her account.

Calculating Compound Interest

To calculate the amount of money Isabel will have in her account after 4 years with an initial deposit of $6,000 at an annual interest rate of 1.5% compounded monthly, we can use the compound interest formula:

V(t) = P(1 + r/n)nt

P = principal amount (initial investment) = $6,000

r = annual interest rate (as a decimal) = 0.015

n = number of times the interest is compounded per year = 12

t = number of years the money is invested or borrowed for = 4

Substituting these values into the formula, we get:

V(4) = $6,000(1 + 0.015/12)12(4)

This simplifies to:

V(4) = $6,000(1 + 0.00125)48

Calculating the value inside the parentheses first:

1 + 0.00125 = 1.00125

Then raising it to the 48th power gives us:

1.0012548 ≈ 1.061678

Multiplying this by the principal:

V(4) ≈ $6,000 × 1.061678 ≈ $6,370.07

After 4 years, Isabel's account will have approximately $6,370.07.

Answer:$6,370.07

Step-by-step explanation:

To determine the wall space needed for Mr. Hart's picture, calculate the area of the rectangle formed by the picture's dimensions: length (13 inches) times width (9 inches), resulting in 117 square inches of wall space.

The student's question about Mr. Hart hanging a picture on a wall involves calculating the wall space the picture will occupy. This is essentially a question about finding the area of a rectangle. To find the area, one must multiply the length by the width of the rectangle. In this case, the length of the picture frame is 13 inches and the width is 9 inches. The calculation will be:

Area = Length × Width

Area = 13 inches × 9 inches

Area = 117 square inches

Therefore, the picture will need 117 square inches of wall space.

Answer:

The answer is A) 2.

Step-by-step explanation:

The best way would be to use intervals of 2.

We know that the shortest persons 48 inches and the tallest 60 inches.

The difference between the tallest person and the shortest is:

60 - 48 = 12 inches

Since the difference is small, we might use intervals smaller than 12 because if we used intervals of 12, we wouldn't know for sure the heights of the other students, and we would have to estimate their heights.

Using intervals of 8 would be the same, we would have to estimate the heights of most students.

Using 5 , would also not be a good choice because 5 is not a multiple of 48, 60 or 12, therefore, that

Therefore, 2 would be the best option, as you don't have to estimate and the intervals would match the shortest and tallest height.

The probability that the result is a multiple of 5 and a multiple of 2 is 6/11

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For this case, we're given that:

Take E = Event of spinner's spin resulting in multiple of 5 or multiple of 2

S = results of Sample

Then, favorable results (in favor of E) are: 2,4,5,6,8,10 (total 6 in count)

All possible results are 1, 2, ... , 11  (total 11 in count)

Thus, we get:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{6}{11}[/tex]

Thus, the probability that the result is a multiple of 5 and a multiple of 2 is 6/11

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In a spinner numbered 1 through 11, there is only one number (10) that is both a multiple of 5 and a multiple of 2. As there are 11 possible outcomes in a single spin, the probability of spinning and landing on 10 is 1/11.

The subject of this question is mathematical probability. Given that there is a spinner with 11 equal areas numbered 1 through 11, we are asked to find the probability of landing on a number that is both a multiple of 5 and a multiple of 2 when the spinner is spun once.

Firstly, we identify the numbers which are both multiples of 5 and 2 between 1 and 11. In this case, only one such number exists, which is 10. Hence, there is only one favorable outcome. The total number of outcomes are 11 (as the spinner has 11 equal areas).

Probability is defined as 'number of favorable outcomes' divided by the 'total number of outcomes'. In this case, since there is 1 favorable outcome (i.e. landing on '10') and 11 possible outcomes (any of the numbers 1 to 11), the probability is therefore 1/11.

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The height of the drive-in movie theater screen can be determined using proportions and similar triangles. The total height of the screen is found to be 11.7 feet.

To find the height of the screen, you'll need to use similar triangles, as the triangle formed by your line of sight to the top and bottom of the screen is similar to the triangle formed by the screen and the ground. The proportion of the vertical distance from your eye to the ground and the horizontal distance from you to the screen is equal to the proportion of the height of the screen and the horizontal distance from you to the screen. Hence, you can calculate the height of the screen using a cross-multiplication.

So, we have the equation: 5.7/11 = h/11, where h is the height of the screen from your eye level. Solving this gives us h=5.7 feet. Thus, the total height of the screen is the height from the ground to your eye level plus the height of the screen from your eye level. So, the total height = 5.7 feet + 6 feet = 11.7 feet.

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the length of side VY is equal to the height, which is 19.4 units. The formula for the perimeter of a rectangle is given as `2 * (base + height)`.

It's correctly stated that the base of the rectangle is `3y + 1`, and the height is `2y + 3`. The perimeter is given as `90 units`.

To find the dimensions, we set up an equation using the formula for the perimeter:

  90 = 2 * [(3y + 1) + (2y + 3)]

  This equation represents that the perimeter is equal to twice the sum of the base and height.

The equation is then simplified:

  90 = 2 * [5y + 4]

  By dividing both sides by 2, it becomes:

  5y + 4 = 45

  Solving for y:

  5y = 45 - 4

  5y = 41

  y = 41 / 5

  y = 8.2 units

  So, the value of y is correctly determined as 8.2 units.

With the value of y known, the base and height expressions are evaluated:

  Base: `3y + 1 = 3 * 8.2 + 1 = 24.6 + 1 = 25.6 units`

  Height: `2y + 3 = 2 * 8.2 + 3 = 16.4 + 3 = 19.4 units`

The dimensions of the rectangle are correctly calculated as follows:

  Base: 25.6 units

  Height: 19.4 units

  It's also mentioned that the length of side VY is equal to the height, which is 19.4 units.

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Answer:

Red kite has maximum altitude with 23.1 feet higher.

Step-by-step explanation:

Given : Emma enjoys flying kites. her red kite has a maximum altitude of 117.46 meters, and her black kite has a maximum altitude of 362.26 feet.

one foot is the same as 0.3048 meters.

To find : Which kite has a higher maximum altitude, and how many feet higher is it?

Solution :

First we have to convert meter into feet.

We have given, 1 feet = 0.3048 meters.

[tex]1 \text{ meter }=\frac{1}{0.3048} \text{ feet}[/tex]

So, red kite has a maximum altitude of 117.46 meters

In feet, red kite has a maximum altitude of

[tex]117.46\text{ meter }=\frac{117.46}{0.3048}=385.36 \text{ feet}[/tex]

Now, Red kite has a maximum altitude of 385.36 feet

Black kite has a maximum altitude of 362.26 feet.

385.36>362.26 feet.

Difference is 385.36-362.26=23.1 ft.

Therefore, Red kite has maximum altitude with 23.1 feet higher.

The solution is: The box plot is attached.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

We first order the data from least to greatest:

112, 116, 134, 134, 135, 141, 149, 154, 156, 156

We find the median (middle value).  There are 10 data values, which puts the median between 135 and 141:

(135+141)/2 = 276/2 = 138

The Upper Quartile (UQ) is the median of the upper half of data, cut by the median.  This is 154.

The Lower Quartile (LQ) is the median of the lower half of data, cut by the median.  This is 134.

The middle line of the box is drawn at the median, 138.  The left side of the box is at the LQ, 134.  The right side of the box is at the UQ, 154.  There is a whisker drawn from the right side to the highest value, 156.  There is a whisker drawn from the left side to the smallest value, 112.

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Using Frequency table, Option: (d) is correct.

Frequency refers to "the number of times an event or values occurs".

According to the question,

The number of deer spotted in preserve is

32,27,15,1,42,35,46,29,38,18,40,38,32,34

The number deer appear in the interval 10 - 19 is 3

The number deer appear in the interval 20 - 29 is 2

The number deer appear in the interval 30 - 39 is 6

The number deer appear in the interval 40 - 49 is 3

From the above data, we can form frequency table

Deer                  10 - 19          20 - 29     30 - 39         40 - 49

Frequency           3                    2              6                    3

Hence, the answer is Option: (d)

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Answer:

Option: A is the correct answer.

      A)  Period: 3 , amplitude : 1.5

Step-by-step explanation:

We know that Period of a function is the smallest value such that the function repeats after a fixed time.

and also the amplitude of the function is the height above or below the mid-line.

After looking at the graph we see that the period of the function is: 3

Since the function is repeating itself after every x=3.

Also, the mid-line of the function is: y= -0.5.

Hence, the height above the mid-line is: 1+0.5 = 1.5

        Hence, amplitude= 1.5

What is the interquartile range of this data? 6 7 8 9 Box-and whisker plot titled Temperatures in Celsius ranging from 12 to 48 with the five number summary from left to right 18, 25, 28, 33, and 42

Solution:

The problem is not clear.

But, considering data set is:

18,25,28,33,42

So, if we consider the data set, Interquartile Range is the difference of Quartile3-Quartile1

IQR=Q3-Q1

To find, Q1 and Q3. Let us find the median, or, Q2 first.

Median is the middle term of the data set.

So, Median, Q2=28

Q1 is the median of first half of the data set. That is, 18,25,28

So, Lower Quartile, Q1=25

Q3 is the median of second half of data set. That is, 28, 33,42

So, Upper Quartile, Q3=33

IQR=Q3-Q1

=33-25=8

Answer: IQR=8

If we consider data set: 6,7,8,9

Median, Q2=[tex] \frac{(7+8)}{2}=\frac{15}{2} [/tex]=7.5

Lower Quartile, Q1=6.25

Upper Quartile, Q2=8.75

IQR=Q3-Q1=8.75-6.25=2.5

IQR=2.5

Answer- C(16,12)

C(n,r) = n! / r!* (n-r)!

So,

C(16,4) = 16!/ 4! * 12!

C(16,12) = !6!/ 12! * 4!