What is the length of each leg in the right triangle shown?
45
7sqrt2
45°

Answer: -8<x> 2

Step-by-step explanation:

open circles indicate that the number shown is not included therefore x must lie in-between -8 and 2

Answer:

[tex]r=14\mathring{}[/tex]

Step-by-step explanation:

[tex](5r-5)\mathring{}+(8r+3)\mathring{}=180\mathring{}\\5r-5+8r+3=180\mathring{}\\13r-2=180\mathring{}\\13r=180\mathring{}+2\\13r=182\mathring{}\\r=\frac{182}{13} \\\\r=14\mathring{}[/tex]

The measure of ∠R of the given parallelogram is 52°.

What is a parallelogram?

A parallelogram is a simple quadrilateral with two sets of parallel sides. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of a similar measure.

Some of the properties of a parallelogram are,

Given,

Length of  PS = 3

Length of RS = 5

∠Q = 128°

Since it is a parallelogram,

PS = QR = 3 and RS = QP = 5

∠Q + ∠R = 180

m∠R = 180 - ∠Q = 180-128 = 52°

Therefore the measure of ∠R of the given parallelogram is 52°.

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Answer:

Step-by-step explanation: 2 00

22

Answer:

<LJK = 69 degrees

Step-by-step explanation:

Triangle HKL and LJK are congruent, therefore their angles will be as well. Divide HJK by 2; 138 / 2 = 69

Answer:

The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.

The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.

So, the impulse on the ball is -80 kg m/s.

Answer:

To find out how many of the first 76 slices sold during lunch tomorrow should be pepperoni pizza, we can use the information provided about the proportion of pepperoni pizza slices sold today. We can use the following formula to calculate the expected proportion:

(number of pepperoni slices / total number of slices) * 100

Plugging in the numbers we have:

(44 / (44 + 15 + 29)) * 100 = 44 / 88 * 100 = 50%.

So we can expect 50% of the first 76 slices sold during lunch tomorrow to be pepperoni pizza slices, which is equivalent to:

76 slices * 50% = 38 slices

Therefore, we expect 38 of the first 76 slices sold during lunch tomorrow should be slices of pepperoni pizza.

Step-by-step explanation:

The total amount that he will be charged for the shipping is given as follows:

$34.88.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Jerry is charged $2.25 per pound for shipping, hence the constant is given as follows:

k = 2.25.

Meaning that the equation for the total cost for a weight of x pounds is given as follows:

y = 2.25x.

The total weight is given as follows:

3.2 + 3.8 + 4 + 4.5 = 15.5 pounds.

Hence the total cost is given as follows:

y = 2.25 x 15.5

y = $34.88.

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The probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music cannot be determined (E).

Here 'x' denotes the no. of puzzles completed by an individual within 5 minutes. Given that the probability distribution of 'x' as,

[tex]$$\begin{array}{ccccc}x: 1 & 2 & 3 & 4 \\p(x): & 0.2 & 0.4 & 0.3 & 0.1\end{array}$$[/tex]

'D' is the difference in the number of puzzles saved by two randomly selected subjects. Let [tex]X_{1}[/tex] be the number of puzzles solved by first individual and [tex]$X_2$[/tex] be the number of puzzles solved by [tex]$2^{n d}$[/tex] individual.

Then, D=[tex]X_1-X_2$[/tex] where [tex]$X_1$[/tex] and [tex]$X_2$[/tex] are independent and follow the above

[tex]$$\begin{aligned}& \therefore \text { Variance }(D)=V(D)=v\left(x_1-x_2\right) \\& =V\left(x_1\right)+v\left(x_2\right) \\& =2 \times v\left(x_1\right) \quad\left(\because v\left(x_1\right)=v\left(x_2\right)\right. \\& \text { Now, } V\left(x_1\right)=V(x)=E\left(x^2\right)-[E(x)]^2 \\& =0.2+0.8+0.9+0.4 \\& =2.3 \\&\end{aligned}$$[/tex]

[tex]$$\text { and } \begin{aligned}E\left(x^2\right) & =\sum_{R(x)} x^2 P[x=x] \\& =\sum_{x=1}^4 x^2 P[x \cdot x] \\& =\left(1^2 \times 0.2\right)+\left(2^2 \times 0.4\right)+\left(3^2 \times 0.3\right)+\left(4^2 \times 0.1\right) \\& =6.1 \\\Rightarrow V(x) & =k\left(x^2\right)-[k(x)]^2 \\& =6.1-(2.3)^2 \\& =0.81\end{aligned}$$[/tex]

[tex]$\therefore$[/tex] Variance of D,

[tex]$$\begin{aligned}V(D) & =2 \times v\left(x_1\right) \\& =2 \times 0.81=1.62\end{aligned}$$$\therefore$ Standard deviation of $D$ is,$$\sqrt{V(0)}=\sqrt{1.62} \simeq$$[/tex] 1.27.

Therefore, the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music is, 1.27.

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The length of the rectangular pool is 98 m.

The area of Rectangle is length times of width.

Given that the perimeter of a rectangular pool is 368m.

The width of the pool is 86m

We need to find the length of the pool.

Perimeter of rectangle=2(Length+width)

368=2(Length+86)

368=2Length+172

368-172=2length

196=2length

Divide both sides by 2

98=length

Hence, the length of the rectangular pool is 98 m.

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A good way to save money in an interest-bearing account is using a savings account with intereste

The future of management relies on flexibility, adaptation and pragmatism.

The following ideas can help you make a plan to save and maximize your interest earnings.

1. High-Yield Savings Account. .

2. High-Yield Checking Account. .

3. CDs and CD Ladders.

4. Money Market Account.

5.. Treasury Bills.

Research suggests that thinking about the future,a process known as prospection,can help us lead more generous and fulfilled lives. Mindfulness is all the rage these days, and for good reason. Focusing on the moment can improve our well-being, foster compassion, and help our relationships.

For a better well-being we have to think about the future.

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Check the picture below.

The volume and radius of the ice cream and the ice cream cone are;

(a) Volume of the ice cream is about 6.3 cubic inches

(b) Radius of needed for the cone to contain 14.5 cubic inches per serving is about 1.422 inches

The volume of a solid is the space the solid occupies, which is the amount of cube units that fills the solid.

Rotation of a quarter circle to form an hemisphere, by integration is presented as follows;

[tex]\int\limits^1_0 \pi \times ({\sqrt{1-x^2} })^2 \, dx = \frac{2}{3} \cdot \pi[/tex]

The volume of the cone carrying the hemisphere = (1/3)×π×1²×4 = (4/3)·π

The volume of the ice cream = The volume of the cone + The volume of the hemisphere

Therefore;

Volume of the ice cream = (2/3)·π + (4/3)·π = (6/3)·π = 2·π  ≈ 6.3

(b) Volume of ice cream contained in the new ice cream cone, V = 14.5 cubic inches

The formula for the volume of the ice cream, V = (2/3)·π·r³ + (4/3)·π·r²

Therefore;

V = (2/3)·π·r³ + (4/3)·π·r² (substitution property)

V = (2/3)·π·r³ + (4/3)·π·r²

14.5 = (2/3)·π·r³ + (4/3)·π·r²

(2/3)·π·r³ + (4/3)·π·r² - 14.5 = 0

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Operation sign between two of the digits is 96 ÷ 2 × 5 + 8 × 0 - 7 = 8,818

This question uses the Order of Operations (PEMDAS) theory.

The order of operations states that we should work through equations in the following order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

In this question, the first operation was division (96 ÷ 2), followed by multiplication (48 × 5), then addition (240 + 8), then multiplication (248 × 0), and finally subtraction (0 - 7).

Step 1: 96 ÷ 2 = 48

Step 2: 48 × 5 = 240

Step 3: 240 + 8 = 248

Step 4: 248 × 0 = 0

Step 5: 0 - 7 = -7

Step 6: -7 = 8,818

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Answer:

The area of the first lawn is 64 = 24 square meters.

The area of the second lawn is 6 times bigger, so it is 246 = 144 square meters.

As the second lawn has the same width as the first one, 4 meters, we can calculate the length of the second lawn by dividing the area of the second lawn by its width.

So, the length of the second lawn is 144/4 = 36 meters.

1. Mean time to complete a specific task for 30 workers from this company refers to A: sample.

2. All employees from this company are known as F: population

3. A employee from this company is called an C: individual

4. Mean time to complete a specific task for all workers from this company is said to be as B: parameter.

5. 30 employees from this company make E: statistic

6. Time to complete a specific task is called a D: variable

"Sample" refers to a subset of a larger population that is selected for study. In this case, the "sample" is the 30 workers from the company whose times to complete the task have been recorded.

"Population" refers to the entire set of units or items under study. In this case, the "population" is all workers from the company.

"Individual" refers to a single unit or item in a set. In this case, an "individual" is a single worker from the company.

"Parameter" refers to a characteristic or value that describes a population. In this case, the "parameter" is the mean time it will take all workers from the company to complete the task.

"Statistic" refers to a value that describes a sample. In this case, the "mean time to complete a certain task for 30 workers from this company" is a statistic.

"Variable" refers to a value that can change within a set. In this case, "time to complete a certain task" is the variable of interest.

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Answer:

C

Step-by-step explanation:

How do we get from 4 to 20? Multiply 4 * 5 = 20.

How do we get from 20 to 100? Multiply 20 * 100.

Thus the answer is C where you multiply 5 by the previous function output.

I saw this pattern from experience, however you could also solve another way:

Simply plug in to the given functions in each answer choice.

For example, A:

f(1) = 4

f(n) = 16 * f(n - 1), for n >= 2

Now test values of n and check if they match the table.

f(1) = 4. This matches the table

f(2) = 16 * f(2 - 1) = 16 * f(1) = 16 * 4 = 64. This does not match the table.

You continue this process with the rest of the answer choices until you find a function, f(n), that gives the correct output of the table.

Answer:

(i) To calculate the present value of 6 months of rent for the first apartment, we can use the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value (6 months of rent, or $900 x 6 = $5400), r is the interest rate (8% converted to a monthly rate, or 0.08/12 = 0.0067), and n is the number of periods (6 months). So, PV = $5400 / (1 + 0.0067)^6 = $4911.46

(ii) To find the range of rent for the new apartment such that Lee would switch, we need to find the monthly rent that would result in a present value equal to or greater than $4911.46. Using the same formula, we can solve for the monthly rent (R) by setting PV equal to $4911.46 and n equal to 6. So, $4911.46 = R*(1+0.0067)^6. Solving for R, we get that the monthly rent must be between $732.32 and $766.58 in order to be more favorable than the first apartment.

Answer:

12.96

Step-by-step explanation:

13 members are missing today.

You can calculate this by subtracting the percentage of members present (81%) from 100% and then multiplying that number by the total number of team members (16).

100-81 = 19

19/100*16 = 3.04

16-3.04 = 12.96 = 13 (rounded)

Answer:

3 members MISSING

Step-by-step explanation:

0.81 x 16 = ~13

16 - 13 = 3 missing members

The measure of the angle MNO is 79 degrees

The midpoint of KM and O is also the midpoint of LM as expressed in the information given.

We have the parameters;

Note that the midpoint of the triangle is expressed as;

m/MKL = m/MNO

Now, substitute the values, we get;

61 + 9x = 2x + 75

collect like terms

9x - 2x = 75 - 61

add or subtract the like terms

7x = 14

Now, divide both sides by the coefficient of x, we get;

7x/7 = 14/7

Divide the values

x = 2

Substitute the value into the expression

m/MNO = 2x + 75

m/MNO = 2(2) + 75

expand the bracket

m/MNO = 79

Hence, the value is 79

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Given the problem:

Explain what are the figure below functions or not

The left graph is not a function, the right table is a function. To see if a graph is a function, use the vertical line test. Simply draw vertical lines down the graph, or you don't have to if you can imagine it. None of the vertical lines can pass through any points twice. So in this case, look at (6, 4) and (6, 6). Draw a vertical line down at x=6. It fails the vertical line test because the vertical line passes through the two points.

Next, the table on the right. It is a function. To determine whether a table is a function or not, look at the x values. No x value can duplicate. In this case, all x values are different.

Hope this helped.

There are (e) 125 positive integers that satisfy the n condition

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

(130n)^50 > n^100 > 2^200

[tex]\sqrt[50]{}[/tex][(130n)^50] > [tex]\sqrt[50]{}[/tex](n^100) > [tex]\sqrt[50]{}[/tex](2^200)

130n > n^2 > 2^4

130n > n^2 > 16

Solving each part, we get:

n^2 > 16

n > √16

n > 4

130n > n^2

130 > n^2/n

130 > n

130 > n > 4

Therefore the answer is the number of positive integers over 4 and 130 which is 129 - 5 + 1 = 125

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Correctly written question:

How many positive integers n satisfy the following condition (130n)⁵⁰ > n¹⁰⁰ > 2²⁰⁰ ? (a)0 (b)7 (c)12 (d)65 (e)125

The fraction for the value of tan Z is 39/80

Trigonometric Identities are simply described as equalities that involves several trigonometry functions and also one that holds true for all the values of variables given in the equation.

The types of trigonometric functions as;

From the information given, we have that;

Hypotenuse = 89

Opposite side = 39

Adjacent = 80

tan Z = opposite/adjacent

substitute the values

tan Z = 39/80

Hence, the equation is 39/80

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Answer:

Greg borrowed $20,000.

Step-by-step explanation:

To calculate the principal (the amount borrowed), we can use the formula for simple interest:

I = Prt

where I is the interest, P is the principal, r is the annual interest rate, and t is the time in years.

Given that:

I = 1400

r = 7% (expressed as 0.07)

t = 4

P = I / (r * t) = 1400 / (0.07 * 4) = $20,000

Therefore, Greg borrowed $20,000.

The two column proof that shows congruency of ΔACD ≅ ΔBDC is as detailed below.

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

We want to prove that ΔACD ≅ ΔBDC

Statement 1: AD ⊥ DC, BC ⊥ DC, ∠DAC ≅ ∠CBD, AD ≅ BC, BD ≅ AC

Reason: Given

Statement 2: BC ≅ BC

Reason 2: Reflexive Property of Congruence

Statement 3: ∠DAC ≅ ∠DBC

Reason 3: Corresponding Angles

Statement 4: ∠ACD ≅ ∠BDC

Reason 4: Corresponding Angles

Statement 5: ΔACD ≅ ΔBDC

Reason 5: CPCTC( Corresponding Parts of Congruent Triangles are Congruent.)

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The slope of the inequality y > x - 3 is 1

The slope of a line is the ratio of the amount that y increases as x increases some amount

To change the inequality y > x - 3 into slope,

substract x from both sides of the inequality

y- x > x - 3-x

= y-x>-3

= y<-3+x

From the inequality y<-3+x the co-efficient of x is 1

Hence, The slope of the inequality is 1

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Answer:

~$76.99

Step-by-step explanation:

Right now, ~¥129.89 is equivalent to $1.  Your dinner costs ¥10,000. To solve, divide the total cost of your dinner with the equivalent yen price compared to the dollar:

(¥10,000)/(¥129.89) = ~76.99 (rounded to the nearest cent).

~$76.99 would be your answer.

~

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We know that the sum of angles of a triangle are 180°

If you don't know how to find the angles of a triangle

We use the formula,

[tex](n-2)X180[/tex]

Where n replicates the sides of a polygon

Applying the sides into the formula we get

[tex](3-2)X180\\1X180\\180[/tex]

Now in order to find x we sum up all the angles into a equation

90°+ 65°+ x - 10° = 180°

145 + x = 180

We then transpose 145 to the Right Hand Side (RHS)

x = 180 - 145

x = 35°

Hence , the value of x is 35°