A community is building a square park with sides that measure 110 meters. To separate the picnic area from the play area, the park is split by a diagonal line from the opposite corners Determine the approximate length of the diagonal line that splits the square.

Answer:

x = 0     y = 2

Step-by-step explanation:

4x + 2 = -2x + 2

6x + 2 = 2

6x = 0

x = 0

y = 4(0) + 2

y = 2

The discount amount would be $1470.00

the new cost of the car would be $19530.00

For given question,

A car dealer gave a 7% discount to the first 50 people through the door.

the car you are interested in cost $21,000.00

We need to find the discount amount and the new price of the car.

A car dealer gave a 7% discount.

this means, to find the discount amount, we need to find the 7 percent of $21,000.00

⇒ discount amount = 7 percent of $21,000.00

⇒ discount amount = (7 / 100) × 21,000.00

⇒ discount amount = $1470.00

So, the new price of the car would be,

the new price of the car = original price - discount amount

⇒ the new price of the car = $21,000.00 - $1470.00

⇒ the new price of the car = $19530.00

Therefore, the discount amount would be $1470.00

the new cost of the car would be $19530.00

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Answer:

120cm

Step-by-step explanation:

168/7=24

24x5=120cm

Answer:

2x - 0.4x ;

8x/5 ;

Yes

Step-by-step explanation:

Let number of miles = x

Arlene:

Double number of miles = 2 * x = 2x

Subtract 20% of the result :

2x - 20% of 2x ;

2x - 0.4x

Raul:

Divides Number of miles by 5 ; x / 5

Multiplies result by 8 ;

8 * (x/5) = 8x /5

To know if expressions are equivalent :

Let x = 10 miles

Using Arlene's expression:

2x - 0.4x

x = 10

2(10) - 0.4(10) = 16

Using Raul's expression :

8x / 5

(8*10) / 5

80/5

= 16

Since they give the same result, we can conclude that the expression are equivalent

We have to solve this quotient with factorials:

Answer: the simplified expression is 2/7.

Complete question

Asif wants to open a lemonade stand during a town fair. He buys a pitcher and lemonade concentrate from a store for this purpose. At the lemonade stand, the cost for each cup of lemonade will be the same. If Asif sells 32 cups of lemonade, he will have a profit of $0. If he sells 45 cups of lemonade, he will have a profit of $16.25. Determine the rate of change for a function that represents Asif's profit, y, in dollars, from selling x cups of lemonade.

Answer:

Step-by-step explanation:

The rate of Change for the function that determines profit :

Slope value, m ;

Slope, m = Rise / Run = (y2-y1) / (x2 - x1)

y2 = 16.25 ; y1= 0 ; x2 = 45 ; x1 = 32

m = (16.25 - 0) / (45 - 32)

m = 16.25 / 13

m = 1.25

Hence, the rate of change in in profit for selling x k cuos of lemonade = $1.25

Given the table:

X -3 , 0 , 3 , 6

Y 3, 7, 11, 15

We can write the ordered pairs of the function:

(-3, 3), (0, 7), (3, 11), (6, 15)

Any pair of ordered pairs can be used to calculate the slope, assuming they all belong to the line.

Let's pick the points (-3, 3) and (0, 7). The formula to calculate the slope is:

Substituting:

It can be verified that the slope is 4/3 regardless of the points selected to calculate it.

Answer: 4/3

Yes, the function f(x) = x / (x + 2) satisfies the hypotheses of the mean value theorem on the given interval [1, 4]. This is because f is continuous on [1, 4] and differentiable on (1, 4).

Given f(x) = x/ x + 2

We are asked to check whether the function satisfies the hypotheses of the mean value theorem on the given interval [1, 4].

Mean Value Theorem: If f(x) is continuous on the closed interval [a, b] and is differentiable on the open interval (a, b), then there exists a number c in (a, b) such that: f(b) − f(a) / b − a = f'(c)

For the given function, we have the interval [1, 4]. The function is continuous on [1,4].

Also, the function is differentiable on (1,4).

Therefore, the given function satisfies the hypotheses of the mean value theorem on the given interval [1, 4]. Hence, the correct option is Yes, f is continuous on [1,4] and differentiable on (1,4).

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Answer:

21.72

Step-by-step explanation:

0.07 x 20.30

Answer

Calculator.net

i hope you use this it will help a lot

Answer:

7.a) 5

7.b) 1/2

8. 1

Step-by-step explanation:

7.

a)

Read the points on the graph (0, 0) and (1, 5).

slope = (5 - 0)/(1 - 0) = 5/1 = 5

b)

read the points on the graph (0, 0) and (4, 2).

slope = (2 - 0)/(4 - 0) = 2/4 = 1/2

8.

Points (1, 4) and (5, 8)

slope = (8 - 4)/(5 - 1) = 4/4 = 1

The angle measures for this problem are given as follows:

The quadrilateral A'B'C'D' is similar to quadrilateral ABCD, meaning that they have the same angle measures, and thus we have to obtain the angle measures of quadrilateral ABCD.

To obtain the angle measures of the quadrilateral ABCD, we must first obtain the angle measures of the triangle.

The sum of the measures of the internal angles of a triangle is of 180º, and the measures are given as follows:

Angle D is vertical with the angle of 77º, hence:

m < D' = 77º.

Angle B is supplementary with it's external angles, hence:

m < B' = 180 - 80 = 100º.

Angle C is congruent with the angle of 80º.

m < C' = 80º.

The sum of the measures of the internal angles of a quadrilateral is of 360º, hence:

m < A' + 100 + 77 + 80 = 360

m < A' = 103º.

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Answer:

1/41664

Step-by-step explanation:

porches have 41664 choices, one of them is red and yellow, and blue

Answer: 2 5/6 I think.

Wait no. I just did the math and it would be 2 1/2

\( {\qquad\qquad\huge\underline{{\sf Answer}}} \)

Let's solve ~

Area of shaded region is equal to :

Area of rectangle - Area of two triangles ~

1. Area of rectangle :

\(\qquad \sf  \dashrightarrow \: length \times width\)

\(\qquad \sf  \dashrightarrow \: 20 \times 15\)

\(\qquad \sf  \dashrightarrow \: 300 \: \: cm {}^{2} \)

2. Area of first triangle :

\(\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)\)

\(\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (20 - 18) \times (15)\)

\(\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (2) \times (15)\)

\(\qquad \sf  \dashrightarrow \: 15 \: \: cm {}^{2} \)

3. Area of second triangle :

\(\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)\)

\(\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (6) \times(20)\)

\(\qquad \sf  \dashrightarrow \: 3 \times 20\)

\(\qquad \sf  \dashrightarrow \: 60 \: \: cm {}^{2} \)

Area of shaded region is :

\(\qquad \sf  \dashrightarrow \: 300 - (15 + 60)\)

\(\qquad \sf  \dashrightarrow \: 300 - 75\)

\(\qquad \sf  \dashrightarrow \: 225 \: \: cm {}^{2} \)

Step-by-step explanation:

Given,

length of rectangle(l)= 8cm

area of rectangle(A) = 48cm2

breadth of rectangle(b) = ?

Perimeter of rectangle (P)=?

We know ,

Area of rectangle(A) = l×b

or, 48cm2 = 8cm×b

or, 48cm2 = 8bcm

or, 48cm2/8cm = b

or, 6cm = b

or, b = 6cm

therefore, b = 6cm

Perimeter of rectangle (P) = 2(l+b)

= 2(8cm+6cm)

= 2×14cm

= 28cm

therefore, Perimeter of rectangle(P) = 28cm

Now,

According to the question,

Perimeter of rectangle(P) = Perimeter of square(P)

So,

Perimeter of square(P) = 28cm

length of square(l) = ?

Area of square (A) = ?

We know,

Perimeter of square (P) = 4l

or, 28cm = 4l

or, 28cm/4 = l

or, 7cm = l

or, l = 7cm

therefore, l = 7cm

Now,

Area of square (A) = l^2

= (7cm)^2

= 7cm×7cm

= 49cm^2

therefore, area of square (A)= 49cm^2

The area of the square based on the information is 49cm².

Since the rectangle has length 8 cm and area 48 cm², the width will be:

= 48/8 = 6cm.

Therefore, the perimeter will be:

= 2(l + w)

= 2(8 + 6)

= 28cm

Therefore, the length of the square will be:

= 28/4 = 7

Area of the square will be:

= 7cm × 7cm

= 49cm²

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So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The probability of getting at least 2 fours is the sum of the probabilities of getting exactly 2, 3, 4, or 5 fours:

P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5)

Using the binomial formula, we can calculate each of these probabilities:

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

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n distinct items.

P(X=2) = (5 choose 2) (1/6)² (5/6)³ = 0.1608

P(X=3) = (5 choose 3) (1/6)³ (5/6)² = 0.0322

P(X=4) = (5 choose 4) (1/6)⁴ (5/6)¹ = 0.0013

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

Therefore,

P(X ≥ 2) = 0.1608 + 0.0322 + 0.0013 + 0.00003 = 0.1943

So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

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The rate of change for a health club is, 24.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

A health club charges a $20 one-time sign-up fee and a monthly membership fee of $54 per month.

Hence, The equation to represents that the health club charges,

⇒ y = 24x + 54

Since, The general form of the slope - intercept equation is :

⇒ y = mx + c

Where, m = slope = rate of change in y per change in x

Therefore, By comparing the expressions, the slope of the cost function given is 24.

Hence, The rate of change = 24

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Answer:

(b^2+1)/b

Step-by-step explanation:

The reciprocal of b is written as 1/b

The sum of b and 1/b is expressed as;

b + 1/b

Sind the LCM

= b(b)+1/b

= (b^2+1)/b

Hence the sum of b and its reciprocal is  (b^2+1)/b

Answer:

Step-by-step explanation:

A fifth-grade polynomial requires a minimum of 6 different points to create an adequate graph. Let is \(X\) the dominion of the polynomial, such that \(0\), \(1\), \(2\), \(3\), \(4\), \(5\) \(\in X\). The values of the function for each value are calculated herein:

x = 0

\(f(0) = 6\cdot 0^{5}+8\cdot 0^{4}-7\cdot 0^{3}-5\cdot 0^{2}+10\)

\(f(0) = 10\)

x = 1

\(f(1) = 6\cdot 1^{5}+8\cdot 1^{4}-7\cdot 1^{3}-5\cdot 1^{2}+10\)

\(f(1) = 12\)

x = 2

\(f(2) = 6\cdot 2^{5}+8\cdot 2^{4}-7\cdot 2^{3}-5\cdot 2^{2}+10\)

\(f(2) = 254\)

x = 3

\(f(3) = 6\cdot 3^{5}+8\cdot 3^{4}-7\cdot 3^{3}-5\cdot 3^{2}+10\)

\(f(3) = 1882\)

x = 4

\(f(4) = 6\cdot 4^{5}+8\cdot 4^{4}-7\cdot 4^{3}-5\cdot 4^{2}+10\)

\(f(4) = 7674\)

x = 5

\(f(5) = 6\cdot 5^{5}+8\cdot 5^{4}-7\cdot 5^{3}-5\cdot 5^{2}+10\)

\(f(5) = 22760\)

The table is now presented:

 x                 y

 0                10

 1                 12

 2               254

 3               1882

 4               7674

 5              22760

Finally, the graphic is now constructed by using an online tool (i.e. Desmos). The image is included below as attachment.

We need to determine the score a student must achieve to place in the top 5% of all students taking the SAT Verbal test with an N(\(515, 109\)) distribution, which came out to be \(695\) marks.

Identify the mean (μ) and standard deviation (σ) of the distribution: In this case, µ \(= 515\) and σ\(= 109\).

Determine the percentile rank: To place in the top \(5%\)% of students, we need to find the score corresponding to the \(95th\) percentile, as this represents the point where \(95\)% of students have a lower score.

Use a standard normal (Z) table or calculator to find the Z-score corresponding to the \(95th\) percentile: A Z-score represents the number of standard deviations a data point is from the mean.

For the \(95th\) percentile, the Z-score is approximate \(1.645\).

Apply the Z-score formula to find the required SAT score: \(X =\) µ \(+ Z*\) σ. In this case, \(X = 515 + (1.645 *109)\).Calculate the result: \(X = 515 + (1.645 *109)\)

\(=515 + 179.305 = 694.305\).

Round up to the nearest whole number: Since a student's SAT score must be a whole number, round up to \(695\). A student must score \(695\) or higher on the SAT Verbal test to place in the top \(5\)% of all students taking the test, given the N(\(515, 109\)) distribution.

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Answer:

The slope-intercept form of the given line is: y = -1/3x+1

Step-by-step explanation:

Answer:

523.8 miles

Step-by-step explanation:

The drawing attached represents the question. We create a triangle with the distances from each pair of cities, and we call the distance from B to C by 'd'.

First, we need to find the angle BAC:

55° + BAC + 7° = 90°

BAC = 28°

Then, we can use the law of cosines to find the value of d:

d^2 = 470^2 + 890^2 - 2*470*890*cos(BAC)

d^2 = 470^2 + 890^2 - 2*470*890*0.8829

d^2 = 274365.86

d = 523.8 miles

a) Null Hypothesis: H₀: P>0.22

Alternative hypothesis: H₁:P<0.22

b) Test statistic  Z = 2.5

The sample size is n = 1100.

Given the information, political research selected 1100 voters from the town and discovered that 25% of the citizens supported the building.

Given sample percentage "p" = 25% = 0.25, this follows.

A campaign strategist decided to check the assertion that more than 22% of people support building based on available data.

Assuming Population Proportion 'P' = 22% = 0.22

Q = 1 - p = 1 - 0.22=0.78

Given the available information, a political strategist wishes to test the assertion that more citizens prefer building than 22%, thus we assume the null hypothesis is true.

Null Hypothesis: H₀: P > 0.22

Alternative hypothesis: H₁: P < 0.22

The test of statistic

Z = (p - P) ÷ √(PQ ÷ n)

Z = (0.25 - 0.22) ÷ √(0.22 × 0.78 ÷ 1100)

Z = 2.5

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x = original price or 100%

so if we discount "x" by 12%, that means the new price is 100% - 12% = 88%, let's see how much is 88% of "x"

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{88\% of x}}{\left( \cfrac{88}{100} \right)x}\implies 0.88x\)

now if we grab that new price, or the new 100%, and discount it further by 5%, what's leftover is simply 95%, because we'll be taking off 5% off of it and thus left with 100% - 5% = 95%.

so what's 95% of 0.88x?

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{95\% of 0.88x}}{\left( \cfrac{95}{100} \right)0.88x}\implies 0.836x\)

so the new discounted price is just 0.836x or 83.6% of our original "x".

from 100% originally to 83.6%, the difference is 16.4%, and that's the total discount.

Answer:

Step-by-step explanation:

Let's call the three numbers we're trying to find "a", "b", and "c". We know that their sum is 3, so we can write:

a + b + c = 3

We also know that their difference is 21. However, we don't know if that difference is positive or negative, so we'll write two equations:

a - b - c = 21

b - a - c = 21

Now we have a system of three equations with three unknowns. We can solve for one variable in terms of the other two, and then substitute that expression into the other two equations to get a system of two equations with two unknowns. From there, we can solve for one variable and use that to find the other two.

Here's one way to solve the system:

a + b + c = 3

a - b - c = 21

b - a - c = 21

Adding the second and third equations, we get:

a - c = 42

Substituting this into the first equation, we get:

b + 42 = 3

b = -39

Substituting b and a - c into the second equation, we get:

a - (-39) - (a - c) = 21

a + 39 - a + c = 21

c = -18

Now we can find a by adding b and c to 3:

a = 3 - b - c

a = 3 - (-39) - (-18)

a = 24

So the three numbers are 24, -39, and -18, and their sum is 3 and their difference is 21.

The missing angle of the given diagram is: x = 70°

We are given that:

∠NMR = 150°

∠QNM = 40°

PQ ║ MR

If we imagine that the line RM is extended to meet QM at a point O.

Now, since PQ is parallel to MR, we can also say that PQ is parallel to OR.

Thus, by virtue of alternate angles theorem, we can say that:

∠PQN = ∠QOR = x

Sum of angles in a triangle sums up to 180 degrees. Thus:

∠OMN + ∠NMR = 180

∠QOR = ∠OMN + ∠ONM = 70

Thus:

x = 70°

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the actuarial expression for the account balance after the final deposit is made as:\(FV = $5000 \times [(1.03^{(n-10)}+1)(1.02)^{(204)}-1]/(0.02) + $5000 \times [(1.03^{10}+1)(1.02)^{(104)}-1]/(0.02)\)The account balance after the final deposit is made is \($62,297.36.\)

The account balance after the final deposit is made, the formula for the future value of an annuity due with a growth rate.

Actuarial expression for the account balance after the final deposit is made:

A be the annual deposit amount, n be the number of deposits, i be the nominal annual interest rate, m be the number of compounding periods per year, and g be the annual growth rate of the deposits.

The formula for the future value of an annuity due with a growth rate is:

\(FV = A \times [(1+g)\times (1+i/m)^{((n-1) \times m)+1}] / (i/m)\)

Louis' situation, we have:

\(A = $5000\) for the first 10 years, and then \(A = $5000 \times 1.03^{(n-10)}\) for the remaining 20 years.

n = 30 years

i = 8% nominal annual interest rate, compounded quarterly, so i = 2% per quarter

m = 4 quarters per year

g = 3% annual growth rate for each deposit after the 10th year

The account balance after the final deposit is made:

The above actuarial expression and substituting n=30, we get:

\(FV = $5000 \times [(1.03^{20}+1)(1.02)^{80}-1]/(0.02) + $5000 \times [(1.03^{10}+1)(1.02)^{40}-1]/(0.02)\)

Simplifying this expression gives:

\(FV = $5000 \times (1.03^{20} \times 1.02^{80} + 1.03^{10} \times 1.02^{40})\)

Using a calculator, we get:

\(FV = $5000 \times (10.4619 + 1.7958)\)

\(FV = $62,297.36\)

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Light is about 874052.5 times faster than sound

From the question, we are to determine the magnitude by which light is faster than sound

From the given information,

The speed of light is about 2.998 x 10⁸ meters per second.

and

The speed of sound is about 343 meters per second.

To determine how many rimes faster the speed of light is than the speed of sound, we will divide the speed of light by the speed of sound

That,

The magnitude by which light is faster than sound = (2.998 x 10⁸) / 343

The magnitude by which light is faster than sound = 874052.5

Hence, light is about 874052.5 times faster than sound

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