Every 8th customer gets a $50 gift certificate.

$50

$10.

Every 6th customer gets a \$10 gift certificate.

To celebrate its grand opening, a store is giving customers gift certificates. Which customer is the first to get two gift certificates?

The value of cot(x/2) is -3.73

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Given that, Csc(x) = -2

Since,

cscx = 1/sinx

Therefore,

1/sinx = -2

sinx = -1/2

sinx = -sin30°

x = -30°

Therefore,

cot (x/2) = cot(-15)

= -1/tan15

= -3.73

Hence, the value of cot(x/2) is -3.73

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a) For two distinct real roots: x > 0 or x > m

b) For two distinct real roots: x > 0 or x > 2m

c) For two distinct real roots: x > 0 or x > 4

This is based on the quadratic equation.

Only non-negative integer powers of x are present in the quadratic equation, making it a polynomial equation. In actuality, the Latin word quadratus, which means square, is the root of the term quadratic. The quadratic equation has the generic form ax² + bx + c = 0. where x is an unknowable variable and a, b, and c are mathematical coefficients.

a) Quadratic equation: x² - 4x + m = 0

The discriminant: Δ = b² - 4ac

Δ = (2x)² - 4.x.(m)

Δ = 4x² - 4mx

Δ = 4x (x - m)

For two distinct real roots: Δ > 0

4x (x - m) > 0

x > 0 or x > m

For two real roots: Δ ≥ 0

4x (x - m) ≥ 0

x ≥ 0 or x ≥ m

For a repeated root: Δ = 0

4x (x - m) = 0

x = 0 or x = m

(b) Quadratic equation: mx² + 3x + 2 = 0

The discriminant: Δ = b² - 4ac

Δ = (3x)² - 4.mx.(2)

Δ = 4x² - 8mx

Δ = 4x (x - 2m)

For two distinct real roots: Δ > 0

4x (x - 2m) > 0

x > 0 or x > 2m

For two real roots: Δ ≥ 0

4x (x - 2m) ≥ 0

x ≥ 0 or x ≥ 2m

For a repeated root: Δ = 0

4x (x - 2m) = 0

x = 0 or x = 2m

(c) Quadratic equation: x² - mx + 1 = 0

The discriminant: Δ = b² - 4ac

Δ = (x)² - 4.x.(1)

Δ = x² - 4x

Δ = x (x - 4)

For two distinct real roots: Δ > 0

x (x - 4) > 0

x > 0 or x > 4

For two real roots: Δ ≥ 0

x (x - 4) ≥ 0

x ≥ 0 or x ≥ 4

For a repeated root: Δ = 0

x (x - 4) = 0

x = 0 or x = 4

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A member of the senate will serve for (h+4) years.

An expression, in mathematics, is a finite set of combinations and/ or numbers and variables that accurately represents the the context in question. When two or more expressions are connected using the equality sign then an equation is formed.

Here, we are given that in the US government a member of the senate serves for 4 years longer than a member of the House of Representatives.

Also the House of Representatives serves for- h years

Thus, the number of years a member of the Senate will serve will be 4 more than the number h

= h + 4

Thus, a member of the senate serves for (h+4) years.

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The linear function for the given graph is y = x + 20.

What is a linear function?

A straight line on the coordinate plane is represented by a linear function. It has one independent variable and one dependent variable. For slope (m) and y-intercept (b) form, the equation is given by:

y = mx + b

From the graph,

The coordinates of the given graph are (0,20) and (20,40)

Then, slope (m) = (40-20)/(20-0) = 20/20 = 1

and y-intercept (b) = 20

So, the equation will be y = 1x + 20

Hence, the linear function for the given graph is y = x + 20.

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The x-intercept of the function is (-1/3, 0) and (5, 0)

Given is a graph of a parabola having equation y = -3x²+14x+5, we need to find the x-intercept of the graph,

So to find the x-intercept put y = 0,

Therefore,

-3x²+14x+5 = 0

-3x²+15x-x+5 = 0

-3x(x-5)-1(x-5) = 0

(-3x-1)(x-5) = 0

Therefore,

x = -1/3 and x = 5

Hence the x-intercept of the function is (-1/3, 0) and (5, 0)

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Answer:

\(y=\frac{1}{6}x+6\)

Step-by-step explanation:

Let \((x_1,y_1)\rightarrow(-6,5)\) and \((x_2,y_2)\rightarrow(6,7)\)

Determine slope

\(m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{7-5}{6-(-6)}\\ \\m=\frac{2}{6+6}\\ \\m=\frac{2}{12}\\ \\m=\frac{1}{6}\)

Use either ordered pair to find the y-intercept

\(y=mx+b\\\\7=\frac{1}{6}(6)+b\\\\7=1+b\\\\6=b\)

Final equation

\(y=\frac{1}{6}x+6\)

The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (d) 0.04

The margin of error is a statistic that describes how much random sampling error there is in survey results.

Given in question,

n = 400

p = 317/400

  = 0.7925

Confidence Level = 95%

                          = 0.95

Formula for margin error, E = \(z\sqrt{\frac{p(1-p)}{n} }\)

Confidence level corresponding to 95 % confidence interval, z = 1.96

Therefore,

Margin Error, E = \(1.96\sqrt{\frac{0.7925(1-0.7625)}{400} }\)

                         = 0.0397

                         ≈ 0.04

Hence, The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is 0.0397 which is closest to 0.04.

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Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

Answer:

cheetah, 3 hours antelope, 5 lion, 6 elephant, 10

Step-by-step explanation:

The time taken by each animal to reach another jungle are:

Cheetah = 3 hours

Antelope = 5 hours

Lion = 6 hours

Elephant = 10 hours

Speed is a scalar quantity that refers to how fast an object is moving.

Given are the speeds of different animals,

Cheetah = 50 mph

Antelope = 30 mph

Lion = 25 mph

Elephant = 15 mph

Speed = distance/time.

Time = distance/speed

Distance = 150 miles

Time taken by each :

Cheetah = 150/50 = 3 hours

Antelope = 150/30 = 5 hours

Lion = 150/25 = 6 hours

Elephant = 150/15 = 10 hours

Hence, The time taken by each animal to reach another jungle are:

Cheetah = 3 hours

Antelope = 5 hours

Lion = 6 hours

Elephant = 10 hours

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Step-by-step explanation:

I just did in the other posting. how often did you post it ?

this is a trick question. the triangle at the top is not an isoceles triangle.

we use Pythagoras for an the steps.

so, the left part of the baseline (split by the height) is calculated by

12² = 10² + part²

144 = 100 + part²

part = sqrt(44) = 6.633249581... ft

the other part is then

20 - 6.633249581... = 13.36675042... ft

and the second leg of the large triangle is

leg² = 10² + 13.36675042...² = 278.6700168...

leg = 16.69341238... ft

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft

please see the answer to the other posting for more details.

The expression without absolute value bars is 3.84.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

|√10 - 7 |

= | 3.16 - 7 |

= | -3.84 |

= 3.84

Thus,

The value of the expression is 3.84.

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Inequality shown is -3 ≤ x < 2.

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given,

Graph of inequality

Line drawn on the number line between circle on -3 and circle on 2.

Here, -3 < 2

If x is the variable, it is between -3 and 2

then, -3 < x < 2

The circle on -3 is filled which means value of x can be equal to -3

then inequality becomes,

-3 ≤ x < 2

Hence, -3 ≤ x < 2 is the inequality shown on the number line.

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The function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The coordinate points from the graph are (10, 550) and (30, 200).

Here, slope = (200-550)(30-10)

= -350/20

= -35/2

= -17.5

Substitute m= -17.5 and (x, y)=(10, 550) in y=mx+c, we get

550=-17.5(10)+c

c=550+175

c=725

So, the equation is y= -17.5x+725

Thus, f(n)= -17.5n+725

a) The fine at every speed should go up by $10.

So, the coordinates are (10, 560) and (30, 210)

New slope (m)= (210-560)(30-10)

= -350/20

= -35/2

= -17.5

Substitute m= -17.5 and (x, y)=(10, 560) in y=mx+c, we get

560=-17.5(10)+c

c=550+175

c=735

So, the equation is y= -17.5x+735

Thus, f(n)= -17.5n+735

b) The fine at every speed should be doubled in construction zones.

So, the coordinates are (20, 550) and (60, 200)

New slope (m)= (200-550)(60-20)

= -350/40

= -8.75

Substitute m= -8.75 and (x, y)=(20, 550) in y=mx+c, we get

550=-8.75(10)+c

c=550+87.5

c=637.5

So, the equation is y= -8.75x+637.5

Thus, f(n)= -8.75n+637.5

Therefore, the function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.

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Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

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Answer:

Therefore, the solution to the equation -x + 3y = 11 is x = -34/11 and y = 29/11.

Step-by-step explanation:

The given equation is:

-x + 3y = 11

To solve this equation by elimination, we need to add or subtract one or both equations to eliminate one of the variables. In this case, we can eliminate the variable x by adding the equation with another equation that has x with the same coefficient, but opposite sign.

Let's suppose we have another equation with x, for example:

2x + 5y = 7

We can eliminate x by multiplying the first equation by 2 and the second equation by 1, so that the coefficients of x are opposite:

-2x + 6y = 22 (multiply the first equation by -2)

2x + 5y = 7 (the second equation)

Now we can add the two equations to eliminate x:

-2x + 2x + 6y + 5y = 22 + 7

Simplifying the equation, we get:

11y = 29

Dividing both sides by 11, we get:

y = 29/11

Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

-x + 3y = 11

Substituting y = 29/11, we get:

-x + 3(29/11) = 11

Simplifying the equation, we get:

-x + 87/11 = 11

Subtracting 87/11 from both sides, we get:

-x = 11 - 87/11

Multiplying both sides by -1, we get:

x = 87/11 - 11

Simplifying the equation, we get:

x = (87 - 121)/11

x = -34/11

Answer:

The numbers are 19 and 5

Step-by-step explanation:

Given

Let the numbers be \(x\ and\ y.\)

So:

\(x = 9 + 2y\) --- First statement

\(x*y = 95\) --- second statement

Required

Find x and y

Substitute \(x = 9 + 2y\) in \(x*y = 95\)

\((9 + 2y) * y = 95\)

\(9y + 2y^2 = 95\)

Rewrite as:

\(2y^2 + 9y - 95 = 0\)

Expand

\(2y^2 -10y +19y- 95 = 0\)

Factorize

\(2y(y -5) +19(y- 5) = 0\)

\((2y +19)(y- 5) = 0\)

Solve for y

\(2y + 19 =0\) or \(y - 5 = 0\)

\(2y = -19\) or \(y = 5\)

\(y = -\frac{19}{2}\) or \(y=5\)

Since the numbers are positive, we take only:

\(y=5\)

Substitute \(y=5\) in \(x = 9 + 2y\)

\(x = 9 + 2 * 5\)

\(x = 9 + 10\)

\(x = 19\)

The numbers are 19 and 5

Answer: Hello attached below is the complete question

answer :

It is convergent ,  sum = 7/12

Step-by-step explanation:

Sn = 1/3 + 1/4 - 1/n - 1/n+1

It is convergent  and the sum = 7/12

attached below is the remaining part of the solution

Answer:She receives a monthly salary of $2,500 for which she must sell $20,000 wo

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

There are 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters and 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.

The prοduct οf all pοsitive integers less than οr equal tο a given pοsitive integer and denοted by that integer and an exclamatiοn pοint. Thus, factοrial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factοrial zerο is defined as equal tο 1.

If the chοice matters (i.e., the οrder οf the chοsen οbjects matters), then there are 3 pοssible chοices fοr the first οbject and 2 pοssible chοices fοr the secοnd οbject.

Thus, there are 3 * 2 = 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters.

If the chοice dοes nοt matter (i.e., the οrder οf the chοsen οbjects dοes nοt matter), then there are 3 chοοse 2 = 3!/((3-2)!*2!) = 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.

Therefοre,  there are 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters and 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.

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The given statement is true.

Answer:

A

Step-by-step explanation:

Becuase the proability of drawing a red marble is 10/20 or 50% and drawing a green marble is 4/20 or 20% and drawing a red marble is 6/20 or 30%

We prooved the paragraph proof of Theorem 3.8 that if two lines are perpendicular to the same line, then they are parallel to each other.

In the given question we have to explain the a paragraph proof of Theorem 3.8.

Let the lines that cross line a be m and n. Let m be parallel to a. As a result, the intersection of m and a produces four 90° angles.

Let n be parallel to a. This indicates that each of the four angles created by the intersection of n and an is 90 degrees.

The same-side internal angles (between lines m and n) are also congruent because all of the angles are congruent. The lines are parallel if two internal angles on the same side are congruent.

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The right question is:

Write a paragraph proof of theorem 3-8: in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: (3 {a}^{2} - 7xy)(3 {a}^{2} + 7xy) = 9 {a}^{ 4 } - 49 {x}^{2} {y}^{2} \)

____________________________________

\( \large \tt Solution \: : \)

\(\qquad \tt \rightarrow \: (3 {a}^{2} - 7xy)(3 {a}^{2} + 7xy)\)

\(\qquad \tt \rightarrow \:(3 {a}^{2} \sdot3 {a}^{2} ) + (3a {}^{2} \sdot7xy) - (7xy \sdot3 {a}^{2} ) - (7xy \sdot7xy)\)

\(\qquad \tt \rightarrow \:9 {a}^{4} + 21a {}^{2} xy- 21 {a}^{2} xy - 49 {x}^{2} {y}^{2} \)

\(\qquad \tt \rightarrow \: 9 {a}^{ 4 } - 49 {x}^{2} {y}^{2} \)

or

Apply property :

\(\qquad \tt \rightarrow \: (p + q)(p - q) = {p}^{2} - {q}^{2} \)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Step-by-step explanation:

Answer:

(L-6)(L+2)

Step-by-step explanation:

Let L be the length of the flower garden.

Then the width will be L-4.

The area of the flower garden = L*(L-4) =L²-4L

The area of the birdbath is 3*4 = 12 ft²

The area of the remaining space for planting is

= Area of flower garden - area of birdbath

We can factor the expression as follows:

taking common frome each two terms

Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.

Answer:

4

Step-by-step explanation:

The units digit will be 4, because 7*2 = 14, (units digit is 4)

Answer:

Lines of symmetry.

Step-by-step explanation:

Hope it helps!!!!

Answer:

where is the graph?

Step-by-step explanation: