8. A school cafeteria
purchased 256
hotdogs, 332 apples,
and 154 cookies. How
many items did they
purchase in all?

The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the profit (P) in thousands for security camera with price of x, hence for a profit of at least $471, 000:

-(x - 32)² + 1000 ≥ 471

-(x² - 64x + 1024) + 1000 ≥ 471

-x² + 64x - 1024 + 1000 - 471 ≥ 0

-x² + 64x - 495 ≥ 0

x = 55 or x = 9

The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9

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the original height of the plant was 2mm. The correct option is the second one.

We know that the function:

y = 2 + 4x

Represents the height of a plant in mm, as a function of x, the hours kepts in sunlight.

The y-intercept is the value that y takes when we evaluate in x = 0.

So, the y-intercept is the height of the plant when it is exposed to zero hours of light.

In this case:

y = 2 + 4*x

Evaluating in x = 0

y = 2 + 4*0 = 2

This means that the original height of the plant was 2mm. The correct option is the second one.

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Answer: The absolute values of 7 and -7 are equal because they are both a distance of 7 units from 0 on the number line.

By simplifying the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex], we get [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and

[tex]$x= -2n\pi -\frac{\pi}{3}[/tex].

Trigonometric Identities exist as the equivalencies that apply trigonometry operations and have true for all the values of variables shown in the equation. There exist different trigonometric identities concerning the side length as nicely as the angle of a triangle.

How to simplify the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]?

Given:

[tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]

General solution for [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]

then from the general equation, we get

[tex]$\frac{\pi}{2}-x = \frac{\pi}{6}+2n\pi[/tex] and

[tex]$\frac{\pi}{2}-x = \frac{5\pi}{6}+2n\pi[/tex]

Solve [tex]$\frac{\pi}{2}-x = \frac{\pi}{6}+2n\pi[/tex] then [tex]$x= -2n\pi +\frac{\pi}{3}[/tex]

Solve [tex]$\frac{\pi}{2}-x = \frac{5\pi}{6}+2n\pi[/tex]then [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]

Therefore, [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]

Radians, [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]

Degree, [tex]$x = 60 \degrees- 360\degree n[/tex], [tex]$x = -60\degree- 360\degree n[/tex]

By simplifying the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex], we get [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and

[tex]$x= -2n\pi -\frac{\pi}{3}[/tex].

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Answer:

Probability of rolling a sum of 5 is 1/9.

There are 36 different combinations because 6(first roll)*6(second roll) = 36. The only possible combinations are {1,4},{2,3}{2,3}and{4,1}

4/36 = 1/9

Answer:

14.8 feet

Step-by-step explanation:

since this is creating a right triangle you can use the Pythagorean theorem which is a^2 + b^2 = c^2, and by plugging in the one leg length and the hypotenuse length you get 14.8324 which rounds up to 14.8

The  distance between the ground and the top of the ladder is 14.8 feet.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

Hypotenuse= 16 foot,

Base = 6 feet

Using Pythagoras theorem,

H² = B² + P²

16² = 6² + P²

256 = 36 +P²

P² = 256-36

P= 14.83 feet

Hence, the distance between the ground and the top of the ladder is 14.8 feet.

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Answer: A

Step-by-step explanation:

The expressions are equivalent by the distributive property.

Answer:

The first step in solving the equation should be to add 3 to both sides.

Step-by-step explanation:

Adding 3 to both sides will cancel out the -3 on the left hand side of the equation, leaving only the 2x term. On the right hand side, adding 3 will cancel out the -6, leaving only 0. This will give you the equation 2x = 0, which is much easier to solve.

Answer:

Hope it helps!!

Answer:

[tex]a < 0[/tex]   False

[tex]|a| > 0[/tex] True

[tex]|a|=0[/tex]  False

________________________________________________

a is on the right side of 0,

which means a is positive.

The absolute value is the distance to zero (always positive)

Which means the absolute value of a is also positive.

[tex]a < 0[/tex]   is wrong because a is positive

[tex]|a| > 0[/tex]  is correct because a is larger than 0

[tex]|a|=0[/tex]  is wrong because [tex]a[/tex] ≠ [tex]0[/tex]

________________________________________________

Hope this helps :)

The expression after factorisation is 4w⁴x² (7y⁷ + 3w⁵x⁶)

An expression is defined as a mathematical statement consisting of variables , constants and mathematical operators.

The expression given is

28w⁴x²y⁷+12w⁹x⁸

Factors of the given expression will be the common terms in both the terms

w⁴x² is common in the variable term

The HCF of 28 and 12 is 4

4w⁴x² (7y⁷ + 3w⁵x⁶)

The expression after factorisation is 4w⁴x² (7y⁷ + 3w⁵x⁶)

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The number of cases of flu on day 15 will be 1001 flus

Exponential functions are expressed as y = ab^x

Given the expression below

[tex]f(x)=10001+999e^{-0.6030x}[/tex]

In order to determine the number of cases of flu on day 15, we will substitute x = 15 into the expression to have:

[tex]f(x)=10001+999e^{-0.6030(15)}\\f(x)=10001+999e^{-9.045}\\f(15) = 10001+0.11786\\f(15) \approx 10001[/tex]

Hence the number of cases of flu on day 15 will be 1001 flus

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Answer:

Step-by-step explanation:

Evaluate the function for the value x=15.

f(x)f(15)f(15)=10001+999e−0.6030x=10001+999e−0.603(15)≈894.565217

Rounded to the nearest whole number, there will be 895 cases on day 15.

Answer:

b.) 0

Explanation:

⇒ f(g(-1))

go from right to left while solving such function questions.

⇒ f(-1 + 2)

⇒ f(1)

⇒ (1)² -2(1) + 1

⇒ 0

Step-by-step explanation:

[tex]f(x) = {x}^{2} - 2x + 1[/tex]

[tex]f(x) = {(x - 1)}^{2} [/tex]

[tex]g(x) = x + 2[/tex]

[tex] \: [/tex]

[tex] = f(g( - 1))[/tex]

[tex] = {(x - 1)}^{2} [/tex]

[tex] = {((x + 2) - 1)}^{2} [/tex]

[tex] = {(( - 1 + 2) - 1)}^{2} [/tex]

[tex] = {(1 - 1)}^{2} [/tex]

[tex] = {0}^{2} [/tex]

[tex] = 0[/tex]

The answer is B.

The perimeter of the rectangle is 1 1/7 units

The formula for calculating the perimeter of a rectangle is given as:

P = 2(l + w)

Given the following

length. = 1/7 units

width = 1/2 units

Substitute

P = 2(1/7 + 1/2)

P = 2(9/14)

P = 9/7 = 1 1/7

Hence the perimeter of the rectangle is 1 1/7 units

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Answer:

  A.  KM

Step-by-step explanation:

A circle is named by its center. Circle K has its center at point K.

A radius is a line segment that extends from the center of the circle to a point on the circle. Point K must be one end of any radius.

Segment KM is a radius.

Segments between points on the circle are chords. The other named segments in the answer choices are all chords of the circle.

If Erica earned a total of $15450 last year from both the jobs then he earns $2840 from college if she earned 1250 more than four times the amount from college from store.

Given Total amount earned=$15450,Amount earned from store is 1250 more than 4 times earned from college.

Amount from store forms an equation.

let the amount earned from college is x.

According to question:

Amount earned from store=4x+1250

Amount earned from college=x

Total amount earned=4x+1250+x

5x+1250=15450

5x=15450-1250

5x=14200

x=14200/5

x=2840

Put the value of x in 4x+1250 to get amount earned from store=4(2840)+1250=$12610.

Hence the amount earned by Erica from college is $2840.

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Step-by-step explanation:

The value of X is given so put the value of X in 1/4 (2)^x

Answer: B

Step-by-step explanation:

Plug in x for 3. Then solve.

4*(1/3)^3

4*1/9

4/9

The equation of the line is: y + 3 = -6(x + 2) [point-slope form] or y = -6x - 15 [slope-intercept form].

Given a point (-2, -3) and a slope (m) of -6, you can write the equation of the line in point-slope form by substituting (a, b) = (-2, -3) and m = -6 into y - b = m(x - a):

y - (-3) = -6(x - (-2))

y + 3 = -6(x + 2) [point-slope form]

Rewrite in slope-intercept form as:

y + 3 = -6(x + 2)

y + 3 = -6x - 12

y = -6x - 12 - 3

y = -6x - 15 [slope-intercept form]

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An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equivalent to -(1/6)y + 1/3 is,

-(1/6)y + 1/3

Take 1/6 common from both first and the last term,

1/6 (-y + 2)

Hence, the correct option is C.

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Answer:

I think 5m is the correct answer

Answer:

Hello! The answer to your question is [tex]\sqrt{29}[/tex], or approximately 5.39.

Step-by-step explanation:

(Two methods)

Method 1:

To solve this problem, we will use the Pythagorean theorem. To create the triangle, you can connect all the points with lines. This will leave you with the base of the triangle as 2 and the leg as 5. We do not know the hypotenuse. Now, we can use the Pythagorean theorem formula:

[tex]a^2 + b^2 = c^2[/tex]

[tex]\sqrt{2^2 + 5^2 } \\= \sqrt{4 + 25} \\= \sqrt{29}\\or 5.39[/tex]

Now, we can substitute our values:

Method 2:

To solve this problem, we will use the distance formula:

[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

Our points are:

A(-3, 1) and B(-1, -4)

Now, we substitute our values into the distance formula provided:

[tex]\sqrt{(-1 - (-3))^2 + (-4 - 1)^2} \\= \sqrt{(-1 + 3))^2 + (-5)^2} \\= \sqrt{(2)^2 + (-5)^2} \\= \sqrt{4 + 25} \\= \sqrt{29} \\or 5.39[/tex]

Answer:

3

Step-by-step explanation:

AD/AB = AE/AC

8/10 = 12/AC

AC = 12(10/8)=15

EC = 15 - 12 = 3

The ratio of the measurements written as a fraction is 8/9.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator.

In order to convert the ratio to fraction, the units of measurements have to be the same. So, pounds would be converted to ounces.

3 x 16 = 48 ounces

48 / 54 = 8/9

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Answer:

Volume of a cylinder = 1,100cm³

Step-by-step explanation:

Volume of a cylinder = πr²h

Given

π = 22/7

r = 5cm

h = 14cm

Substitute the given information in the problem.

Volume of a cylinder = 22/7 × (5cm)² × 14cm

Volume of a cylinder = 22/7 × 25cm² × 14cm

Volume of a cylinder = 1,100cm³

Answer:

First one

Step-by-step explanation:

First one ....pick a point ....say C    for 'x'   add 8    for y   subtract 3  and you will be at C'

The transformed function is y = 1/3(log(x/3 + 4)) + 1

The parent logarithmic function is

y = log(x)

When shifted left by 4 units, we have:

y = log(x + 4)

When shifted up by 3 units, we have:

y = log(x + 4) + 3

When compressed vertically by 1/3, we have:

y = 1/3(log(x + 4) + 3)

This gives

y = 1/3(log(x + 4)) + 1

When stretched horizontally by 3, we have:

y = 1/3(log(x/3 + 4)) + 1

Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1

We have:

f(x) = log[-(x – 5)] + 4

Set the radicand greater than 0

-(x - 5) > 0

Divide by -1

x - 5 < 0

Add 5 to both sides

x < 5 -- this represents the domain

A logarithmic function can output any real number.

So, the range is [tex]-\infty < f(x) < \infty[/tex]

In the domain, we have:

x < 5

This means that the interval of decrease is [tex]-\infty < x < 5[/tex]

Rewrite as an equation

x = 5 --- this represents the equation of asymptote

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Answer:$986,4000



Step-by-step explanation:

Answer:

A. 81

Step-by-step explanation:

F(x)=[tex]3^{x}[/tex]

if x=4, then F(4) = [tex]3^{4}[/tex] = 3×3×3×3=81

Answer:

g(x)=-32x

Step-by-step explanation:

When something is reflected over the x-axis. The x doesn't change, it's the y that changes. So let's just generally say you have the point (x, y). Reflecting this over the x-axis means the y is changing, so it becomes (x, -y). And since the g(x) represents the y, you multiply the entire thing by -1. So the new equation becomes: g(x) = -(8(4x)) = -8(4x) = -32x. So the equation is g(x) = -32x or -8(4x) if you want to leave it like how it was before.

Answer:

x + 7 and x + 5 are possible dimensions

Step-by-step explanation:

x² + 12x + 35 ← factor the quadratic

consider the product of the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (+ 12)

the factors are + 7 and + 5 , since

7 × 5 = + 35 and 7 + 5 = + 12 , then

x² + 12x + 35 = (x + 7)(x + 5) ← in factored form

now the area A = length × breadth , that is

A = x² + 12x + 35 = (x + 7)(x + 5) , then

length = x + 7 or x + 5

breadth = x + 5 or x + 7