10. A truck travelling at x km/h, where 30 ≤x≤ 120, uses gasoline at the rate of r(x) L/100 km, where r(x) = 1(4900 + x). If fuel costs $1.15/L, what speed will result in the lowest fuel cost for a trip of 200 km? What is the lowest total cost for the trip?​

Answer: 1 3 4

Step-by-step explanation:

Answer:

12 root 3

Step-by-step explanation:

first, you can say that QRP is similar to PRS

with the ratios, you can say that

[tex]\frac{QR}{PR} = \frac{PR}{RS}\\[/tex]

by substituting values, you have

[tex]\frac{6}{PR} = \frac{PR}{18}\\[/tex]

[tex]PR^2=108[/tex]

[tex]PR=6\sqrt{3}[/tex]

using pythagorean theorem, you can determine that

[tex]PS^2=(6\sqrt{3})^2+18^2[/tex]

[tex]PS^2=432[/tex]

[tex]PS=\sqrt{432}=12\sqrt{3}[/tex]

Answer:

12√3

Step-by-step explanation:

cos∠RSP = 18/PS

cos∠PSQ = PS/24

∠RSP=∠PSQ     (the angle at S)

18/PS = PS/24

(PS)² = (18)(24) = 432

PS = √432 = 12√3

Answer:

3/8

Step-by-step explanation:

Two triangles = one square

Since there are 4 squares, then there are 8 triangles

We see one triangle is shaded.

We also see one square is shaded, which means 2 triangles are shaded.

2 + 1 = 3 triangles shaded. Since there are a total of 8 triangles, then the fraction would be 3/8

The value of the expression is -3.

Integer tiles are one way of using a material representation to introduce the concept of adding and subtracting integers.

This model can be useful for working on the type of problem that many students find harder, that is, problems like -4 + -5.

Given that, Allison is evaluating the expression Negative 5 minus (negative 2) using integer tiles.

Allison has 5 negative tiles

So,

she  needs to remove 2 negative tiles,

then, subtract -2 to 5 to get left  3 negative tiles.

(-5) -(-2)  =   (-5+2)  

= -3

Hence, The value of the expression is -3.

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Answer:

its actually remove 2 negative tiles

Step-by-step explanation:

i did it on my exam

Answer:y = 4x-5.

Step-by-step explanation:

222222222222222222222

"The A minor scale uses the white notes on the keyboard from A to A, but with G# instead of G." is True Option A

Generally, The tonic of a minor scale, which is the first note of the scale, is located a minor third above the root note of the scale. A minor scale is a sort of musical scale that consists of seven notes.

The A minor scale is a 7-note, the diatonic scale made up of the notes A, B, C, D, E, F, & G. It's the only minor scale that doesn't contain any sharps or flats.

A Natural Minor is A, B, C, D, E, F, G, A. Notice that the A Natural Minor Scale has no notes with accidentals. Let's build a G# Natural Minor Scale. Our starting note will be G#.

Therefore, Option A is true

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The graph would replicate itself starting at (0,0) if we wanted to start there (4,0).

A sine function, a periodic function that oscillates smoothly between high and low values, serves as the foundation for a sinusoidal function. Cosine functions can also be used as the foundation for sinusoidal functions because they are essentially a horizontal shift of sine functions.

We must establish the amplitude, period, and vertical shift of the periodic phenomenon in order to establish a sinusoidal function that models it. Determining whether to utilize a sine or a cosine function and the ensuing phase shift is also necessary.

The interval over which the graph repeats itself can be inferred from the graph. The graph would replicate itself starting at (0,0) if we wanted to start there (4,0). So, four is the era.

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Answer:The statement "The bank has the best decors and paintings in their branch" should not be one of Macky's reasons for choosing a bank. While the appearance of a bank branch may be important to some customers, it is not a primary factor in choosing a bank account. Macky should focus on more important factors such as interest rates, fees, customer service, and overall financial stability of the bank.

Step-by-step explanation:

The statement "The bank has the best decors and paintings in their branch" should not be one of Macky's reasons for choosing a bank. While the appearance of a bank branch may be important to some customers, it is not a primary factor in choosing a bank account. Macky should focus on more important factors such as interest rates, fees, customer service, and overall financial stability of the bank.

The expression "15 more than a number" can be represented using the variable n as n + 15.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
The variable mentioned in the question is n.
To write an expression for 15 more than a number, we have to add the number with 15.
So,
Expression = 15 + n

Thus, the expression "15 more than a number" can be represented using the variable n as n + 15.

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Step-by-step explanation:

4

Ws

Number of packs of cups to be purchased = 5 packs and Number of cups remaining if 80% lemonade is sold = 85 cups.

The volume of cone is calculated using the formula (1/3)r2h, where "h" stands for the cone's height and "r" for the base radius. As a result, (1/3)r2 is the cone's volume in terms of the slant height "L." (L2 - r2).

Volume of a cone is given by the expression,

V = 1/3πr²h

Here,

r = radius of the cone

h = Height of the cone

Radius of the cone =  = 4 cm

Height of the cone = 11 cm

Amount of lemonade = 10 gallons

Volume of one cone = 1/3π(4)²× 11

 = 184.307 cm³

Covert the gallons into cubic cm,

  ∵ 1 gallon = 3785 cm³

  ∴ 10 gallons = 37850 cm³

  ∵1 cones are represented by a volume of 184.307 cm3.

∴ 1 cm³ will represent the volume = 1/184.307 cup

∴ 37850 cm³ will represent the volume = 37850/184.307 cups

                                                                  = 205.36 cups

                                                                   = 205 cups

Therefore, number of packs of cups to be bought = 205/50

                                                                                    = 5 packs

b). If 80% of the lemonade are sold, amount of lemonade sold = 10 × 80/100

= 8 gallons

Volume of 8 gallons lemonade in cm³ = 8 × 3785

                                                                    = 30280 cm³

Therefore, number of cups to be used = 30280/184.307 cups

= 164.29 cups

≈ 164 cups

Number of cups purchased = 250

And there are 250 cups left after subtracting 164.

                                                                = 86 cups

Therefore, number of cups remaining are 86 cups.

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The correct option is A. 30° for the value of x in the similar triangles right triangles DEF and WXY.

The hypotenuse-leg congruent theorem states that if two right-angled triangles have congruent legs, then their hypotenuses are also congruent.

it also implies that angle D is equal to angle W and angle F is equal angle Y

so;

x + 2x + 90 = 180° {sum of interior angles of a triangle}

3x + 90° = 180°

3x = 180° - 90° {subtract 90° from both sides}

3x = 90°

x = 90°/3 {divide through by 3}

x = 30°

Therefore, the value of x in the similar triangles right triangles DEF and WXY is equal to 30°

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The percentage of the employees at the water slides are temporary​ is 88%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.

To find the percentage of the employees that are temporary

66/75 x 100/1

=88%

Hence, 88% is the percentage of the employees at the water slides are temporary​

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The number -4 as an exponent of 2 is is (√-4)^2

From the question, we have the following parameters that can be used in our computation:

-4

Express the exponent of teh expression as 1

So, we have the following representation

-4^1

Express 1 as 2/2

-4^2/2

So, we have

(√-4)^2

Hence, the solution is (√-4)^2

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The required solution is as follows,
(A) The value of the limit is -∞, as 7 is an odd number.
(b) Graf of the function has been shown.

Limit, which can be defined as every nearby value of a variable for a function that exists, is called limits

Here,
According to the question,
[tex]y = \lim_{x \to \ a} 1/[x-a]^n[/tex]

Put a = 2 and n = 7
[tex]y = \lim_{x \to \ 2} 1/[x-2]^7[/tex]

As n = 7 is odd, from the theorem,
y = -∞, as 7 is an odd number.

Thus, the required solution is as follows,
(A) The value of the limit is -∞, as 7 is an odd number.
(b) Graf of the function has been shown.

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Answer:

A rate is two variables that relies on each other so a example would be a projectile and a cannon, in relation the cannon goes no where while the projectile is flying through the air

Step-by-step explanation:

The value of DC is of 80, hence the statement is false.

Similar triangles share these two features listed as follows:

The similar triangles for this problem are given as follows:

AOB and COD.

Hence the proportional relationship established between the side lengths is given as follows:

OA/OC = OB/OD = 1/4 = AB/DC.

Taking the last two terms, considering that AB = 20 cm, the length of DC is given as follows:

DC = 4 x AB

DC = 4 x 20 cm

DC = 80 cm.

Hence the statement is false, as the length is of 80 cm and not of 120 cm.

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If the repayment period is the same length for both loans, the interest option that will result in the least amount of interest added to the loan is B. Option A will have the least amount of interest because simple interest generates earnings from principal only.

The simple interest is the interest system that does not compute interest on accumulated interest.

Unlike simple interest, compound interest charges interest on accumulated interest.

Thus, the simple interest system applies the interest rate on the principal only for each period to determine the amount of interest.

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Answer: Option A will have the least amount of interest because simple interest generates earnings from principal only.

Step-by-step explanation: because it says it’s right on the computer;p

Check the picture below.

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-5}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{5}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-5) ~~ )^2 ~~ + ~~ ( ~~ y-5 ~~ )^2~~ = ~~5^2\implies \boxed{(x+5)^2 +(y-5)^2 = 25}[/tex]

On solving the provided question we cans ay that the increasing order of the function is  y = 5/2x +10 < y = 3/2x+1/2 < y = 1/2x - 2 < y = 3/4x - 7/3 < y = -1/2x + 1/2 < y = 3/2x - 11/2

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

the increasing order of the function is

y = 5/2x +10 < y = 3/2x+1/2 < y = 1/2x - 2 < y = 3/4x - 7/3 < y = -1/2x + 1/2 < y = 3/2x - 11/2

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The total cost of Mr.Bhavsar's order after the coupon for 25% off, a 6% tax, and $7 shipping will be $72.19.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The cost of the new Star Wars after a coupon for 25% off and a 6% tax will be given as,

⇒ $82 x (1 - 0.25) x (1 + 0.06)

⇒ $82 x 0.75 x 1.06

⇒ $65.19

The total cost after shipping will be given as,

Total cost = $65.19 + $7

Total cost = $72.19

The total cost of Mr.Bhavsar's order after the coupon for 25% off, a 6% tax, and $7 shipping will be $72.19.

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To put the streamer on the whole wall we need at least 32 Square feet of the streamer.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given,  to put streamers from concern to corner in both directions and the wall is 4 ft wide and 8ft high.

Since the area of a rectangle:

Area  = Length * width

Thus,

The area of the wall  = 4 * 8

The area of the wall  = 32

So,

The Streamer required = 32 square feet

Therefore, We need at least 32 square feet of streamer to cover the entire wall.

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Answer:

"w" (and any subsequent words) was ignored because we limit queries to 32 words.

w = 0.33 so, w lies before A, B, and C.

Option A is the correct answer.

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

We have,

Average weight.

w = Sum of all the weight / 3

w = (0.5 + 0.3 + 0.2) / 3

w = 1/3

w = 0.33

Now,

A = 3, B = 6, and C = 7 on the number line.

0.33 lies before A, B, C

Thus,

w lies before A.

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a) The probability that the player makes exactly 3 of the 5 shots = 0.3087

b) The probability that the player makes exactly 4 of the 5 shots = 0.36015

c) The probability that the player makes all 5 shots = 0.16807

d) The probability that the player makes 3 or 4 of the shots = 0.66885

The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.

The formula for Binomial Distribution is given by

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

where

n = number of trials

x = number of successes

p = probability of getting a success in one trial

q = probability of getting a failure in one trial

q = 1 - p

Given data ,

Let the probability be represented as P

The total number of trials n = 5

The probability of getting a success p = 0.70

The probability of getting a failure q = 0.30

Now , the equation will be

a)

The probability that the player makes exactly 3 of the 5 shots = A

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

n = 5

x = 3

Substituting the values in the equation , we get

A = ⁵C₃ ( 0.70 )³ ( 0.30 )²

A = 10 ( 0.343 ) ( 0.09 )

A = 0.3087

So , probability that the player makes exactly 3 of the 5 shots is 0.3087

b)

The probability that the player makes exactly 4 of the 5 shots = B

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

n = 5

x = 4

Substituting the values in the equation , we get

B = ⁵C₄ ( 0.70 )⁴ ( 0.30 )¹

B = 5 ( 0.2401 ) ( 0.3 )

B = 0.36015

So , probability that the player makes exactly 4 of the 5 shots is 0.36015

c)

The probability that the player makes all 5 shots = C

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

n = 5

x = 5

Substituting the values in the equation , we get

C = ⁵C₅ ( 0.70 )⁵ ( 0.30 )⁰

C = 0.16807

So , probability that the player makes all 5 shots is 0.16807

d)

The probability that the player makes 3 or 4 of the shots = D

D = A + B

D = 0.3087 + 0.36015

D = 0.66885

Hence , the probability is solved

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<NOM = 59° (vertically opposite angles)

<STU = 96°(Exterior angle of a triangle)

There are mathematical statement that can be used to show the relationships between the sides of the triangle this is what we call the theorems of the triangle.

In question 1; Angle NOM = 59° because it is vertically opposite angle POQ

In question 2; Angle UVT = Angle VUT = 42°

Angle UTV = 180 - 2(42)

= 96°

Then;

Angle STU = 96° (This is because the angle STU is the sum of the interior  opposite angles.).

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The solution of the matrix product is:

[tex]\left[\begin{array}{ccc}4&0\\-16&-7\\\end{array}\right][/tex]

Remember that the general product between two 2by2 matrices can be written as:

[tex]\left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\\\end{array}\right] *\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\\end{array}\right] = \left[\begin{array}{ccc}a_{11}*b_{11} + a_{12}*b_{21}&a_{11}*b_{12} + a_{12}*b_{22}\\...&...\\\end{array}\right][/tex]

So we multiply the the rows of the first matrix by the columns of the second one, then our product will be:

[tex]\left[\begin{array}{ccc}1&2\\-4&3\\\end{array}\right] *\left[\begin{array}{ccc}4&1\\0&-1\\\end{array}\right] = \left[\begin{array}{ccc}1*4 + 2*0&1*1 + 2*-1\\-4*4 + 3*0&-4*1 + 3*-1\\\end{array}\right]\\\\= \left[\begin{array}{ccc}4&0\\-16&-7\\\end{array}\right][/tex]

That is the solution of the product.

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Answer:

SP-CP=PROFIT

210-190=20

the profit is 20

Step-by-step explanation:

Answer:

Rs 20

Step-by-step explanation:

S.P. (Selling Price) is the price at which a product is sold. C.P. (Cost Price) is the price at which a product is purchased. When S.P. is greater than C.P., it results in a profit. To calculate profit, the formula is simple:

Profit = S.P. - C.P.

In this case, S.P. is Rs. 210 and C.P. is Rs. 190. So, the profit would be calculated as:

Profit = Rs. 210 - Rs. 190 = Rs. 20.