96 penicals come in a box if 4teachers share 3boxes equally how many penicals does each teacher receive

Answer:

[tex]5\sqrt{3}[/tex] inches long is the other leg

Step-by-step explanation:

Given the statement: If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long.

Hypotenuse side = 10 inches

Let length of other leg be x.

Pythagoras theorem states that in a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Then; by definition of Pythagoras theorem;

[tex]{\text}(Hypotenuse)^2 = (5)^2 + x^2[/tex]

[tex](10)^2 = 5^2 + x^2[/tex]

[tex]100 = 25 + x^2[/tex]

Subtract 25 on both sides we get;

[tex]100-25= 25 + x^2-25[/tex]

Simplify:

[tex]75 = x^2[/tex]

Simplify:

[tex]x = \sqrt{75} = 5\sqrt{3}[/tex] inches

Therefore, the sides of other leg is [tex]5\sqrt{3}[/tex] inches

Final answer:

Using the Pythagorean theorem, and knowing the length of the hypotenuse (10 inches) and one leg (5 inches), we calculate the other leg to be approximately 8.66 inches in length.

Explanation:

The question involves finding the length of the other leg of a right triangle when the lengths of the hypotenuse and one leg are known. By applying the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The theorem is usually written as a² + b² = c².

In this case, the hypotenuse (c) is given as 10 inches, and one leg (a) is 5 inches. To find the length of the other leg (b), rearrange the Pythagorean theorem as b² = c² - a². Substituting the known values gives us b² = 10² - 5² leading to b² = 100 - 25. Therefore, b² = 75. Taking the square root of both sides to solve for b gives us b = √75 which simplifies to approximately 8.66 inches when rounded to two decimal places.

Thus, the length of the other leg in the right triangle is approximately 8.66 inches.

Answer:

a) 5.4%  

Step-by-step explanation:

a) We will use the binomial distribution, with n = 100 and p(success) = 0.95

We need to calculate

P(X=x) = [tex]\binom{n}{x}p^{x}q^{n-x}[/tex]

P(X ≤91) =  [tex]\sum_{k=1}^{91}\binom{100}{k}0.95^{k}0.5^{n-k}[/tex]

As we know that binomial distribution can be approximated to normal distribution if np≥5 and nq≥5 as in this case.

Therefore, P(x,n,p) →N[tex](\mu, \sigma )[/tex]

[tex]\mu[/tex] = np = 95

[tex]\sigma[/tex] = √npq = 2.`79

P(X≤91) ≅ P(X≤91.5)  = P( Z≤[tex]\frac{91.5-95}{2.179}[/tex]

                                 =  P( Z≤ -1.6)

                                 = 0.054

Probability = 5.4%

b) If the probability was less than 5% then we must say that the DHL Shipping company don not ships 95% of its orders on time but as we can see that the probability is more that 5% that is 5.4%. So, we cannot say that the company does not ships the orders on time. But we cannot say with confirmation, we need more samples so as to judge accordingly.

3/17 = x/544

If x=96 then there are 96 grams of zinc.

The amount of zinc that contains in the jar will be 96 grams based on the given ratio.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Suppose the amount of zinc is Z while the copper is C.

The ratio Z/C = 3/17

And, C = 544

Z/544 = 3/17

Z = (3/17)544 = 96 grams.

Hence "The amount of zinc that contains in the jar will be 96 grams based on the given ratio".

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Answer:

Here, x represents the number of 20-pound boxes and y represents the number of 30 pound boxes.

As per the given condition: Vince loads 10 boxes into his truck.Some of the boxes weigh 20 pounds, and some weigh 30 pounds and the total weight of the boxes is 280 pounds.

⇒ x+ y =10                      .....[1]

and

20x+30y = 280               .....[2]

Multiply  equation [1]  by 20 we get;

[tex]20(x+y) = 20\cdot 10[/tex]

Using distributive property: [tex]a\cdot(b+c) = a\cdot b + a\cdot c[/tex]

20x + 20y = 200                   ....[3]

Subtract equation [3] from [2] we get;

[tex]20x+30y-20x-20y = 280-200[/tex]

Combine like terms;

10y = 80

Divide both sides by 10 we get;

y = 8

Substitute this y value in equation [1] we get;

x + 8 = 10

Subtract 8 from both sides we get;

x + 8 -8 =10-8

Simplify:

x = 2

Therefore, the pairs of equation are:  x+ y =10 and 20x+30y = 280

Vince has the number of 20-pound boxes is, 2 and the number of 30 pound boxes is, 8

Answer:

No, Jude’s graph is incorrect. The inequality symbol is “less than,” so -9 is not included. He should have used an open circle on -9.Step-by-step explanation:

2020 on eng

Answer:

6 cup of milk

Step-by-step explanation:

From question

         for 11 cookies → [tex]\frac{2}{3}[/tex] of a cup of milk required

         Now,

                  for 99 cookies

          we multiply both sides by 9.

                        11 × 9 = [tex]\frac{2}{3}[/tex] × 9

                  for 99 cookies = 6 cup of milk

Answer:

V≈ 904.78in³

Step-by-step explanation:

V= 4/3 π r cubed

diameter= 12 cm

radius= 1/2 diameter= 6 cm

3.14= pi

V= 4/3 * 3.14 * 6 cubed

V= 4/3 * 3.14 * 216

V= 1.33 * 3.14 * 216

V= 902.06

[tex]15a^2+45=0\qquad\text{subtract 45 from both sides}\\\\15a^2=-45\qquad\text{divide both sides by 15}\\\\a^2=-3<0\\\\\text{NO REAL SOLUTION}\\\\\text{in the complex set}\\\\a^2=-3\to a=\pm\sqrt{-3}\\\\a=\pm\sqrt{(-1)(3)}\\\\a=\pm\sqrt{-1}\cdot\sqrt3\\\\\boxed{a=-i\sqrt3\ \vee\ a=i\sqrt3}\\\\------------------\\\\i=\sqrt{-1}[/tex]

Answer:

The equation that represents the motion of the string is given by:

[tex]y =Ae^{-kt}\cos(2\pi ft)[/tex]     .....[1] where t represents the time in second.

Given that: A = 0.6 cm (distance above its resting position) , k = 1.8(damping constant) and frequency(f) = 105 cycles per second.

Substitute the given values in [1] we get;

[tex]y =0.6e^{-1.8t}\cos(2\pi 105t)[/tex]  

or

[tex]y =0.6e^{-1.8t}\cos(210\pi t)[/tex]  

(a)

The trigonometric function that models the motion of the string is given by:

[tex]y =0.6e^{-1.8t}\cos(210\pi t)[/tex]

(b)

Determine the amount of time t that it takes the string to be damped so that [tex]-0.24\leq y \leq0.24[/tex]

Using graphing calculator for the equation

[tex]y =0.6e^{-1.8x}\cos(210\pi x)[/tex]

let x = t (time in sec)  

Graph as shown below in the attachment:

we get:

the amount of time t that it takes the string to be damped so that [tex]-0.24\leq y \leq0.24[/tex] is, 0.5 sec

The trigonometric function that models the motion of the guitar string is y(t) = Asin(ωt)e^(-kt). Using a graphing calculator, the time it takes for the string to be damped within the given range can be determined.

a) The trigonometric function that models the motion of the guitar string can be represented by the equation y(t) = Asin(ωt)e^(-kt), where A is the amplitude, ω is the angular frequency, t is the time, and k is the damping constant.

b) To determine the amount of time it takes for the string to be damped so that -0.24 ≤ y ≤ 0.24, you can use a graphing calculator to plot the trigonometric function and find the values of time at which the function crosses these y-values. You should set up the equation as follows: -0.24 ≤ Asin(ωt)e^(-kt) ≤ 0.24 and solve for t.

Please see the attached screenshot for an example of the graph.

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Answer:

16

Step-by-step explanation:

11.2/0.7=16

Answer:

[tex]\$4701.80[/tex]

Step-by-step explanation:

Mrs. Siebenaller bought a bus for 25,000 with a 7% interest rate and she gets a loan payoff of 60 months,

We know that,

[tex]\text{PV of annuity}=P\left[\dfrac{1-(1+r)^{-n}}{r}\right][/tex]

Where,

PV = Present value of annuity = 25000,

r = rate of interest of each period = [tex]\dfrac{7}{12}[/tex]% monthly

n = number of periods = 60 months,

Putting the values,

[tex]\Rightarrow 25000=P\left[\dfrac{1-(1+\frac{0.07}{12})^{-60}}{\frac{0.07}{12}}\right][/tex]

[tex]\Rightarrow P=\dfrac{25000}{\left[\dfrac{1-(1+\frac{0.07}{12})^{-60}}{\frac{0.07}{12}}\right]}[/tex]

[tex]\Rightarrow P=\$495.03[/tex]

Hence total amount paid is,

[tex]=495.03\times 60=\$29,701.80[/tex]

Therefore interest amount is,

[tex]=29,701.80-25,000=\$4701.80[/tex]

Answer: 20

Step-by-step explanation:

h(x) = |3x| - 1

h(7) = |3(7)| - 1

      = |21| - 1

      =  21  - 1

      = 20

The correct statement that interprets the confidence interval is option A: We have 95% confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports.

The correct answer is A. We have 95% confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports.

The confidence interval shows that we are 95% confident that the true mean of the population of all data speeds at the airports is between 13.05 Mbps and 22.15 Mbps.

The other options are incorrect.

Option B states that we have 95% confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the sample mean of the data speeds at the airports.

This is incorrect because the confidence interval is for the population mean, not the sample mean.

Option C states that the limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports.

This is also incorrect because we can never be 100% sure that the true mean is within the confidence interval.

Option D states that the limits of 13.05 Mbps and 22.15 Mbps contain 95% of all of the data speeds at the airports.

This is incorrect because the confidence interval is for the mean of the population, not for all of the data speeds in the population.

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Reference angle is angle C

AT is the opposite side as this leg is not adjacent to angle C (or put another way, point C is nowhere to be found in AT)

AC is the adjacent leg because angle C is part of this segment. It is next to or touching the segment, hence the name "adjacent"

side note: CT is the hypotenuse and always the longest side of the right triangle. It is opposite the largest angle (90 degrees) of this triangle.

Look at the picture.

Use the Pythagorean theorem to calculate x:

[tex]x^2=2^2+4^2\\\\x^2=4+16\\\\x^2=20\to x=\sqrt{20}\approx4.47\ cm[/tex]

[tex]A_1=\dfrac{8+6}{2}\cdot4=14\cdot2=28\ cm^2\\\\A_2=3\cdot6=18\ cm^2\\\\A_3=3\cdot4.47=13.41\ cm^2\\\\A=4A_1+2A_2+2A_3\\\\A=4\cdot28+2\cdot18+2\cdot13.41=174.82\ cm^2\approx175\ cm^2\\\\1mL\to1cm^2[/tex]

A = bh is the area of a rectangle, and also the area of a parallelogram. Any rhombus is also a parallelogram, so you can also use this formula for any rhombus. This helps explain why A = bh shows up three times to account for the three different types of shapes: rectangle, parallelogram, rhombus

A = (1/2)*bh is the area of a triangle which can be written as A = 0.5*b*h

The last formula, which is A = [ (b1+b2)/2 ] *h is the area of a trapezoid. The sides b1 and b2 are the parallel bases

note: the height is always perpendicular to the base

QUESTION 1

The given polynomial function is [tex]y=4x^2-3x+7[/tex]

The degree of the polynomial is the exponent on the leading term of the polynomial after the polynomial has been written in descending powers of [tex]x[/tex].

The leading term is [tex]4x^2[/tex] the exponent of [tex]x[/tex] in this term is [tex]2[/tex], hence the degree is 2.

The coefficient of this term is the leading coefficient which is [tex]4[/tex].

The correct answer is B.

QUESTION 2

The function graphed has two x intercepts.

The first x intercept has a multiplicity that is even. The least positive even integer is 2.

The second x intercept has a multiplicity that is odd.

The least positive odd integer is 1.

Therefore the lowest degree  is the sum of the two least values which is

[tex]2+1=3[/tex]

The correct answer is C

QUESTION 3

The given polynomial function is [tex]y=ax^5+cx^2+f[/tex], where [tex]a,c[/tex] and [tex]f[/tex] are real numbers.

The x intercepts are the roots of the polynomial and we know the maximum number of real roots a polynomial of degree 5 can have is 5.

The maximum number of the x-intercepts of the polynomial is therefore 5.

The correct answer is D

QUESTION 4

To find the y-intercept, we substitute [tex]x=0[/tex] into each polynomial function.

The first function is [tex]y=2x^4+x^2-3[/tex]

When [tex]x=0[/tex], [tex]y=2(0)^4+(0)^2-3=-3[/tex]

The y-intercept is -3

The second function is [tex]y=3x^2+4[/tex].

When [tex]x=0[/tex], [tex]y=3(0)^2+4=4[/tex].

The y-intercept is 4

The third function is [tex]y=-4x^7-5x+3[/tex], when [tex]x=0[/tex],

[tex]y=-4(0)^7-5(0)+3=3[/tex]

The y-intercept is 3

The fourth function is [tex]y=9x^3+3x^2[/tex]

When [tex]x=0[/tex], [tex]y=9(0)^3+3(0)^2=0[/tex]

The y-intercept is 0

The correct answer is C.

QUESTION 5

The given polynomial function is [tex]y=-2x^{13}+25x^8-3[/tex].

This is already in standard form.

The degree of the polynomial is 13, which is odd.

The graph of the polynomial will rise at one end and fall at the other end.

The leading coefficient is negative, so the graph rises on the left and falls on the right.

Therefore as x approaches infinity, y will be approaching negative infinity.

The correct answer is D

The answers to the questions are as follows:

1. The correct option is B. degree=2 leading coefficient=4.

2. The correct option is c. 3. The lowest degree of the function graphed here is 3.

3.The correct option is D. 5.

4. The correct option is C. [tex]\( y = -4x^7 - 5x + 3 \).[/tex]

5.The correct option is d. [tex]\( y \)[/tex] approaches negative infinity.

1. The degree and leading coefficient of the function [tex]\( y = 4x^2 - 3x + 7 \)[/tex]are:

 - Degree = 2

 - Leading coefficient = 4

 Therefore, the correct option is B. degree=2 leading coefficient=4.

The degree of a polynomial is the highest power of the variable [tex]\( x \)[/tex] that appears in the polynomial with a non-zero coefficient. In the given function, the highest power of [tex]\( x \)[/tex] is 2 (in the term [tex]\( 4x^2 \))[/tex], so the degree is 2. The leading coefficient is the coefficient of the term with the highest power, which is 4 in this case.

2. The function graphed has two x intercepts.

The correct answer is C

3. The maximum number of x-intercepts that can be found on a graph with the equation [tex]\( y = ax^5 + cx^2 + f \)[/tex] is:

 - A. 2

 - B. 3

 - C. 4

 - D. 5

The correct option is D. 5.

The degree of the polynomial [tex]\( y = ax^5 + cx^2 + f \)[/tex] is 5, which means it is a fifth-degree polynomial. The maximum number of x-intercepts (real roots) for a polynomial is equal to its degree, provided that the roots are counted with multiplicity and include complex roots. Since we are looking for the maximum number of x-intercepts, we consider the degree of the polynomial, which is 5.

4. The polynomial function that has a y-intercept of 3 is:

 - A. [tex]\( y = 2x^4 + x^2 - 3 \)[/tex]

 - B. [tex]\( y = 3x^2 + 4 \)[/tex]

 - C. [tex]\( y = -4x^7 - 5x + 3 \)[/tex]

 - D. [tex]\( y = 9x^3 + 3x^2 \)[/tex]

 The correct option is C. [tex]\( y = -4x^7 - 5x + 3 \).[/tex]

5. The end behavior of the function [tex]\( y = -2x^{13} + 25x^8 - 3 \) as \( x \)[/tex] approaches infinity is:

 - a. [tex]\( y = -3 \)[/tex]

 - b. [tex]\( y = 13 \)[/tex]

 - c. [tex]\( y \)[/tex] approaches infinity

 - d. [tex]\( y \)[/tex] approaches negative infinity

 The correct option is d. [tex]\( y \)[/tex] approaches negative infinity.

Answer:

17 regular popcorn bags and 23 super size bags.

Step-by-step explanation:

A group of 40 people went to the theme park. While there, each person bought popcorn.

Let the regular popcorn bags be = x

Let the super size bags be = y

[tex]x+y=40[/tex]        ................(1)

Next equation becomes:

[tex]6x+8y=286[/tex]        ...............(2)

Multiplying (1) by 6 : [tex]6x+6y=240[/tex]

Now subtracting this from (2) we get,

[tex]2y=46[/tex]

=> y = 23

And x = [tex]40-23[/tex]

=> x = 17

So, there were 17 regular popcorn bags and 23 super size bags that the group bought.

As given, the current height of Bobby is = 61 inches

Bobby hopes to be taller than 70 inches.

Let the number of inches Bobby needs to grow to reach 70 be = x

So, he needs to grow

[tex]x+61=70[/tex]

Hence, x=9 inches

So, Bobby needs to grow 9 inches to reach a height of 70 inches and more than 9 if he wants to be taller than 70 inches.

Answer:

$3.15

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

5x=7x-10

First get the variables on one side, and numbers on the other

-2x=10

Therefore,

x=5

Answer:

x is the input, or independent variable and f(x) is the output, or dependent variable or quantity. f(2) represents the output (y-value) when x = 2. The value of f(2) is 2.

Step-by-step explanation:

If the values of a variable depends on the other variable, then it called dependent variable.

If the value of a variable does not depend on the other, then it is called independent variable.

If a function is f(x)=x, then x is an independent variable and f(x) is a dependent variable.

The given function is

[tex]f(x)=10-x^3[/tex]

Here, x is the input, or independent variable and f(x) is the output, or dependent variable or quantity.

The notation f(a) represents the output (y-value) when x = a. So, f(2) represents the output (y-value) when x = 2.

Substitute x=2 in the given function.

[tex]f(2)=10-(2)^3[/tex]

[tex]f(2)=10-8[/tex]

[tex]f(2)=2[/tex]

The value of f(2) is 2.

For a function y = f(x) we define x as the independent variable and y as the dependent variable. y = f(x) means that "y depends on x in a given way, defined by f(x)".

Here we know that:

f(x) = 10 - x^3

1) What is the input, or independent variable?

The independent variable is the one inside the function, in this case, is x.

2) What is the output, or dependent variable or quantity?

in this case, the output is f(x), the value of the whole function evaluated in x.

(note that we do not have y = f(x), so y can't be the output, as we can't invent a variable and add it there.)

3) What does f(2) mean?

This means that we need to replace all the "x's" in the function by 2, we get:

f(2) = 10 - 2^3 = 2

so f(2) is the output when x = 2.

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Answer:

[tex]x=\frac{-9}{2}[/tex]

Step-by-step explanation:

We have to find the value of x from the given triangle.

By mid segment theroem which says the midpoint in a triangle of any two sides is parallel to the third side and half of the third side's length

Therefore, [tex]3x+4=\frac{1}{2}\cdot (4x-1)[/tex]

On multiplying the left hand side of the above equation by 2 from right hand side of the equation we will get:

[tex]2(3x+4)=4x-1[/tex]

[tex]\Rightarrow 6x+8=4x-1[/tex]

On simplification

[tex]\Rightarrow 2x=-9[/tex]

[tex]\Rightarrow x=\frac{-9}{2}[/tex]

Answer:

1/6 p -4/5

Step-by-step explanation:

- 2/3p + 1/5 - 1 + 5/6p

When I combine like terms, I put them next to each other.

- 2/3p + 5/6p+ 1/5 - 1

We need to get a common denominator of 6 for the p terms

-2/3 *2/2 p + 5/6 p

-4/6p + 5/6 p

1/6 p

We need to get a common denominator of 5 for the contant terms

1/5 - 1*5/5

1/5-5/5

-4/5

Substituting these in

2/3p + 5/6p+ 1/5 - 1

1/6 p -4/5

Answer: (A) -5

Step-by-step explanation:

 (-2x + 10) - (-6x + 5y + 12) + (x + 8y - 16)  ; x = 5, y = -4

= [-2(5) + 10] - [-6(5) + 5(-4) + 12] + [(5) + 8(-4) - 16]

= [-10 + 10] - [-30 - 20 + 12] + [5 - 32 - 16]

= (0) - (-38) + (-43)

= 0 + 38 - 43

= -5

Answer:

When we add 9 to the function we are shifting the function up 9 units.

Step-by-step explanation:

If it were added inside the function, it woulds shift it left or right.

But since it is outside the function, we will shift it up or down

When we add 9 to the function we are shifting the function up 9 units.

Answer:

add 9 to the function we are shifting the function up 9 units

Step-by-step explanation:

Answer:

I think the answer is b

Step-by-step explanation:

Because Mark has a better probability of getting at least  something

Answer:

C) It is not a fair game. Evan has the advantage.

Step-by-step explanation:

Mark's expected value is 3/6×$1 = $0.50.

Evan's expected value is 2/6×$2 = $0.67.

Cayla's expected value is 1/6×$3 = $0.50.

_____

Evan's expected value exceeds that of the other players. It is not fair.

Answer: hot dog = $1.75

Step-by-step explanation:

Let h represent hot dogs and c represent bags of chips.

Customer 1: 4h + 2c = 9.00  →  3(4h + 2c = 9.00)  →  12h + 6c =  27.00

Customer 2: 5h + 3c = 11.75 → -2(5h + 3c = 11.75)  → -10h - 6c = -23.50

                                                                                       2h        =    3.50

                                                                                      ÷2               ÷2    

                                                                                        h        =    1.75

Final answer:

The cost of one hot dog is determined to be $1.75.

Explanation:

To find the cost of a hot dog, we will use the information given in two different customer purchases to set up a system of linear equations. Let's define H as the cost of one hot dog and C as the cost of a bag of chips. The first customer buys 4 hot dogs and 2 bags of chips for $9.00, which gives us the first equation:

4H + 2C = 9.00 ...(1)

The second customer buys 5 hot dogs and 3 bags of chips for $11.75, which provides us with the second equation:

5H + 3C = 11.75 ...(2)

With two equations, we can solve for H by either substitution or elimination. Let's multiply equation (1) by 3 and equation (2) by 2 to eliminate C:  

Subtracting equation (4) from equation (3) gives us:

2H = 3.50

And dividing both sides by 2:

H = 1.75

Therefore, the cost of one hot dog is $1.75.