Find the sides marked with the letters in Question 9

Answer:

9

Step-by-step explanation:

72/24 = 3

72 is 3 times 24, so you need 3 times as many garbage trucks.

Answer: 9

The Area of Rhombus is 97.5 cm².

The area of a rhombus is equal to half the product of the lengths of the diagonals. The formula to calculate the area of a rhombus using diagonals is given as, Area = (a × b )/2 where, a and b are the diagonals of the rhombus.

Given:

As, diagonals of rhombus bisect perpendicularly.

so, In triangle OAD using Pythagoras theorem

AD² = OD² + OA²

10² = 7.8² + OD²

OD= 6.25 cm

So, length of BD = 2 x 6.25 = 12.5 cm

Now, area of Rhombus = 1/2 x a x b

                                       = 1/2 x 15.6 x 12.5

                                       = 97.5 cm².

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The equation of the quadratic equation whose root are 5 and -9 is x² +4x -45

quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The equation of a quadratic is given as :

x²-(alpha+beta)x + alpha×beta = 0

where alpha and beta are the roots of the quadratic equation.

alpha+beta = 5-9 = -4

alpha × beta = -9× 5 = -45

therefore the equation will be;

x²-(-4)x + ( -45) = 0

x² + 4x -45 = 0

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A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. There are 112 different hats that can be made using the knitted hat pattern, disregarding size.

To find the total number of different hats that can be made using the knitted hat pattern, we need to multiply the number of choices for each feature.

There are 4 styles to choose from and 4 stitch options, so there are 4 x 4 = 16 different combinations of style and stitch.

For each of these style and stitch combinations, there are 7 yarns that can be used, so the number of possible yarn choices is 7.

Therefore, the total number of different hats that can be made, disregarding size, is:

16 (style and stitch combinations) x 7 (yarn choices) = 112

This calculation shows how the multiplication principle of counting can be used to find the total number of outcomes in a multi-stage process where the number of choices at each stage is known. In this case, we multiplied the number of style and stitch combinations by the number of yarn choices to find the total number of different hats that can be made.

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Complete question is:

A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. Disregarding size, how many different hats can be made?

Answer:

Step-by-step explanation:

The result to the factorization of the polynomial is 3x (x + 10) (x - 10).

Factoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.

Writing each term of the longer expression as the product of its elements is the initial step to factorization polynomials.

= 3x³ - 300x

= 3x(x²) - 300x

= 3x(x²) - 3x(100)

= 3x(x² - 100)

= 3x(x² - 10²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = ( a + b ) ( a − b );

where

= 3x (x+10) (x−10)

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Step-by-step explanation:

this is very simple, we only have to divide each side by four to single out our unknown.

[tex]-7=r[/tex]

Answer:

the solution to the equation -28r = 4r is r = 0.

Step-by-step explanation:

To solve the equation -28r = 4r, we can isolate the variable "r" on one side of the equation and find its value. To do this, we can start by subtracting 4r from both sides of the equation:

-28r - 4r = 4r - 4r

-32r = 0

Next, we can divide both sides of the equation by -32 to find the value of "r":

(-32r) / -32 = 0 / -32

r = 0

So the solution to the equation -28r = 4r is r = 0.

Answer:

$0.22.

Step-by-step explanation:

To find the cost per ounce of juice, divide the total cost of 32 ounces of juice by the number of ounces:

7.04 ÷ 32 ounces = 0.22 per ounce

So, the cost per ounce of juice is approximately $0.22.

Answer:

0.22

Step-by-step explanation:

Answer:  Yes, it's wrong.

Step-by-step explanation:

In the equation, it was [tex]A=\pi r^{2}[/tex]3 ft is the circle's diameter, and d is not the r.

r = d/2 = 3/2 = 1.5 ft

[tex]A=\pi r^{2}\\[/tex]

   ≈ 3.14 x 1.5

   = 4.71

Answer: The total number of members in the club is 140 + 695 + 210 = 1,045.

The number of non-senior members is 140 + 695 = 835.

The probability that the first member selected at random will not be a senior member is 835 / 1,045 = 0.798 or 79.8%.

So, the answer is 0.798 or 79.8%.

Step-by-step explanation:

The time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.

What is the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value.

Let W be the total work to be done, which is installing a new deck.

Given Ted alone can complete the work W  in 15 hours.

Using unitary method,

So in one hour, work done by Ted = W/15

Also given Jimmy alone can complete the work W in 16 hours.

So in one hour, work done by Jimmy = W/16

Using unitary method,

In one hour the work done by Jimmy and Ted together = W/15 + W/16 = 31W/240

ie 31W/240 = 1 hour

 So W = 240/31 = 7.7 hours

Therefore the time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.

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Answerk bzijnjlngljntgojengojnetgihnrtgkte4wg

The probability that randomly selected mechanical component weighs: more than 11.5 lbf is 0.0099, less than 8.7 lbf is 0.3208,  less than 5.0 lbf is 0.0228, between 6.2 lbf and 7.0 lbf is 0.1314, between 10.3 lbf and 14.0 lbf is 0.0436, between 6.8 lbf and 8.9 lbf is 0.3464.

We can use the standard normal distribution and z-scores to answer these questions:

P(X > 11.5) = P(Z > (11.5 - 8) / 1.5) = P(Z > 2.33) = 0.0099

Therefore, the probability that a randomly selected mechanical component weighs more than 11.5 lbf is 0.0099, or about 1%.

P(X < 8.7) = P(Z < (8.7 - 8) / 1.5) = P(Z < 0.47) = 0.3208

Therefore, the probability that a randomly selected mechanical component weighs less than 8.7 lbf is 0.3208, or about 32%.

P(X < 5.0) = P(Z < (5 - 8) / 1.5) = P(Z < -2) = 0.0228

Therefore, the probability that a randomly selected mechanical component weighs less than 5.0 lbf is 0.0228, or about 2%.

P(6.2 < X < 7.0) = P((6.2 - 8) / 1.5 < Z < (7 - 8) / 1.5) = P(-1.2 < Z < -0.67) = 0.1314

Therefore, the probability that a randomly selected mechanical component weighs between 6.2 lbf and 7.0 lbf is 0.1314, or about 13%.

P(10.3 < X < 14.0) = P((10.3 - 8) / 1.5 < Z < (14 - 8) / 1.5) = P(1.53 < Z < 2.67) = 0.0436

Therefore, the probability that a randomly selected mechanical component weighs between 10.3 lbf and 14.0 lbf is 0.0436, or about 4%.

P(6.8 < X < 8.9) = P((6.8 - 8) / 1.5 < Z < (8.9 - 8) / 1.5) = P(-0.47 < Z < 0.60) = 0.3464

Therefore, the probability that a randomly selected mechanical component weighs between 6.8 lbf and 8.9 lbf is 0.3464, or about 35%.

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____The given question is incomplete, the complete question is given below:

Suppose that the weight of a mechanical component is normally distributed with mean p = 8.0 Ibf and standard deviation = 1.5 lbf. Answer the following questions: 1. If you randomly select a mechanical component, what is the probability that it weighs more than 11.5 lbf? 2. If you randomly select a mechanical component, what is the probability that it weighs less than 8.7 lbf? 3. If you randomly select a mechanical component, what is the probability that it weighs less than 5.0 lbf? 5. If you randomly select a mechanical component, what is the probability that it weighs between 6.2 lbf and 7.0 lbf? 6. If you randomly select a mechanical component, what is the probability that it weighs between 10.3 lbf and 14.0 lbf? 7. If you randomly select a mechanical component, what is the probability that it weighs between 6.8 lbf and 8.9 lbf?

Answer:

Step-by-step explanation:

The Kansas City Chiefs has a better chance of winning the super bowl 2023.

In 1967's Super Bowl I, Las Vegas sportsbooks gave the Green Bay Packers a 14-point advantage against the Kansas City Chiefs. Nevada was the only state up until 2018 to allow legal Super Bowl sports betting.

The reigning champion Kansas City Chiefs are the early favorited in the Super Bowl 58 odds, according to the top NFL betting companies. At BetMGM, the Super Bowl 58 odds for the Kansas City Chiefs are +600. You can evaluate the odds on a team you prefer to discover the best price because competing sportsbooks provide different odds for each team to win the Super Bowl.

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Answer:

131,072 Zombies:

the equation: 32 x 4^6 = 131,072

the equation in scientific notation form: 3.2 x 4^7 = 131,072

Step-by-step explanation:

The amount of zombies starts at 32. It quadruples per hour, so we need to multiply the amount by 4 six times(once for every hour).

We can use an exponent to represent this in an equation:

32 x 4^6 = 131,072

Or, if we put it in scientific notation,

3.2 X 4^7 = 131,072.

The equation which represents the number of zombies is;

= [tex]1.31072[/tex]×[tex]10^{5}[/tex]

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Given that

The amount of zombies = 32.

And It quadruples per hour,

Therefore,

Multiply the amount by 4 six times (as it occurs once for every hour).

The the exponent form to represent this equation:

32 x 4^6 = 131,072

Hence, in scientific notation the equation is,

= [tex]1.31072[/tex]×[tex]10^{5}[/tex]

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Answer:

Step-by-step explanation:

Let's call the length of each shorter piece of the first pipe x. Then the total length of the first pipe would be 5x + 27 cm.

Similarly, the length of each shorter piece of the second pipe would be x and the total length of the second pipe would be 11x + 15 cm.

Since both pipes were cut into the same length pieces, we can set the two equations equal to each other:

5x + 27 = 11x + 15

Solving for x, we can find the length of each shorter piece:

6x = -12

x = -2

This means that each shorter piece of both pipes was -2 cm long, which is not physically possible. So, this solution is not valid. This means that the problem is underdetermined and that we cannot determine the length of each piece.

The linear function giving the amount remaining after buying x cups of coffee is given as follows:

A(x) = -3x + 15.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Each cup of coffee costs $3, hence the slope m is given as follows:

m = -3.

(for each cup purchased, the balance decays by $3).

Hence:

A(x) = -3x + b.

Buying 4 cups of coffee, the balance is of $3, hence the intercept b is obtained as follows:

3 = -3(4) + b

b = 15.

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5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.

What is the definition of square root?

The square root of a number is a value that, when multiplied by itself, yields the original number. The square root is the opposite of squaring a number. As a result, squares and square roots are ideas that are connected.

If x is the square root of y, it is denoted as x=√y, or the same equation may be expressed as x² = y. √" is the radical symbol used to symbolise the numerical root here. When a positive number is multiplied by itself, it represents the number's square. The square root of a positive number yields the original value.

Now,

Given that square root of the cube root of 5 i.e. √∛5=?

=√5¹÷³

=5¹/²*¹/³

=5¹/⁶

hence,

          5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.

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The answer is given below:

Binomial distribution is a discrete  probability distribution in which it gives two values that is either success or failure.

A local donut shop began putting an extra donut in some of the boxes.

The shop owner claimed that one in seven boxes had an extra donut.

Nine customers each bought one box of donuts at the shop.

Probability of success fixed is, [tex]p=\frac{1}{7}[/tex]

A value of n fixed, n=9.

We can use binomial distribution to solve this problem,

The probability mass function for the Binomial distribution is given as:

Assume  X is a binomial distribution, [tex]B(n=9,p=\frac{1}{7}=1.143)[/tex].

[tex]P(X)=(nCx)(p)^{x} (1-p)^{n-x}[/tex]

The mean is given by:

[tex]E(X)=np=9*\frac{1}{7}=1.29\\[/tex]

The variance is given by,

[tex]Var(X)=np(1-p)=9*\frac{1}{7}(1-\frac{1}{7} )[/tex]=1.1094

From variance, the standard deviation is given by, [tex]std(X)=\sqrt{1.1094}[/tex]=1.05.

Two of the nine customers buy a box of donuts with an extra donut. Compute P(X ≥ 2) and use the result to justify your answer.

[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)][/tex]

And if we find the individual probabilities we got,

[tex]P(X=0)=(9C0)(0.143)^{0} (1-0.143)^{9-0}=0.249\\P(X=1)= (9C1)(0.143)^{1} (1-0.143)^{9-1}=0.374[/tex]

[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)]\\[/tex]

                      = 1-[0.249+0.374]

                       = 0.377

Hence, [tex]P(X\ge2)=[/tex] 0.377.

This case makes sense the claim since the probability is higher or equal than the expected with the claim.

Corrected question:

To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes had the extra donut and the shop owner claimed that one in seven boxes had an extra donut. Nine customers each bought one box of donuts at the shop. Let X = the number of customers that bought a box containing an extra donut.A. Is X a binomial random variable? Explain.B. What is the mean and standard deviation of X? Provide an interpretation for each value in context.C. Two of the nine customers buy a box of donuts with an extra donut. Is the shop's claim accurate? Compute P(X ≥ 2) and use the result to justify your answer.

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The number of panels that Plant B produced is; 11000 panels

We are told that Plant A produced 4000 fewer panels than Plant B did.

Thus;

A = B - 4000    -----(1)

Four percent of the panels from Plant A and 2% of the panels from Plant B were defective. Thus;

0.04A + 0.02B = 500   ------(2)

Put eq 1 in eq 2 to get;

0.04(B - 4000) + 0.02B = 500

0.04B - 160 + 0.02B = 500

0.06B = 660

B = 660/0.06

B = 11000 panels

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It is not possible to graph f(x) = 100(0.772) without additional information. A function needs at least two points to graph a line. The expression f(x) = 100(0.772) represents a constant value, not a function of x, so it cannot be graphed on its own.

Answer: knvsvvs

Step-by-step explanation:

4A. The number of whole pie shaded are 2

4B . The number of partial pie shaded is 3

4C.  The mixed number formed is 2 3/5

5A. The whole number part which is 2 is the quotient

5B.  The remainder is 3

In mathematics, a fraction is a number that represents a part of a whole. It consists of two parts: a numerator, which is the part of the fraction that represents the number of parts being considered, and a denominator, which is the number that represents the total number of parts in the whole.

A mixed number is a combination of a whole number and a fraction. It represents a quantity that is greater than the fraction but less than the next whole number.

For example, In the division problem, the dividend is 13 and and the divisor is 5. the division results to mixed number of value 2 3/5.

The mixed number 2 3/5 represents a quantity that is equal to

two whole and three fifths.

converting to improper fractions gives 13/5

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Answer:

The height of the kite above the ground is; approximately 50.69 feet.

What are trigonometric identities?

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

The height of his hands above the ground, h is given by 3 feet

Angle of elevation of the string (above the horizontal), θ = 32°

Length of the string, l is given as 90 feet

The height of the kite above the ground is given by trigonometric ratios as ;

Sin∅ =h /90

Sin 32°= h/90

0.52 =h /90 (Sin32°= 0.52)

so h= 47.69 feet

Then height from ground is (H) = 3 +47.69  

H = 50.69 feet

The height of the kite above the ground ,  ≈ 50.69 feet

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Step-by-step explanation:

Answer:

25 minutes

Step-by-step explanation:

Subtract the two times to find the duration.

Answer:

Step-by-step explanation:

c

a

The height of the tree to the nearest foot is 27 feet.

The height of the tree can be found as follows:

The height of the tree can be found using trigonometric ratios. Therefore,

let

tan ∅ = opposite / adjacent

Therefore,

opposite side = adjacent tan ∅

Hence,

height of the tree = 20 + x tan 45° = x tan 75°

20 + x tan 45° = x tan 75°

20 tan 45 + x tan 45° = x tan 75°

20 tan 45 =  x tan 75° -  x tan 45°

20 tan 45 =  x(tan 75 - tan 45)

20 tan 45 = x(3.73205080757 - 1)

2.73205x = 20

x = 20 / 2.73

x  = 7.32600732601

x = 7.34

Therefore,

height of the tree = x tan 75°

height of the tree = 7.34 × tan 75°

height of the tree = 27.3186119114

height of the tree = 27 ft

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Answer:

[tex]-\dfrac{4}{5}[/tex]

Step-by-step explanation:

We have the following expression

[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x[/tex]

and asked to evaluate this expression at  [tex]\[x = {2\over\displaystyle 5\][/tex]

First convert [tex]3 \; \dfrac{1}{2}[/tex]   and  [tex]5 \; \dfrac{1}{2}[/tex]  to mixed fractions

[tex]3 \; \dfrac{1}{2} = \dfrac{3 \times 2 + 1}{2} = \dfrac{7}{2}\\[/tex]

[tex]5 \; \dfrac{1}{2} = \dfrac{5 \times 2 + 1}{2} = \dfrac{11}{2}[/tex]

Therefore
[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x\\\\= \dfrac{7}{2}x - \dfrac{11}{2}x\\\\= \dfrac{7 - 11}{2} x\\\\= -\dfrac{4}{2}x \\\\= -2x\\\\[/tex]

[tex]\mathrm{For \;x =\dfrac{2}{5}},\\\\= -2x \\= - 2 \times \dfrac{2}{5}\\\\= -\dfrac{4}{5}[/tex]

get rid of y. that's all you have to do.

The average rate of change of f(x) over the interval 3≤x≤4 is 15

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

The table of values

On the table, we have

f(3) = -4

f(4) = 11

The average rate is then calculated as

Average rate = [f(4) - f(3)]/[4 - 3]

Substitute the known values in the above equation, so, we have the following representation

Average rate = (11 + 4)/(4 - 3)

Evaluate

Average rate = 15

Hence, the average rate is 15

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Complete question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.

X f(x)

3 -4

4 11

5 8

6 10

7 11

8 14