Find the prime factorization of
the number 90.
Order the factors from least to greatest.
Remember, 1 is not a prime number.
[?] × [ ] × [ ] × [ ]
X
X
Enter the number that belongs in the green box.

Answer:|x-1|-2

Step-by-step explanation: see picture below!

The equation is [tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].

What is meant by zeroes of polynomials?

All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.

It is given that degree of the equation is 5. so the highest power is 5 and there will be 5 zeroes.

It is given that 2 zeroes at x=1 and 3 zeroes at x= 3.

So, the equation is [tex]y=a(x-1)^{2} (x-3)^{3}[/tex].

We will substitute x=2 and y= 87 in the above equation.

[tex]87=a(2-3)^{3} \\a=-87[/tex]

Therefore now the equation will be:

[tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].

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(i) The probability that the bulb that lang selects will last exactly 9950 hours is 0.3085.

(ii) The probability that the bulb that lang selects will last at most 9950 hours is 0.5

(iii) The probability that the bulb that lang selects will last at least 9950 hours is 0.6915.

(iv) The probability that the bulb that lang selects will last less than 9000 hours or more than 11,500 hours is 0.0668

(v) The probability that the bulb that lang selected will last between 9000 hours and 11,000 hours, inclusively is  0.6826.

(vi) The life length represents the 95th percentile is 11,645

The lifespan of the Lights of America light bulb is normally distributed, with a mean of 10,000 hours and a standard deviation of 1000 hours. This means that the majority of bulbs will last around 10,000 hours, but there will be some that last longer or shorter than this.

(i) To find the probability that the bulb selected by Lang will last exactly 9950 hours, we need to use the normal distribution formula. We know that the mean is 10,000 hours and the standard deviation is 1000 hours. Using these values, we can calculate the z-score (standardized value) for 9950 hours.

z = (9950 - 10000) / 1000 = -0.5

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. Therefore, the probability that the bulb will last exactly 9950 hours is 0.3085.

(ii) To find the probability that the bulb will last at most 9950 hours, we need to find the area under the normal curve to the left of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).

z = (9950 - 10000) / 1000 = -0.5

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at most 9950 hours, we need to add the area under the normal curve to the left of -0.5, which is 0.3085 + 0.1915 = 0.5. Therefore, the probability that the bulb will last at most 9950 hours is 0.5.

(iii) To find the probability that the bulb will last at least 9950 hours, we need to find the area under the normal curve to the right of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).

z = (9950 - 10000) / 1000 = -0.5

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at least 9950 hours, we need to add the area under the normal curve to the right of -0.5, which is 1 - 0.3085 = 0.6915. Therefore, the probability that the bulb will last at least 9950 hours is 0.6915.

(iv) To find the probability that the bulb will last less than 9000 hours or more than 11,500 hours, we need to find the areas under the normal curve to the left of 9000 hours and to the right of 11,500 hours, and add them together. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,500 hours.

For 11,500 hours: z = (11,500 - 10,000) / 1000 = 1.5

Then the corresponding probability from Z table is written as,

=> 0.0668

(v) To find the probability that the bulb will last between 9000 hours and 11,000 hours, inclusively, we need to find the area under the normal curve between the z-scores for 9000 hours and 11,000 hours. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,000 hours.

For 9000 hours: z = (9000 - 10,000) / 1000 = -1

For 11,000 hours: z = (11,000 - 10,000) / 1000 = 1

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -1 (for 9000 hours), which is 0.1587, and the probability of a z-score of 1 (for 11,000 hours), which is 0.8413. Subtracting the area under the normal curve to the left of -1 from the area under the normal curve to the left of 1, we get the probability of the bulb lasting between 9000 hours and 11,000 hours inclusively, which is 0.8413 - 0.1587 = 0.6826.

(vi) To find the lifelength that represents the 95th percentile, we need to find the z-score that corresponds to the 95th percentile of the normal distribution. We can use a standard normal distribution table or calculator to find this value, which is approximately 1.645.

Using the z-score formula, we can solve for the life length that corresponds to a z-score of 1.645:

1.645 = (x - 10,000) / 1000

Multiplying both sides by 1000 and adding 10,000, we get:

x = 11,645

Therefore, the life length that represents the 95th percentile is 11,645 hours, which means that only 5% of bulbs will last longer than this value.

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The total volume of the space dome theatre is 41867 m³.

In geometry, a sphere is a three-dimensional solid figure, which is round in shape.

The surface area is 4πr².

The volume is (4/3)πr³.

The diameter is 2×radius of the sphere.

A cylinder is a three-dimensional solid object having two similarly circular bases that are joined by a curving surface that is positioned a certain distance from the center.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, The space dome theatre has a base radius of 20m.

Therefore, The volume of the hemispherical dome is,

= (2/3)π(20)³.

= (2/3)π×8000.

= (16000/3)π m³.

And, As the dome base has a radius of 20 m the cylindrical shape will also have the same.

Therefore, The volume of the cylindrical shape is,

= π(20)²×20.

= 8000π m³.

And, The total volume is the sum of the volumes of two shapes,

= 8000π + (16000/3)π m³.

= [(24000 + 16000)/3]π m³.

= (40000/3)π m³.

= 41867 m³.

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Answer: 151 minutes

Step-by-step explanation:

95.40 - 35 =

60.40

60.40/.40 = 151

Answer:

The possible values of the constant b are:

[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]

Step-by-step explanation:

The coefficient of x² in the expansion of (2 - x)(3 + bx)³ can be found by expanding the brackets.  

Expand the cubed part by using the (a + b)³ formula:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Therefore:

[tex]\begin{aligned}(3 + bx)^3 &= (3)^3 + 3(3)^2(bx) + 3(3)(bx)^2 + (bx)^3\\&= 27 + 27bx + 9b^2x^2 + b^3x^3\end{aligned}[/tex]

So:

[tex](2-x)(3 + bx)^3 = (2-x)(27 + 27bx + 9b^2x^2 + b^3x^3)[/tex]

To find the coefficient of the term in x², multiply the constant in the first parentheses by the coefficient of the term in x² in the second parentheses and add this to the product of the coefficient of the term in x in the first parentheses and the coefficient of the term in x in the second parentheses:

[tex](\bold{2}-x)(27 + 27bx + \bold{9b^2}x^2 + b^3x^3)\\\phantom{.}\underbrace{\uparrow \qquad \qquad\qquad\qquad\;\uparrow}\\ \phantom{wlwww}\text{multiply}[/tex]

[tex](2-x)(27 + \bold{27b}x + 9b^2x^2 + b^3x^3)\\\phantom{bbb..}\underbrace{\uparrow \qquad \quad\;\uparrow}\\ \phantom{ww.w}\text{multiply}[/tex]

Therefore, the expression for the coefficient of x² is:

[tex]2 \cdot 9b^2 + (-1) \cdot 27b[/tex]

Since the coefficient of x² in the expansion is 45, set the expression to 45 and solve for b:

[tex]\begin{aligned}2 \cdot 9b^2+(-1) \cdot 27b&=45\\18b^2-27b&=45\\18b^2-27b-45&=0\\9(2b^2-3b-5)&=0\\2b^2-3b-5&=0\\2b^2-5b+2b-5&=0\\b(2b-5)+1(2b-5)&=0\\(b+1)(2b-5)&=0\\\\ \implies b+1&=0 \implies b=-1\\ \implies 2b-5&=0 \implies b=\dfrac{5}{2}\end{aligned}[/tex]

Therefore the possible values of the constant b are:

[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]

Rounding this to the nearest cent, the total amount that was wanted to be saved is $64.29.

To solve this problem, we can set up a proportion using the given information. Let x be the total amount that was wanted to be saved.

We know that the amount saved ($45) is 70% of the total amount that was wanted to be saved. Therefore, we can write:

45 = 0.7x

To solve for x, we can divide both sides by 0.7:

x = 45 ÷ 0.7

x = 64.28571429

The answer to the problem is $64.29, rounded to the nearest cent. This means that the total amount that was wanted to be saved was $64.29, and 70% of this amount is equal to the amount that was actually saved ($45). To check our work, we can multiply 64.29 by 0.7 to see if it equals 45. When we do this, we get:

64.29 x 0.7 = 45.003, which rounds to $45, so our answer is correct.

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Answer: .75 + .25x ≤ 7

Step-by-step explanation: The x equals the amount that you can buy for each item.

Check the picture below.

so the polygon is really just a 5x7 rectangle with a triangle that has a base of 7 units(vertically) and a height of 2 units.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(5)(7)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(7)(2)}}\implies 35~~ + ~~7\implies \text{\LARGE 42}~units^2[/tex]

Answer:

y = -5 [tex]\frac{1}{5}[/tex] o r -5.02 as a decimal

Step-by-step explanation:

-5(y + 0.2) = 25  Distribute the -5

-5(y) + -5(0.2) = 25   Adding a negative is the same as subtracting a positive

-5y - 1 = 25   add 1 to both sides

-5y - 1 + 1 = 25 + 1

-5y = 26  Divide both sides by -5

[tex]\frac{-5y}{-5}[/tex] = [tex]\frac{26}{-5}[/tex]

y = -5 [tex]\frac{1}{5}[/tex] o r -5.02 as a decimal

Answer: To solve the equation -5(y + 0.2) = 25, we need to isolate y by performing the following steps:

Distribute the -5 to the expression inside the parenthesis:

-5 * y - 5 * 0.2 = 25

-5y - 1 = 25

Add 1 to both sides of the equation to isolate -5y on one side:

-5y - 1 + 1 = 25 + 1

-5y = 26

Divide both sides of the equation by -5 to find y:

(-5y) / -5 = 26 / -5

y = -5.2

So, the solution to the equation -5(y + 0.2) = 25 is y = -5.2.

Step-by-step explanation:

Answer: 57

Step-by-step explanation: I recommend learning angle properties, pictures on the internet might help ya out

Ivan would expect to make $43.67 in profit if he had 50 customers.

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

Expected Profit = 1.45 • Customers – 28.83.

If Ivan had 50 customers, using the least squares regression equation, the expected profit would be:

Expected Profit = 1.45 * 50 - 28.83

So, we have

Expected Profit = 72.5 - 28.83

Evaluate the difference

Expected Profit = 43.67

Hence, the expected profit is $43.67

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Complete question

Ivan has a lemonade stand. He keeps records of his daily profits and how many customers he had that day. The scatter plot shows his profits versus the number of customers for 25 days.

The least squares regression equation is:

Expected Profit = 1.45 * Customers - 28.83.

How much profit would Ivan expect to make if he had 50 customers?

Answer:

To solve the system of equations graphically, you can plot the two lines on a coordinate plane and find the point where they intersect, which represents the solution to the system.

First, let's start by rewriting the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

For the first equation:

3x + y = 15

y = -3x + 15

For the second equation:

3x - 4y = 0

y = (3/4)x

Next, we can plot these two lines on a coordinate plane by using any two points on each line and connecting them with a straight line.

Once the lines are plotted, we can find the point where they intersect, which represents the solution to the system. In this case, the solution is (2, 9), meaning that at x = 2 and y = 9, both equations are satisfied.

So, the solution to the system of equations is (2, 9), which means that the two lines intersect at the point (2, 9).

Answer: 19

Step-by-step explanation: 15 x 19 = 285ft^2

A. passenger train 36mph

B. freight train 18mph

What is meant by speed?

Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.

Given that, A freight train departs from a train depot and let us consider it is travelling at an 'x' mph

and An hour later a passenger train departs the same train depot with a speed 'of x+18 mph.

After 2 hours the passenger train overtakes the freight train.

The total distance travelled by both trains when the passenger train overtakes the freight is equal.

Distance travelled by freight train = x*3

Distance travelled by passenger train = (x+18)*2

Now, 3x = 2x + 36

x = 18

and x + 18 = 36

Therefore, The speed of the passenger train and freight train are 36mph, and 18mph respectively

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On solving the provided question, we cans ay that  in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in this triangle by Pythagorean theorem

[tex]A^2 = B^2 + C^2[/tex]

AC = [tex]\sqrt{14^2 - 9^2}[/tex]

AC  = [tex]\sqrt{196 - 81}[/tex]

AC = [tex]\sqrt{115}[/tex]

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A graph of the system of linear equations y = -2x + 2 and y = -2x + 1 is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the given system of equations has no solution because both lines have the same slope and are parallel.

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The approximate arc length of one slice of pic is 5.24 inches according to the circle circumference.

Let us assume that the pic is equally cut into 6 pieces. Also given that the diameter of the pie is 10 inches.

Diameter (D)=10.

So the radius will be D/2.

Radius (R)=10/2=5.

The pie's circumference is given by:

C=2πR

C=2π*5

C= 10π (in)

Because the pie is divided into six pieces, the circumference of the pie is divided into six equal-length arcs. So,

Length of Arc (L)= 10π/6

L = 5π/3

L= 5(3.14)/3

L=5.234=5.24

Therefore the approximate arc length of one slice of pie is 5.24 inches.

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The total cost of the item would be [tex]$115[/tex].The original price of oranges purchased by Mr. S Ralph can be calculated by subtracting the sales tax from the total cost.

Sales tax is calculated as a percentage of the original price. In this case, the sales tax is 15%, meaning that the original price can be found by dividing the total cost (which includes the sales tax) by 1.15.To calculate the original price of the oranges, divide the total cost of $165.31 by 1.15. This gives us a total of $143.87. Thus, the original price of the oranges purchased by Mr. S Ralph is $143.87 without the sales tax included.Sales tax is a form of taxation imposed by governments on goods and services. Generally, for the majority of goods and services, the sales tax is calculated as a percentage of the original price. This means that the total cost of the goods or services can be calculated by adding the percentage of sales tax to the original price.For example, if an item costs $100, and the sales tax rate is 15%, the total cost of the item would be calculated by multiplying the original price by 1.15 (100% + 15% = 115%). The total cost of the item would be [tex]$115[/tex].

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Answer:

$90

Step-by-step explanation:

180 - 50% or 180 x .50 = $90

Answer:

The required measure of Street K between Street C and D is 337.5 ft.

Step-by-step explanation:

have a nice day.

The system of equations that correctly represents the situation of Lina and Sarika's ages are:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations is called simultaneous equations.

The sum of Lina and Sarika's ages = 31

Lina's age > Sarika's by 5 years

Let Lina's age = L

Let Sarika's age = S

L + S = 31... Equation 1

L - S = 5... Equation 2

2L = 36

L = 18.

Substituting L = 18 into either Equation 1 or 2:

18 + S = 31

S = 31 - 18

S = 13

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The solution to the equation 2n + 5 = 6( n² - 5 ) is n = ( 1 - √(211 )) / 6 and n = ( 1 + √(211 )) / 6

Given the quadratic equation in the question;

2n + 5 = 6( n² - 5 )

First we simplify the given equation;

2n + 5 = 6( n² - 5 )

2n + 5 = 6n² - 30

6n² - 2n - 5 - 30 = 0

6n² - 2n - 35 = 0

To solve for n, we use the quadratic formula.

n = (-b±√(b² - 4ac)) / (2a)

Compare 6n² - 2n - 35 = 0 to the quadratic equation in its standard form an² + bn + c = 0.

Plug the values into the quadratic formula

n = (-b±√(b² - 4ac)) / (2a)

n = ( -(-2) ±√( (-2)² - 4 × 6 × -35 )) / (2 × 6 ))

n = ( 2 ±√( 4 + 840 )) / ( 12 )

n = ( 2 ±√( 844 )) / ( 12 )

n = ( 2 ±2√(211 )) / ( 12 )

n = ( 1 ± √(211 )) / 6

n = ( 1 - √(211 )) / 6 or n = ( 1 + √(211 )) / 6

Therefore, the values of n are ( 1 - √(211 )) / 6 and ( 1 + √(211 )) / 6.

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The exponential function for the given table will be y=0.01(2)ˣ where x=positive integer.

What exactly are exponential functions?

An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is termed the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis.

Growth that is exponential

The amount expands extremely slowly at first, then rapidly in Exponential Growth. The rate of change accelerates with time. As time passes, the pace of growth accelerates. The quick expansion is designed to represent a "exponential rise".

The exponential growth formula is: y = a (1+ r)ˣ, where r is the growth percentage.

Now,

as given in the table initial value = 0.01

and it is increasing into multiples of 2ˣ where x=positive integer

Then for the value of y for any value of x will be

y=0.01(2)ˣ where x=positive integer

Hence,

           The exponential function for the given table will be y=0.01(2)ˣ.

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Answer:

CD = 36°

Step-by-step explanation:

the measure of secant angle BFE is half the difference of the measures of the intercepted arcs , that is

[tex]\frac{1}{2}[/tex] (BE - CD) = ∠ BFE

[tex]\frac{1}{2}[/tex] (128 - x) = 46 ( multiply both sides by 2 to clear the fraction )

128 - x = 92 ( subtract 128 from both sides )

- x = - 36 ( multiply both sides by - 1 )

x = CD = 36°

Answers:

===========================================

Work Shown:

[tex]15 \text{ m} = (15 \text{ m})*\frac{100 \text{ cm}}{1 \text{ m}} = 1500 \text{ cm}\\\\\\1.6 \text{ km} = (1.6 \text{ km})*\frac{1000 \text{ m}}{1 \text{ km}}*\frac{100 \text{ cm}}{1 \text{ m}} = 160,000 \text{ cm}\\\\\\467 \text{ mm} = (467 \text{ mm})*\frac{1 \text{ cm}}{10 \text{ mm}} = 46.7 \text{ cm}[/tex]

Each conversion fraction is set up to cancel out any unit that isn't "centimeters".

Side notes:

The length of the third side of ALMN is 20 units.

If AGHI and ALMN are similar, then their corresponding sides are proportional.

Let's call the length of the third side of ALMN "x". We can set up the proportion using the two sides of AGHI and ALMN that we know:

10/8 = 15/12 = x/16

To find x, we can cross-multiply and simplify:

15 × 16 = 12x

240 = 12x

x = 240/12

x = 20

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The volume of the rectangular prism will be 270 cm³. The correct option is B.

The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.

The volume of the rectangular prism will be the multiplication of the three parameters which are Length, Width, and Height of the prism.

The volume will be calculated by the formula:-

Volume = L x W x H
Volume = 2 x 9 x 15

Volume = 270 cubic cm

The volume of the rectangular prism will be 270 cm³.

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The complete question is given below and the missing image is attached with the answer below.

A ringtoss toy is composed of a rectangular prism on top of a cylinder.

The rectangular prism is completely filled with water.

The dimensions of the rectangular prism are shown in the diagram.

What is the volume of the rectangular prism in cubic centimeters?

A) 26 cm3

B) 270 cm3

C) 165 cm3

D) 348 cm3