Mrs, Hansen usually makes a disinfecting solution by adding 1 2/3 cups of bleach to 5 gallons of water. Today, however, she is using only 3 1/2 gallons of water. She wants to make the solution so that it has the same disinfecting strength. How much bleach should she use?

An absolute value inequality that expresses the actual temperature in your city, given that the average January temperature is 45° F and the temperature can vary up to 5° F warmer or colder, would be: | x - 45 | ≤ 5.

Where x represents the actual temperature in degrees Fahrenheit.

An inequality with an absolute value expression is referred to as an absolute value inequality. A quantity is enclosed in vertical bars (| |), which stand for the distance between that quantity and zero on the number line, to indicate an absolute value statement. The absolute value of an integer is always positive, hence regardless of the sign of x, |x| indicates the distance of x from zero.

Finding all feasible values of the variable that meet the inequality is the goal when resolving an absolute value inequality. To accomplish this, we first isolate the expression defining the absolute value, and then divide the inequality into two cases, one for positive and one for negative expressions defining the absolute value. Then, we resolve each case separately and combine the solutions.

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Answer:

49u² - 154u + 121  factored is  (7u - 11)²

Step-by-step explanation:

To factor the given quadratic expression, 49u² - 154u + 121, rewrite in the form a² - 2ab + b².

Rewrite 49 as 7² and 121 as 11²:

[tex]\implies 7^2u^2-154u+11^2[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^n \cdot c^n=(ac)^n:[/tex]

[tex]\implies (7u)^2-154u+11^2[/tex]

Rewrite 154u as 2 · 7u · 11 :

[tex]\implies (7u)^2-2 \cdot 7u \cdot 11+11^2[/tex]

Compare with the form a² - 2ab + b²:

Apply the perfect square formula: a² - 2ab + b² = (a - b)²

[tex]\implies (7u)^2-2 \cdot 7u \cdot 11+11^2=(7u-11)^2[/tex]

Answer:

A and D

Step-by-step explanation:

They both dont touch and go in the sam direction

Answer:

Below

Step-by-step explanation:

It APPEARS that First and last choices are true.....the lines do not cross in the picture...BUT you cannot say for SURE they are parallel  without more information about the angles at  D E H and I    ....or markings

Using the unitary method, we found that the unit rate of slime is 0.2 cups per container.

What is meant by 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. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.

Given,

 Number of cups of slime = 7.2

  Number of containers = 36

 Unit rate = Amount of slime in each container

Using the unitary method we can find the unit rate.

7.2 cups = 36 containers

1 container = 7.2/36 = 0.2 cups.

Therefore using the unitary method, we found that the unit rate of slime is 0.2 cups per container.

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"When solving an inequality, if you the coefficient is negative, as in-3x > 9, the inequality" statement becomes: true

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers. The equals sign in the equation-like phrase 7x 4 > 2x + 5 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 7x 4, is larger than the right part, 2x + 5, in the equation. Finding the values of x for which the inequality holds true will be of importance to us.

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Answer:

54 and 47

Step-by-step explanation:

Lets first number be "x" and second number be "y"

x = y + 7

x + y = 101

(y + 7) + y = 101

2y + 7 = 101

2y = 94

y = 47

x = 47 + 7

x = 54

Triangle is a polygon with 3 sides. The record of the letters in your triangle from left to right is EGFBIHDCA.

A triangle is a polygon with 3 sides. Also, It has three vertices.

As the example is given to us, ABCDEFGHI is the record of the letters that are when seen from top to bottom, therefore, if we rotate the triangle such that the left side of the triangle is on the upper side, then the triangle we will get is given below.

Thus, the record of the letters in your triangle from left to right is EGFBIHDCA.

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Answer:

Step-by-step explanation:

The formula for calculating the future value of a continuously compounded investment is:

FV = PV * e^(rt)

where PV is the present value, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.718.

Plugging in the given values, we get:

FV = 5100 * e^(0.08 * 13) = 5100 * e^1.04 = 5100 * 2.856116786 = 14536.86

So, the future value of the investment after 13 years at an 8% interest rate compounded continuously would be approximately $14,536.86. Rounded to 2 decimal places, this is $14,536.86.

Answer:

a -3.9

Step-by-step explanation:

Subtract 13 from both sides which makes it -19 > 5x. then divide by 5 on both sides

Possible answers are:

3

4

5

6

7

8

9

When x changes from 2 to 5, the average velocity (or average rate of change of y with respect to x) is 9.33 m/s. When x changes from 2 to 2 + h, the average velocity is 2 + hm/s.

Average speed is determined by dividing the total distance you travelled by the total time, whereas average velocity is determined by dividing your displacement (a vector Throughout the entire period, position to your finish position).

(A) The following formula is used to get the average velocity when x changes from 2 to 5:

value of y at x = 2

= 2²+2 = 6 m

value of y at x = 5

= 5²+5 = 30 m

displacement equals 30 – 6 = 24 m.

Time is 5 - 2 = 3 seconds.

average velocity

= displacement /Time duration

= 24/3 = m/s

B) Value of y at x = 2 = 5 for x changing from x to x plus ie for minimal change in x.

Displacement during a little change in x will be 0 because the value of y will once again be 5.

C )  

y(x) = x² + x

dy / dx = 2x + 1

dy / dx  represents instantaneous  velocity

so when x = 2

instantaneous velocity = 2 x 2 +1

= 5 m /s

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The binomial distribution P( x = 4 ) if n = 5 and p = 0.7 is 0.3602.

Binomial probability distribution determines the probability of a discrete random variable.

Given that;

Using the formula, probability mass function;

P( X = x ) = ⁿCₓPˣ( 1 - P )ⁿ⁻ˣ

P( X = x ) = ⁵Cₓ × 0.7ˣ × ( 1 - 0.7 )⁵⁻ˣ

Now for P( x = 4 )

P( X = 4 ) = ⁵C₄ × 0.7⁴ × ( 1 - 0.7 )⁵⁻⁴

P( X = 4 ) = ⁵C₄ × 0.7⁴ × ( 1 - 0.7 )

P( X = 4 ) = 5 × 0.2401 × 0.3

P( X = 4 ) = 0.3602

Therefore, the value of P( x = 4 ) is 0.3602.

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To find the x-intercept of the equation 3x + 5y = 9, we set y = 0 and solve for x.When y = 0, the equation becomes 3x + 5(0) = 9, which simplifies to 3x = 9.Solving for x, we get x = 3.The x-intercept of the equation 3x + 5y = 9 is (3, 0).

What is x-intercept ?

An x-intercept is a point where a graph or a line crosses the x-axis. It is the value of the independent variable (x) when the dependent variable (y) is equal to zero. In other words, it is the point at which a function or equation intersects the x-axis, and its coordinates are of the form (x, 0). To find the x-intercept of a graph or equation, you can set y=0 and solve for x.

To find the x-intercept of the equation 3x + 5y = 9, we need to set y = 0 and solve for x.

So, we have:

3x + 5(0) = 9

3x = 9

x = 3

Therefore, the x-intercept of the equation 3x + 5y = 9 is (3,0), which means the point where the line intersects the x-axis is (3,0).

To verify, we can graph the equation and see that the point (3,0) is indeed on the x-axis.

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Answer: a) The probability that the system will fail during a 3-month period can be calculated as the sum of the probabilities of subsystem A and subsystem B failing, since the system fails if either one fails. The probability of subsystem A failing in 3 months is given by P(A) = 1 - e^(-0.2 * 3) * (1 + 0.2 * 3 + (0.2 * 3)^2 / 2!) = 0.0664. The probability of subsystem B failing in 3 months is given by P(B) = 1 - e^(-1.2 * 3) * (1 + 0.2 * 3 + (0.2 * 3)^2 / 2!) = 0.36. Therefore, the probability that the system will fail in 3 months is P(system) = P(A) + P(B) = 0.0664 + 0.36 = 0.4264.

b) To find the probability that there will be no more than two failures of the system during a 6-month period, we need to use the cumulative distribution function (CDF) of the Poisson distribution. Let X be the number of failures of the system in 6 months. The CDF is given by F(x) = P(X <= x) = 1 - P(X > x), where P(X > x) is the probability that there will be more than x failures. Therefore, the probability that there will be no more than two failures of the system during a 6-month period is given by F(2) = 1 - P(X > 2). We can use the formula for the Poisson distribution to find P(X > 2), which is P(X > 2) = e^(-6 * (P(A) + P(B))) * ((6 * (P(A) + P(B)))^3 / 3! + (6 * (P(A) + P(B)))^2 / 2! + 6 * (P(A) + P(B)) / 1! + 1). Plugging in the values for P(A) and P(B) from part (a), we get F(2) = 1 - e^(-6 * 0.4264) * ((6 * 0.4264)^3 / 3! + (6 * 0.4264)^2 / 2! + 6 * 0.4264 / 1! + 1) = 1 - 0.2079 = 0.7921.

c) To find the probability that the next system failure will occur within a year, we need to find the cumulative distribution function (CDF) of the time between failures, which is the sum of the time between failures of subsystem A and subsystem B. Let X be the time between failures of subsystem A, which follows an exponential distribution with rate 0.2 per month. Let Y be the time between failures of subsystem B, which also follows an exponential distribution with rate 1.2 * 0.2 = 0.24 per month. Then the CDF of the time between failures is given by F(t) = P(X + Y <= t) = 1 - P(X + Y > t0.2 * 12) * e^(-0.24 * 12) = 1 - 0.17 = 0.83. Therefore, the probability that the next system failure will occur within a year is 0.83.

Step-by-step explanation:

The equation for the graphed quadratic function is:

y = -1*(x - 3)^2 + 2

Here we have the graph of a quadratic equation. Remember that if the leading coefficient is a and the vertex is (h, k) then we can write:

y = a*(x - h)^2 + k

Here the vertex is at (3, 2) then we can write:

y = a*(x - 3)^2 + 2

We can see that it also passes through the point (1, -2), replacing these values we will get:

-2 = a*(1 - 3)^2 + 2

-2 = a*4 + 2

-2 - 2 = a*4

-4/4 = a = -1

Then the quadratic equation is:

y = -1*(x - 3)^2 + 2

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Answer:

ummmm i would say unbiased fam only bc i love ice cream and i always wonder whichwtch one does people like more.

Step-by-step explanation:

C - this equation is simplified to a numeric identity. the variable has infinite solutions.

8k - 14 = -4k + 10 + 12(k - 2) --> use distributive property

8k - 14 = -4k + 10 + 12k -24 --> combine like terms

8k - 14 = 8k -14 --> combine like to each side

8k - 8k = -14 + 14 --> simplify

0 = 0

note, the variable cancels out, therefore there is no identity and ANY numeroc value can be used, as ant value will cancel itself out.

this means there is an infinite numbers of solutions.

Shipping Central charges $0.51 more than Globe Delivery for any given weight of the package.

The cost for shipping a package that weighs x pounds from Boise to Los Angeles is shown below.

Company                    Cost ($)

Shipping Central        3x+3.50

Globe Delivery          2x + 2.99

To determine the amount more Shipping Central charges than Globe Delivery, you can subtract the cost function for Globe Delivery from the cost function for Shipping Central.

The difference between the two cost functions is:

3x + 3.50 - (2x + 2.99) = x + 0.51 = $0.51 + x

This means that, for any given weight of the package, Shipping Central charges $0.51 more than Globe Delivery.

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Answer:

12756pi km

Step-by-step explanation:

Circumference = pi * diameter

Diameter = radius * 2

kilometer = meter/1000

6378000*2= 12756000

diamter = 12756000 meters

12756000/1000 = 12756 kilometers

diameter = 12756 kilometers

12756pi km= circumference

The distance from the apex, or top of the pyramid, to each vertex of base is 10.9.

A right rectangular pyramid is a pyramid, with four slant sides, and a rectangular base, such that all the sides are congruent and the vertex is atop of the midpoint of the base rectangle.

Suppose the base of the pyramid has length = l units, and width = w units.

Suppose that the height of the pyramid is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]

is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

Given that;

Altitude of pyramid= 10

Each side base of pyramid= 6

Now,

So using pythagorean theorem,

x2=y2+(10)2....1

with y half of the length of the diagonal of the base.

2y=length of the diagnol

and (2y)2 = 72

4y2=72

y = 3√2.

So substitute y in eq1 and get x

( 3√2)2+(10)2=(x)2

(x)2=118

x=10.86.

x≈10.9

Therefore, the side of  right square pyramid will be 10.9.

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The values of x and y would be   [tex]x=\frac{20 \sqrt{3}}{3}[/tex] and [tex]y=\frac{40\sqrt{3}}{3}[/tex].

What are trigonometric ratios?

Trigonometric ratios are mathematical functions that describe the relationship between the angles and sides of a right triangle. The three main trigonometric ratios are the sine, cosine, and tangent.

In the given figure, by using trigonometric ratios, we can find x

tan60° = 20/x

√3 = 20/x

x = 20/√3

=> [tex]x=\frac{20 \sqrt{3}}{3}[/tex]

Now by using the ratio sin60°

sin60° = 20/y

√3/2  = 20/y

y = 40/√3

[tex]y=\frac{40\sqrt{3}}{3}[/tex]

Hence, the values of x and y would be   [tex]x=\frac{20 \sqrt{3}}{3}[/tex] and [tex]y=\frac{40\sqrt{3}}{3}[/tex].

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Answer:

simple interest is $6.8

Miguel pay the amount to Julio at the end of 6​ months was $206.8

Step-by-step explanation:

Given : Miguel Rodriguez borrowed ​$200 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.8​%.

To Find : ​a) How much will the interest amount​ to?

​b) What amount must Miguel pay Julio at the end of 6​ months?

Solution :

Formula for simple interest :

Where rate is in decimal

Time is in years

So, rate of interest = 6.8 % = 0.068

Time = 6 months = 6/12=0.5

Principal = $200

Thus= 200x0.068x0.5=6.8

Answer:

2) 47 snow globes (51+8-12) 23) 130 snowballs (46+59+25) 4) 92 penguins (83+69-55)

Step-by-step explanation :

Sum of first 50 terms for the AP:

[tex]\dashrightarrow { \boxed{\sf S = \dfrac{n}{2} (2a + (n - 1)d )}}[/tex]

where ,

On substituting the values , we get :

[tex]\dashrightarrow \sf S = \dfrac{50}{2}(2 \times 8 + (50 - 1) \times 12) \ \\ \\ \dashrightarrow \sf S = 25(16 + 49 \times 12 ) \\ \\ \dashrightarrow \sf S = 25(16 + 588 )\\ \\ \dashrightarrow \sf S = 25(604 )\\ \\ \dashrightarrow \sf S = 15100 \\ [/tex]

[tex] \therefore[/tex] Sum of the first 50 terms is 15100

The angle measure m<T is equivalent to 78 degrees

Similar triangles are triangles that have similar sides and angles.

From the given triangle

<A = <R

<B = <S

<C = <T

Since the sum of angle in a triangle is 180 degrees, hence;

<A + <B + <T = 180

24 + 78 + <T = 180

102 + <T = 180

<T = 180 - 102
<T = 78 degrees

Hence the measure of m<T from the triangle is 78 degrees

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Size of the house should be 2900 ft².

Correct option is B.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Equation for the line that expresses price of house

y = 0.06x + 60.5

where y is the price in thousand dollars, x is area in square feet.

Price of the house = $235000

⇒ y = 235

Then,

235 = 0.06x + 60.5

0.06x = $235 - 60.5

0.06x = 174.5

x = 174.5/0.06

x = 2908.33 ≈ 2900

Hence, 2900 ft² should be the size of the house.

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The function for the given zeros is f(x)=2x³-8x²+8x-32.

The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.

Given that, n=3.

x=4 and x=2i

We then know that the third root must be x=-2i

Now, f(x)=a(x-4)(x-2i)(x+2i)

= a(x-4)(x²-(-2i)²)

= a(x-4)(x²-(-4))

= a(x-4)(x²+4)

= ax²(x-4)+4(x-4)

f(x)= a(x³-4x²+4x-16)

f(1)=a(1³-4×1²+4×1-16)

-30=a(1-4+4-16)

a=2

Now, f(x)=2(x³-4x²+4x-16)

f(x)=2x³-8x²+8x-32

Therefore, the function is f(x)=2x³-8x²+8x-32.

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The measure of angle that is an exterior angle to B is 95°.

The angle created by any extended side of a triangle and its neighboring side is referred to as the external angle of a triangle. A triangle has three external angles. It should be noticed that every outside angle and corresponding interior angle constitute a linear pair. We are aware that a triangle's internal angle is created when its sides come together at its apex.

Given that,

The measure of angle 4 is 120°, and the measure of angle 2 is 35°.

Triangle A B C. Angle A is 2, angle B is 1, and angle C is 3. The exterior angle to angle B is 5, and the exterior angle to angle C is 4.

The sum of an interior and exterior angle is 180°,

∠4 + ∠3 = ∠1 + ∠5 = ∠2 + ∠6 = 180°

and ∠2+ ∠1 +∠3 = 180°

Also, ∠3 = 180 - ∠4

∠3 = 180 - 120 = 60°

Substitute the values,

∠2+ ∠1 +∠3 = 180°

35 + ∠1 + 60 = 180

∠1 = 180 - 95

∠1  = 85°

Now, ∠1 + ∠5 = 180

∠5 = 180 - 85

∠5 = 95°

Hence, the measure of angle that is an exterior angle to B is 95°.

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The correct question is:

Answer: A) 95 Degrees

Step-by-step explanation: