a conical salt spreader is spreading salt at a rate of 3 cubic feet per minute. the diameter of the base of the cone is 4 feet and the height of the cone is 5 feet. how fast is the height of the salt in the spreader decreasing when the height of the salt in the spreader (measured from the vertex of the cone upward) is 3 feet? give your answer in feet per minute.

the probability of an archer hitting her target is 83%.The mean of x is 16.6 (16.6 targets hit).

The probability of the archer hitting her target is 83%. This means that for each shot she takes, the probability of her hitting her target is 0.83. Since she has 20 shots to take, the expected number of targets hit is 20 x 0.83, which is 16.6.

The mean of x, which is the number of targets hit, is therefore 16.6. This can be calculated by taking the probability of success (0.83) multiplied by the number of trials (20), which gives the expected value of 16.6.

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Answer:

(6,0)

Step-by-step explanation:

Solving a system of equations is finding where 2 (or more) lines intersect.

Graph the lines:

y = x/6 - 1

and

y = -2/3x + 4

(linked)

Look at where they intersect (meet).

(6,0)

Answer:

[tex] \sf \: \frac{29m - 15}{25} \: (or)1 \frac{4}{25}m - \frac{3}{5} [/tex]

Step-by-step explanation:

Given expression,

→ 1 2/5m - 3/5(2/5m + 1)

Simplifying the given expression,

→ 1 2/5m - 3/5(2/5m + 1)

→ (7/5)m - 3/5(2/5m + 1)

→ (7/5)m - (6/25)m - (3/5)

→ (35/25)m - (6/25)m - (3/5)

→ ((35 - 6)/25)m - (3/5)

→ (29/25)m - (3/5)

→ (29m - 15)/25

→ 1 4/25m - (3/5)

Hence, answer is 1 4/25m - (3/5).

For given functions f and g, the sum of the areas of the enclosed regions is 2.004 sq. units. and the sum of the volumes of the enclosed regions is 1.283 cubic units

In this question we have been given two functions f and g defined by

f(x) = 1 + x + e^x^2 - 2x and g(x) = x^4 - 6.5x^2 + 6x + 2.

There are two regions on the interval 0 x 2 which are enclosed / and g. We need to find the sum of the areas of the enclosed regions and the sum of the volumes of the enclosed regions.

The graph of functions is as shown below.

We can observe that the graphs of y = f(x) and y = g(x) intersect in the first quadrant at the points (0, 2), (2, 4), and (A, B) = (1.032832, 2.401108).

The sum of the areas of the enclosed regions is given by

A = ∫[0-A] (g(x) - f(x)) dx + ∫[A - 2] (f(x) - g(x)) dx

A = 0.997427 +1.006919

A = 2.004

And the sum of the volumes of the enclosed regions is given by

Volume V =∫[0-4]  [[ƒ(x) − g(x)]² dx

V = ∫[0-4] [1 + x + e^x^2 - 2x - x^4 + 6.5x^2 - 6x - 2]^2 dx

V = 1.283

Therefore,  the sum of the areas of the enclosed regions is 2.004 sq. units. and the sum of the volumes of the enclosed regions is 1.283 cubic units

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Math

-

Because point B is midpoint of AC , so AB = BC . Therefore :

8x + 4 = 10x - 6

10x - 8x = 4 + 6

2x = 10

x = 5 ✓

_____

The interest rate for Rebeka's account is 5%.

What is the meaning of interest rate?

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given that, Rebeka deposits $1500. She earn $131.25 as interest after 21 months.

The formula of simple interest is

I = PRT

I = interest

P = Principal

R = Rate of interest

T = time

In the given question,

P = $1500

I = $131.25

T = 21 months = 21/12 years.

Putting P = $1500, I = $131.25, T = 21/12 years in I = PRT:

131.25 = 1500 × R × (21/12)

Divide both sides by 1500 × (21/12):

R = 131.25 /[1500 × (21/12)]

R = [131.25 × 12] /[1500 × 21]

R = 0.05

R = 5%

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Answer:

I) 70°

II) 120°

Step-by-step explanation:

In a regular polygon the sum of all its internal angles is equal to

180° × (n – 2)

where:

n = number of sides of the polygon

the formula as one logarithm with a coefficient of 1 with a expression. assume all variables represent positive real numbers. 1/4logbx^5y^7-4/7logbx^4y is logbx^4y^11/28

Since the coefficients of the expression of two logs are not the same, we need to adjust the exponents in order to combine them into one logarithm. Since the first logarithm has a coefficient of 1/4, we multiply the exponent of the second logarithm by 4/7 to get 4/7*4 which is equal to 4. We then add 4 to the exponent of the first logarithm to get 11. This gives us a combined logarithm of logbx^4y^11/28.

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The number 25209 rounded to the largest place value is 30000.

Every digit in a number has a place value, which is a numerical value determined by the digit's position.

Step 1: First, decide which location value has the highest worth.

The number that is farthest to the left has the highest place value.

Providing the value is not zero.

In the number 25209,

2 is the largest place value.

Step 2: Next, take a look at the number that is closest to the largest place value.

The greatest place value remains the same if the number is 0, 1, 2, 3, or 4.

The highest place value increases by one if the number to the right is a 5, 6, 7, or 9.

We have number 5 to the right of 2.

The number rounded to the largest place value is 30000.

Therefore, the required number is 30000.

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The Angle ∠MTU from the figure is 65°

The study of shapes and their measurements falls under the umbrella of geometry, a subfield of mathematics. It also emphasizes how the shapes are arranged in relation to one another and their spatial characteristics. We are aware that geometry is divided into 2D and 3D categories. All geometrical shapes are first created by the intersection of points, lines, rays, and plane surfaces. The distance measured between two lines is referred to as a "Angle" when the rays or lines converge at a single point.

Given,

∠STM=31X-3;

∠MTU=20X+5;

∠STU=155°;

From the figure we can say that

∠STU= ∠STM+∠MTU;

⇒ 155=31x-3+20x+5;

⇒155=51x+2;

⇒x=3;

Now substitute x in ∠MTU;

⇒∠MTU=20(3)+5=65°

The Angle ∠MTU from the figure is 65°

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The linear function for D is defined as follows:

D(t) = -35t + 280.

The slope of 35 means that Nathan is traveling at a velocity of 35 miles/km per hour.

The linear function for this problem is defined in slope-intercept format, as follows:

y = mx + b.

The coefficients of the function are given as follows:

From the table, two points are given as follows:

(3, 175) and (5,105).

Given two points, the slope is calculated as the change in y divided by the change in x, hence:

m = (105 - 175)/(5 - 3) = -35.

This slope represents that Nathan is traveling at a velocity of 35 miles/km per hour.

Hence:

D(t) = -35t + b

When x = 3, y = 175, hence the intercept b is obtained as follows:

175 = -35(3) + b

b = 280.

Thus the function is of:

D(t) = -35t + 280.

The table is given by the image shown at the end of the answer.

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Answer:

Step-by-step explanation:

To graph the points (0.5, 4.5) and (-0.5, -4.5) on a coordinate plane, you can use a ruler or a graph paper to plot the points.

To plot the point (0.5, 4.5), start by drawing the horizontal and vertical axes of the coordinate plane. The horizontal axis, or the x-axis, is the line that runs horizontally across the plane, and the vertical axis, or the y-axis, is the line that runs vertically. The intersection of the two axes is called the origin.

Next, locate the point (0.5, 4.5) on the coordinate plane. To do this, find the point that is 0.5 units to the right of the y-axis and 4.5 units above the x-axis. This point is the point (0.5, 4.5).

To plot the point (-0.5, -4.5), locate the point that is 0.5 units to the left of the y-axis and 4.5 units below the x-axis. This point is the point (-0.5, -4.5).

The resulting graph should look like this:

  |

4.5|       * (0.5, 4.5)

  |

  |

  |

  |

0.5|       * (-0.5, -4.5)

  |

  |

  |

 -4.5

 -4.5 -2.5 -0.5  0.5  2.5  4.5

         -0.5

Answer:

  20

Step-by-step explanation:

You want to know how many daily chores Haley has if 40% of them are 8 chores.

Let c represent the number of daily chores. The number of chores accomplished in the morning was ...

  0.40c = 8

Dividing by 0.40, we find ...

  c = 20

Haley has 20 daily chores.

The difference of 4h5k and -7hk5 Not possible.

Which of the following provides an example of to calculate the difference between 4h5k and -7h5k

Changing the situation 4h^5k - (-7hk^5)= 4h^5k +7hk^5

Making the distinction

4h^5k - (-7hk^5)

= 4h^5k +7hk^5

assemble similar phrases

Take note of similar phrases is  hk(4h^4+7k^5)

There can be no difference, therefore.

= hk(4h^4+7k^5)

As a result, the difference is Not possible.

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The coordinate of the point N that divides the line segment MP will be (9, -5).

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

The coordinates of the endpoint are (-6, 5) and (21, -13). And the ratio is 5:4. Then the coordinate of the point N is given as,

x = (21 × 5 + (-6) × 4) / (5 + 4)

x = 81 / 9

x = 9

y = ((-13) × 5 + 5 × 4) / (5 + 4)

y = - 45 / 9

y = - 5

The coordinate of the point N that divides the line segment MP will be (9, -5).

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Answer:

Y-Intercept is equal to 100

Y-Intercept in Coordinate for is (0,100)

Answer:

1

Step-by-step explanation:

the height is 2/3ft because it makes a right angle with the surface

base is 3 ft

area: 1/2 x 3 x 2/3 = 1 ft^2

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The statement describes the domain and range of the exponential function f(x) = – 4ˣ is

A.The domain and range are both the set of all real numbers.

The y-axis on a graph represents the possible output values, or range.

while the domain is the input values.

The domain of the exponential function f(x) = – 4ˣ is set of all real numbers

The range considering the domain is also set of all real numbers since it can be positive or negative depending on the value of the domain

It is worthy to note that the domain and range of the graph may be larger than the values seen if the graph extends beyond the area that is visible.

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The Subtotal for 25 flash drives is $250.00. You can save $62.50. The new Subtotal becomes $187.50. Sales tax of 4% will equal $7.50. The Total for the 25 flash drives will be $187.50 + $7.50 which gives $195.00

To find the solution, we must solve for the questions individually;

The Subtotal is 25 x $10 = $250.00

You save = 25% of $250

which is 25/100 x 250 = $62.50

The new Subtotal = $187.50

Sales tax of 4% = 4% of $187.50

which gives 4/100 x 187.5 = $7.50

The Total for the 25 flash drives will be $187.50 + $7.50 = $195.00

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Answer: The first three terms of the sequence are: 1^2+1=2, 2^2+1=5, 3^2+1=10

The tenth term of the sequence is: 10^2+1=101.

Step-by-step explanation: To find the first three terms of a number sequence in which the nth term is n^2+1:

For the first term, set n equal to 1 and substitute it into the formula: 1^2 + 1 = 2

For the second term, set n equal to 2 and substitute it into the formula: 2^2 + 1 = 5

For the third term, set n equal to 3 and substitute it into the formula: 3^2 + 1 = 10

To find the tenth term of the same sequence, set n equal to 10 and substitute it into the formula: 10^2 + 1 = 101.

The probability is 0.07777.

What does probability mean?

The number of desired outcomes divided by the total number of outcomes yields a probability.

We are attempting to determine the likelihood, out of 10, that the first chip will be white and the second won't be green while assuming that one chip is white and two are green.

1/10 of the time, the initial chip will be white. If the first chip is white, there is a 7/9 chance that the second chip will be a color other than green. The desired probability is therefore provided by:

Ten chips are present.

white 1

red 4

green 2

Blue 3

the likelihood of selecting the W chip is one in ten, or 0.10

There are now only 9 chips left (the first chip was not replaced)

Selecting a non-green chip has a probability of (9-2)/9 = 7/9 = 0.7777.

you multiply the two probabilities to obtain the overall probability at this point.

probability is 0.1 to 0.7776.

The probability is equal to 0.07777, which implies that it must be less than 0.1.

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Answer:

Step-by-step explanation:

There is a correlation that is likely for the number of car accidents and the weather as wet pavement and rainfall leads to more accidents.

The size and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is expressed as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

Weather-related issues will have an impact on our roads and reduce tire traction. Once more, it is advised to slow down while driving on slick roads, increase our following distance, and take more time to slow down when coming to a stop.

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After 3 years, the value of the car will be approximately $20,959.34.

The depreciation of an asset is the reduction in the value of the asset over time due to wear and tear, obsolescence, or other factors. The depreciation equation is used to calculate the amount by which the value of an asset decreases each year.

The value of the car after 3 years can be represented by the following equation:

V = 26600 * (1 - 0.09)^3

Where V is the value of the car after 3 years and 0.09 is the depreciation rate per year.

Solving this equation gives us a value of V = $20,959.34.

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Answer:20044.9886

Step-by-step explanation:

Option D is correct that is BC = 2

A line is a perfectly straight, one-dimensional shape that is endlessly long and thin in both directions.

She tells us that AC is 15, and we may deduce that AC equals AB plus BC from the figure.

AC Equals AB plus BC.

AB=4X+1, BC=2X-4, and AC=15

15 = 4X +1 + 2X- 4

15 = 6X - 3

18 = 6X

X = 3

We now know that 2X - 4

2(3) - 4 = 2 since we have X = 3.

BC = 2.

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Answer:

55.5 as a fraction is 111/2.

Answer: 55.5 as a fraction is 111/2.

Step-by-step explanation:

Angle F is correspond to angle S. Angle A is congruent to angle U

and Angle R is congruent to angle N.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion

Given that ΔFAR is similar to ΔSUN.

We need to find the corresponding sides.

Corresponding angles are the angles that are in the same position in any different 2-dimensional shapes.

For any two polygons to be congruent, they must have exactly the same shape and size.

This means that all their interior angles and their corresponding sides must be the same measure.

Angle F is correspond to angle S.

Angle A is congruent to angle U.

Angle R is correspond to angle N.

Hence, Angle F is congruent to angle S. Angle A is congruent to angle U

and Angle R is congruent to angle N.

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At x = 4, the function f(x) = (x2 - 16)/(6x - 24) discontinues.

When a number is 0 in the numerator as well as the denominator, a point of discontinuous is reached. There's an point of disconnection there since both the exponent and the denominator are zeros. Plug into the last simplified equation to obtain the value, where is the region of discontinuous.

We are given the function as;

f(x) = (x² - 16)/(6x - 24)

We must find the function's discontinuities.

Now, when x = 4, the fraction 6x - 24 equals 0.

This means that the function is now incomplete when x = 4.

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both directions can be chosen as positive in this example. The right-hand rule solves these ambiguities. The resultant remains the same at 3.2 *10^4 Tm

It is possible for the line integral to go around the loop in either direction (clockwise or counterclockwise), the vector area dS to point in either of the two normal directions and Ienc, which is the net current passing through the surface S, to be positive in either direction—but both directions can be chosen as positive in this example. The right-hand rule solves these ambiguities.

The resultant remains the same at 3.2 *10^4 Tm

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The value of b = 5 , h = -4 and k = -1 for the function f(x) = [tex]log_{5}[/tex](x - 4) - 1

What is a function ?

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

An input is connected to an output by a function. It resembles a device with an input and an output. In addition, the output is somehow connected to the input. The standard way to write a function is f(x) "f(x) =... "

Translated of logarithmic function:

f(x) =  [tex]log_{b}[/tex] (x + h) + k

where b is base, h - horizontal shift, k - vertical shift

According to given function the values are:

b = 5, h = - 4, k = - 1

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