A box has a width of 12 cm and a length of 9 cm. the volume of the box is decreasing at a rate of 541 cubic cm per second, with the width and length being held constant. what is the rate of change of the height, in cm per second, when the height is 6 cm?

Answer:

Since all triangle angles sum to 180 then we can say

2x + 3x + 7x = 180

12x = 180

x = 15

There fore the angles are

2 * 15 3 * 15 and 7 * 15 or

30 45 and 105

Those 3 total 180 degrees

Step-by-step explanation:

Answer:

See attached graph.

Step-by-step explanation:

Use DESMOS graphing software.  Free.

Answer:

[tex]y = \frac{w}{h - 5c^{3}}[/tex]

Step-by-step explanation:

separate y from everything

[tex]w = y(h - 5c^{3})[/tex]

now divide everything by the thing in the parenthesis

[tex]\frac{w}{h - 5c^{3}} = y[/tex]

now flip it

[tex]y = \frac{w}{h - 5c^{3}}[/tex]

that is your answer

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Answer: 7/5 or 1 2/5

Step-by-step explanation:

Ok so the bakery uses 3 3/5 cups cups of oats for 2 4/7 POUNDS of cookies.

You need to find the unit price.

So to get from 2 4/7 to 1, you need to divide 2 4/7 by 2 4/7

You need to do the same thing to 3 3/5 cups.

3 3/5 as an improper fraction is 18/5

2 4/7 as an improper fraction is 18/7

Now to divide you need to keep, change, and flip

keep the 18/5, change the sign to multiplycation, and flip the 18/7 to 7/18

18/5*7/18=7/5

7/5 or 1 2/5 pounds of outs are required to make 1 pound of oatmeal cookies

The proportion of these banks that had an interest rate less than 2.5 percent is 0.724.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 2.5

μ = mean = 2.28

σ = standard deviation = 0.37

z-score = (2.5 - 2.28) / 0.37

z-score = 0.22 / 0.37

z-score = 0.5946

To get the proportion, find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 0.5946

By interpolating the values,

probability = 0.724

proportion = 0.724

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The probability that the transistor will last between 12 and 24 weeks is 0.424

X= lifetime of the transistor in weeks E(X)= 24 weeks

O,= 12 weeks

The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.

X~gamma([tex]\alpha ,\beta[/tex])

E(X)= [tex]\alpha \beta[/tex]                 [tex]\beta[/tex]= [tex]12^{2}/24[/tex]=6 weeks

V(x)= [tex]\alpha \beta ^{2}[/tex]                [tex]\alpha[/tex]=24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X, [tex]\alpha[/tex], [tex]\beta[/tex], False)

P([tex]12\leq X\leq 24[/tex])

P([tex]12/6\leq G\leq 24/6[/tex])

P([tex]2\leq G\leq 4[/tex])

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer:

Step-by-step explanation:

0.424 is the probability that the transistor will last between 12 and 24 weeks.

X= lifetime of the transistor in weeks E(X)= 24 weeks

Standard deviation= 12 weeks

Finding the parameters alpha and beta X~gamma(αβ)

E(X)= αβ             β =6 weeks

V(x)=αβ^2           α =24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X,α,β,False)

P(12≤X≤24)

P(12/6≤G≤24/6)

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer:

-111/2

Step-by-step explanation:

Please look at the attachment below! :D

The number of ounces of meat were used is 52 ounces.

Given that, a sandwich shop serves 4 ounces of meat and 3 ounces of cheese on each sandwich.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

There are 7 ounces of combined meat and cheese in each sandwich (4+3 =7)

Number of sandwiches can make with 91 ounce of meat and cheese

= 91/7

= 13 sandwiches

Number of ounces of meat = 13 × 4 = 52 ounces

Number of ounces of cheese = 13 × 3 = 39 ounces

Therefore, the number of ounces of meat were used is 52 ounces.

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Answer:

Yes, because the last digit is 6, which is divisible by 2.

Step-by-step explanation:

The solution is, Yes, because the last digit is 6, which is divisible by 2.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

26 divisible by 2

i.e. 26/2 = 13

so, it is divisible.

now, we know that,

because the last digit is 6, which is divisible by 2.

Hence, The solution is, Yes, because the last digit is 6, which is divisible by 2.

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Answer:

[tex]\frac{11}{20}[/tex]

Step-by-step explanation:

2[tex]\frac{3}{4}[/tex] ÷ 5

Convert mixed number fraction to improper fraction

[tex]\frac{11}{4}[/tex] ÷ 5

To divide fractions we turn the second fraction (the one you want to divide by) upside down (this is now called a reciprocal) and we multiply

[tex]\frac{11}{4}[/tex] × [tex]\frac{1}{5}[/tex] = [tex]\frac{11}{20}[/tex]

Answer: y = -1x + 3

Step-by-step explanation:

Point-Slope form: y - y1 = m(x-x1)

Replace the form with the values provided:

y - 15 = -1(x+12)

Once you get this, you need to get y by itself in order to get it in slope intercept form.

Distribute:

y -15 = -1x - 12

Add -15 to the right side:

y = -1x + 3

Answer: 8.4cm

Step-by-step explanation:

sin cos tan

SOH CAH TOA

It is cos because CAH does not have opposite (o) in it and we want to find the opposite.

O is opposite (opposite angle)

A is adjacent (next to angle)

H is hypotenuse (opposite right angle)

This is how I remember it

Cos(61)*17.4=8.435

8.4cm

Answer:

x = 11.2 cms.

Step-by-step explanation:

I infer that the units are in centimeters.

8-3 = 5

One side = 5 cm

Other side = 10 cm

By the Pythagorean Theorem:

x² = 5² + 10²

x² = 25 + 100

x² = 125

√x² = √125

x = 11.18 cms

To the nearest tenth:

x = 11.2 cms

The equation using x to represent the number of guests at your party is 300 + 9x = 534

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let x represent the number of guests at your party.

Here, renting a roller rink for your birthday costs $300 plus $9 per person. This will be:

300 + 9x = 534

Collect like terms

9x = 534 - 300

9x = 234

Divide

x = 234 / 9

x = 26

The number of guest is 26.

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The standardized measure of the degree to which the independent variable caused a change in the dependent variable is a standard change.

A dependent variable is what is determined in an experiment or test and is the one that is influenced throughout the experiment. The dependent variable is affected by the independent variable.

In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are explored in an experiment under the assumption or requirement that they are dependent, by some law or rule, on the values of other variables.

In conclusion, the standard change illustrates the change.

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The one half of the dimensions of the frame dog house is obtained.

For the given question, the dimensions of the frame dog house are given as;

Convert the following fraction in improper by the above method;

Now, customer has offered to pay extra if you will make one half the size called for in the plans.

Multiply each dimension with 1/2.

Thus, the one half of the dimensions of the frame dog house is obtained.

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9/25

Step-by-step explanation:

students who have either cat or dog =25-3=22

students who have both= 15+16-22= 9

probabillity that a student chosen at random has both= 9/25

the ratio of zinc to copper is 3 to 14, that menas that for each 3 grams of zinc there are 14 grams of copper, so we can made a rule of three to find

Answer:

A: A unique triangle

B: A unique triangle

C: More than a triangle

we have

1/2 +1/3

Remember that

1/2=0.5

1/3=0.33 -----> rounded 0.3

so

0.5+0.3=0.80

Answer: please help

Step-by-step explanation: I don’t know what the answer is I need help

The location of the center of dilation in the figure and the image formed following the dilation is the point N

The scale factor of the dilation is 0.5

A dilation transformation resizes an object such that the lengths of the sides of the image (the object formed) following the dilation of the original image has sides that are a constant multiple of the side lengths of the original object.

The center of dilation is a reference and fixed point, such that the center of is in the same location relative to the preimage and the image.

The location or point shared by both the figure LMNO and the image of LMNO formed following the dilation, which is figure L'M'N'O' is the point N.

Therefore;

The scale factor of the dilation is found using the definition of a scale factor, which is the ratio of the scale of a new figure to the scale of an original figure, therefore:

[tex]The \ scale \ factor,\, s.f. = \mathrm{\dfrac{Length \ of \ the \ sides \ of \ L'M'N'O'}{Length \ of \ the \ sides \ of \ LMNO}}[/tex]

MN = 6 units

LO = 6 units

ML = ON = √(6² + 2²) = 2·√(10)

M'N' = L'O' = 3 units

M'L' = O'N' = √(3² + 1²) = √(10)

Which gives:

[tex]s.f. = \dfrac{M'L'}{ML} =\dfrac{\sqrt{10} }{2 \cdot \sqrt{10} } = \dfrac{1}{2}=0.5[/tex]

The scale factor of the dilation is, s.f. = 0.5

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Answer:

22

Step-by-step explanation:

We can describe 15x-10 as an expression.

We would describe 6x-2<35 as an inequality.

In mathematics, inequalities characterize the connection between two non-equal numbers. Inequality means being unequal. If two values are not equal, we use the "not equal symbol". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare two numbers on the number line based on their size. In the illustration above, there's a less than sign. This means that it's an inequality.

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It will be similar to the original triangle.

The shape of the density curve for a dataset is like a triangle, that is, as we move to the left of the horizontal axis, it starts from zero height, then rises linearly until some peak, then declines linearly until reaches zero, then stays zero from there onward. If we standardize the dataset by calculating the standard scores, the geometrical shape of the density curve will more or less be the same. i.e., similar to the original triangle. Scale of it will be just changed.

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Answer:

Explanation:

Here, we want to get the probability that the top card is not a heart card

Mathematically, the sum of the probability that an event will occur and that the event will not occur is 1

Let the event that a heart card is the top card be H

We already have P(H) as 0.28

Thus:

JK is perpendicular to a line that has a slope

What is Slope?

The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).

Two lines, L1 and L2, with slopes m1 and m2 are perpendicular if

m1 x m2 = -1.

In our case m1 = 1

1 x m2 = -1

m2 = -2

so the slope of the perpendicular line is -2.

( -2 x (1) = -1).

As x increases, the line with a slope of -2 increases. Line JK is the only line displayed that fits this. Line AB cannot be the solution because it is "falling" as x grows.

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