at what rate is the base of the triangle changing when the altitude is 20 cm and the area is 120 cm2?

Answer:

V = 7234.56 km^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

V = 4/3 (3.14) (12)^3

V = 7234.56 km^3

Answer:

7234, 56 km³

Step-by-step explanation:

π×R³×4/3=3.14×1728×4/3=7234, 56 km³

Tiffany should spend $9.5 for something like the windshield wash's six minutes of services.

A customer is always the one who uses a something or service in the end, even if they didn't buy it. When a client makes a purchase and uses the good or service personally, they are considered a consumer. A consumer always makes a purchase, even if they may not be final users.

Tiffany spent an additional $0.66 per minute at the vehicle wash, so the total fee for her time would come to

= $0.73 * 6

= $4.38

This brings the total fee up to $5.12 when added to the first charge.

= $5.12 + $4.38

= $9.5

Tiffany was thus charged $9.5

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a)the HCF of 12xy and 3x is \(2 \times 3 \times x\), which simplifies to 6x. b)  the HCF of 54xyz and 12x²12 is 2xy. c)  the HCF of 21x²y²z and 7.xyz is xyz. d) the HCF of 3a²b³c³, 9a³b³c³, and 18a²b²c² is 3a²b²c². d) the HCF of 6abc, 7ab³c, and 8abc³ is abc.

a) To find the highest common factor (HCF) of 12xy and 3x, we need to determine the highest power of each common factor that appears in both terms. Here, the common factors are 2, 3, and x. The highest power of 2 in both terms is 1 (from 12xy), the highest power of 3 is 1 (from 3x), and the highest power of x is 1. Therefore, the HCF of 12xy and 3x is\(2 \times 3 \times x\) which simplifies to 6x.

b) The common factors in 54xyz and 12x²12 are 2, 3, x, and y. The highest power of 2 in both terms is 1, the highest power of 3 is 0 (as it appears in only one term), the highest power of x is 1, and the highest power of y is 1. Therefore, the HCF of 54xyz and 12x²12 is 2xy.

c) The common factors in 21x²y²z and 7.xyz are 7, x, y, and z. The highest power of 7 in both terms is 0 (as it appears in only one term), the highest power of x is 1, the highest power of y is 1, and the highest power of z is 1. Therefore, the HCF of 21x²y²z and 7.xyz is xyz.

d) To find the HCF of 3a²b³c³, 9a³b³c³, and 18a²b²c², we consider the common factors and their highest powers. The common factors are 3, a, b, and c. The highest power of 3 in all terms is 1, the highest power of a is 2, the highest power of b is 2, and the highest power of c is 2. Therefore, the HCF of 3a²b³c³, 9a³b³c³, and 18a²b²c² is 3a²b²c².

e) The common factors in 6abc, 7ab³c, and 8abc³ are a, b, and c. The highest power of a in all terms is 1, the highest power of b is 1, and the highest power of c is 1. Therefore, the HCF of 6abc, 7ab³c, and 8abc³ is abc.

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The point estimate for the population mean is 80.875.

The ratio of the overall quantity of data to the total number of data sets is known as the mean. The average and mean are calculated using the same formula.

The ratio of the total number of data points to the total amount of data is also used to determine the average.

The eight midterms chosen at random are 71, 80, 65, 85, 90, 77, 92, and 87. The formula used to compute the mean is

Mean = (  71 +80 + 65 + 85 + 90 + 77 + 92 + 87 ) / 8

Mean = 647 / 8

Mean = 80.875

The population mean is 80.875.

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The otter takes approximately 12.10 seconds to get to the other side if it swims directly across the river. The current will have carried the otter approximately 30.25 meters downstream when it reaches the other side. The otter's velocity, relative to the bank from where it started, is 0.25 m/s.

a) To find the time it takes for the otter to get to the other side, we can use the concept of relative velocity. The otter's swimming speed is 2.75 m/s, and the current velocity is 2.5 m/s. Since the otter is swimming directly across the river, its swimming speed and the current speed are perpendicular. Using the Pythagorean theorem, we can find the resultant velocity of the otter:

Resultant velocity = √(swimming velocity² + current velocity²)

= √(2.75² + 2.5²)

≈ √(7.5625 + 6.25)

≈ √13.8125

≈ 3.72 m/s (rounded to two decimal places)

The time it takes to cross the river is given by the distance divided by the resultant velocity:

Time = Distance / Resultant velocity

= 45.0 m / 3.72 m/s

≈ 12.10 seconds (rounded to two decimal places)

b) To find how many meters downstream the current carries the otter when it gets to the other side, we can calculate the distance using the time it takes to cross and the current velocity.

Distance downstream = Time × Current velocity

= 12.10 s × 2.5 m/s

= 30.25 m

c) The otter's velocity, relative to the bank from where it started, can be calculated by subtracting the current velocity from the otter's swimming velocity.

Relative velocity = Swimming velocity - Current velocity

= 2.75 m/s - 2.5 m/s

= 0.25 m/s

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9514 1404 393

Answer:

  Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 12.

Step-by-step explanation:

The standard form has mutually prime integer coefficients, with the leading coefficient positive. Clearing Katrarina's fraction of 2/3 can be accomplished by multiplying the equation by 3/2, as Sofiya advised.

The standard form is ...

  6x -y = 12

Answer:

26.5 units²

Step-by-step explanation:

I am splitting the figure into a rectangle and two triangles to make this easier for me.

The rectangle is b•h so 5•4 = 20 units²

Area of triangle=1/2bh

The left triangle is \(\frac{1}{2}\)(3•3) ---> \(\frac{1}{2}\)(9) ---> 4.5 units²

The right triangle is \(\frac{1}{2}\)(2•2) --->\(\frac{1}{2}\)(4) ---> 2 units²

Then add it all up: 20+4.5+2 = 26.5 units²

Answer:

Step-by-step explanation:

22.50-3.75=18.75

r ≤ 14

The stem-and-leaf display of the data is

Stem | Leaves

1 | 2

2 | 2

3 | 3

4 | 5, 8

To start, let's assume we have a set of data values, such as 12, 22, 33, 45, 48, 53, 61, 62, 72, 83, 91, 96, 99.

The stem-and-leaf display consists of two parts: the "stem" and the "leaf." The stem represents the leading digit(s) of the data values, and the leaf represents the trailing digit(s). For example, the number 12 has a stem of 1 and a leaf of 2.

Now, let's organize the data values into their corresponding stems:

Stem 1: 12

Stem 2: 22

Stem 3: 33

Stem 4: 45, 48

Next, we list the leaves corresponding to each stem. The leaves are listed in ascending order next to their respective stems:

Stem 1: 2

Stem 2: 2

Stem 3: 3

Stem 4: 5, 8

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Answer:
you saved $10.00

Step-by-step explanation:

Discount = Original Price x Discount %/100

Discount = 40 × 25/100

Discount = 40 x 0.25

Answer:

10

Step-by-step explanation:

What is 25% of 40?

Y is 25% of 40

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 25% * 40

Converting percent to decimal:

p = 25%/100 = 0.25

Y = 0.25 * 40

Y = 10

The linear inequality represented by the graph is given as follows:

y ≤ x/2 + 3.

First we consider the slope-intercept definition of a linear function, given as follows:

y = mx + b.

In which:

From the graph, we have that it crosses the y-intercept at y = 3, hence the intercept b is given as follows:

b = 3.

When x increases by two, y increases by one, hence the slope m is given as follows:

m = 1/2

m = 0.5.

Hence:

y = x/2 + 3.

The inequality is composed by values below the line, with a solid line, hence it is given as follows:

y ≤ x/2 + 3.

The problem is given by the image presented at the end of the answer.

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Answer:

2+ 13

Step-by-step explanation:

2n - 3 + 7 + 9

2n + 13

The obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

(x-3)² + 9 = 0

(x-3)²= -9

(x-3)=√-9

(x-3)=√9×√-1

(x-3)=±3i

x=3±3i

Thus, the obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

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A) the three inequalities that must be satisfied are:

B) Graph shaded and satisfying all conditions is attached.

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 the sizes of two numbers on a number line.

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Answer:

10 - 6 equals 4

50 - 6 = 44

It helps you use 4 again.

That is how it helps you.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can observe the first sequence is arithmetic, with common difference:

The second sequence is geometric with common ratio:

Car 1

Linear function:

Car 2

Exponential function:

Find f(5) for each function and compare:

Car 2 will have greater value

If the diameter of an electric cable is normally distributed, with a mean of 0.7 inch and a standard deviation of 0.02 inch. The probability that the diameter will exceed 0.72 inch is 0.1587.

Given data:

Mean = 0.7

Standard deviation = 0.02

Diameter = 0.72 inch

First is to find the z-score

z(0.72) = (0.72-0.70) /0.02

z(0.72) = 0.02 /0.02

z(0.72) = 1

Now let find the probability using the standard normal distribution table

P(x > 0.72) = P(z > 1)

Standard normal distribution table (1, 100)

= 0.1587

Therefore the probability is 0.1587.

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Answer:

Approximately 10.9

Step-by-step explanation:

\(a^2+b^2=c^2\)

Plug in b (5) and c (12)

\(a^2+5^2=12^2\\a^2+25=144\)

Subtract 25 from both sides

\(a^2+25-25=144-25\\a^2=119\)

Take the square root of both sides

\(\sqrt{a^2} =\sqrt{119}\)

a = approximately 10.9

I hope this helps!

y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given,

y-intercept 4 and slope -1/5

Now y=-1/5x+4

Hence y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

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Answer:

2

Step-by-step explanation:

Both 8 and 1/32 are powers of 2.

2³ is 8, since 2*2*2=8.

2^-5 is 1/32.

2^5 is 2*2*2*2*2, and the negative sign in front of the 5 flips the answer to be 1/32

Step-by-step explanation:

To find the product, we'll be using the FOIL method.

F - Front.

O - Outer.

I - Inner.

L - Last.

When applying the FOIL method:

\(a(a) + - 3(a) + 5(a) - 3(5)\)

Multiplying:

\( {a}^{2} - 3a + 5a - 15\)

Combine Like-Terms:

\( {a}^{2} + 2a - 15\)

a^2 + 2a - 15 is your product.

Answer: you have $31 at the end of the week

Step-by-step explanation:

First, let's put this problem into an algebraic expression. We started off with $42. We then added $25 and took out $36 during the week. The expression for this problem is

42

+

25

−

36

.

Next, add 42 and 25 together to get

67

. We now have

67

−

36

.

Finally, subtract 36 from 67 to get

31

, our answer.

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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Answer:

11°

Step-by-step explanation:

tan ∅ = 20/100 = 0.2

∅ = 11.31°

The repairs have indeed changed the nature of the output of the machine, with an overall improvement in the quality of the parts produced.

To determine if the repairs have changed the nature of the output of the machine, we can compare the percentages of excellent, good, and unacceptable parts before and after the repairs.

Before repairs:
- 80% excellent
- 16% good
- 4% unacceptable

After repairs, we can calculate the percentages based on the sample of 200 parts:
- 157 excellent parts: (157/200) * 100 = 78.5% excellent
- 42 good parts: (42/200) * 100 = 21% good
- 1 unacceptable part: (1/200) * 100 = 0.5% unacceptable

Comparing these percentages, we can see that the output has changed after the repairs:
- Excellent parts decreased from 80% to 78.5%
- Good parts increased from 16% to 21%
- Unacceptable parts decreased from 4% to 0.5%

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Total cost of the food with delivery for Danielle is given by approximately $ 29.69.

Danielle ordered food for a party which costs = $118.75

Now she also gave the delivery person a 25% tip.

So the amount of tip which she paid to the delivery person is given by

= 25 percent of the amount $118.75

= 25% of the amount $118.75

= $(118.75*(25/100))

= $(118.75*(1/4)) [eliminating the similar terms from the numerator and denominator of the fraction 25/100]

= $ 29.6875

= $ 29.69 [Rounding off to the nearest cent]

Hence the total cost of food with the delivery is $ 29.69.

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Using the order, we can evaluate the expression, the answer is 0.

To evaluate this expression, we need to follow the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is:

1. Perform any calculations inside parentheses first.

2. Exponents (ie powers and square roots, etc.)

3. Multiplication and Division (from left to right)

4. Addition and Subtraction (from left to right)

Using this order, we can evaluate the expression as follows:

-31÷(-30)+(-1)

= 1 + (-1)    [since -31 ÷ (-30) = 1]

= 0

Therefore, the answer is 0.

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