The vertices of △DEF are D(1, 19), E(16, −1), and F(−8, −8). What type of triangle is △DEF?

The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second

The length of the ladder = 17

Consider the length of the base as x and the height is h

The rate at which the ladder is sliding = 5 feet per second

dx/dt = 5

Apply the Pythagorean theorem

x^2 + h^2 = 17^2

h^2 = 289 - x^2

h = \(\sqrt{289-x^2}\)

The rate of change of height with respect to x is

dh/dx = - x / (289 - x^2)^(1/2)

dh/dt = dh/dx × dx/dt

Substitute the values in the equation

= - 15 / (289 - 15^2)^(1/2) × 5

= -15/8 × 5

= -75/8 feet per second

Therefore, the rate of change of height when x = 15 is -75/8 feet per second

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1. 9 cans of white paint will she need to mix with 6 cans of blue

2. The rate of white to blue is 9 : 6.

3. The unit rate is 3/2.

Given:

Anne must add 3 cans of white paint to every 2 cans of blue paint.

So, the ratio of white to blue = 3:2

and, for 6 cans of blue paint the white paint needed

= 6 x 3/2

= 3x 3

= 9 cans

2. The rate of white to blue is 9 : 6.

3. The unit rate is 3/2.

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Answer:

I think it is 0 solutions

Step-by-step explanation:

it should be 0 because no matter what number you substitie x for, the right side will always be 9 higher than it, so x never equals x

May I have brainliest please? :)

Answer:

-14

Step-by-step explanation:

isolate x's on one side so subtract 8.5x and add 1 on both sides

\(-14 = 1x\)

simplifies to

x = -14

Answer:

its most likely A

Step-by-step explanation:

Considering it goes at a steady rate with the second variable being reasonably scattered, the level of pure water would obviously go down not up,considering you are adding frogs. than again i havent really reached this degree of mathematics. But through reasoning i beleive it's A

Answer:

Area = y² + 2x + 1

Step-by-step explanation:

You have to combine like terms:

The little square is 1 unit, so 1

The two bars are each worth x, so 2 * x = 2x

The big square is y²

The total area is the sum of all terms:

Area = y² + 2x + 1

-Chetan K

Answer: 140 km

Step-by-step explanation:

240 km in 3 hours

1 3/4 hours = (1 3/4 / 3) x 240

= (7/4 / 3) x 240

= 7/12 x 240

= 7 x 20 = 140

The approximate volume of each slice will be 63.5 inch². The total cake is divided into the four cylindrical slice.

It is defined as a three-dimensional space enclosed by an object or thing.

The volume of the slice is;

\(\rm V = \pi r^2 h\\\\\ \rm 81 \pi = \pi \times (r)^2 \times 4 \\\\ r= 4.5 \ inch\)

If the grandma cut four pieces, is the approximate volume of each slice that Hattie's grandma cut will be;

The approximate volume of each slice will be;

\(\rm V = \PI r^2 h \\\\ \rm V = 3.14 \times (4.5)^2 \times 1 \\\\ V=63.5 \ inch^2\)

Hence, the approximate volume of each slice will be 63.5 inch².

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Answer:

I believe this would be 38in^3

A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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The number of students who scored between 8181 and 8686 can be calculated using the z-score formula to find standard deviation.

z1 = (8181-7676)/55 = 1.89

z2 = (8686-7676)/55 = 3.04

Using a standard normal table, the area under the curve between these two z-scores is approximately 8.5%. So, we can estimate that about 850,085 students scored between 8181 and 8686. We find the z-score of 8181 and 8686 and calculate the area under the standard normal distribution curve between these z-scores.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, while a non-standard normal distribution has a different mean and/or standard deviation. The z-score formula is used to convert a non-standard normal distribution to a standard normal distribution, so that the properties of the standard normal distribution can be applied, such as using a standard normal table to find areas under the curve.

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Answer:

Joe makes 5 dollars a week

Step-by-step explanation:

Joe started with 173 so you will subtract that from the total

208-173=35

You will then divide that number by the number of weeks he has worked

35÷7=5

Therefore joe makes 5 dollars a week

The amount of money that he earns each week will be $5 per week.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Joe has $173 he earns the same amount of money each week for seven weeks and put this money in the bank now Joe has $208 in the bank.

Let 'm' be the amount of money that he earns each week. Then the equation is written as,

208 = 7m + 173

Simplify the equation, then we have

208 = 7m + 173

35 = 7m

m = $5

The amount of money that he earns each week will be $5 per week.

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Answer:

Step-by-step explanation:

im not sure youd have to show a picture

Answer:

not sure because no ammont was given to calculate on

Answer:

8

Step-by-step explanation:

6/8 and 4/32

Simplify each fraction

6/8

Divide the top and bottom by 2

= 3/4

4/32

Divide the top and bottom by 4

= 1/8

We have 3/4 and 1/8

Bot 4 and 8 go into 8

I Hope This Helps :)

Answer:

8

Step-by-step explanation:

The LCM is 2x2x2=8 2 x 2 x 2 = 8

Answer:

Step-by-step explanation:

A corresponds to angle P, so angle P measues 70 degrees.

Similarly, angle Q measures 60 degrees and angle R measures 50 degrees.

The area of the path if the circular pond with a path around it is 34.557 m²

Circle is the locus of a point such that its distance from a fixed point known as the center is constant.

The area of the circle (A) with radius r is given by:

A = πr²

Area of the pond with path = π(5m + 1m)² = π(6)² = 113.097 m²

Area of the pond = π(5m)² = π(5)² = 78.54 m²

Area of path = 113.097 m² - 78.54 m² = 34.557 m²

The area of the path if the circular pond with a path around it is 34.557 m²

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The translation 1 unit left of f ( x ) =–7x+10  then g(x) is -7x + 3.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in its range(involving values of y) or in its domain(involving values of x).

The up and down movements are in the vertical direction by the y coordinate.

The left and right movements are in the horizontal direction by the x coordinate.

When translating a graph, adding units moves the graph to the left, and eliminating units moves the graph to the right.

hence we say that;

f(x) = –7x+10

g(x) = f(x + 1)

= –7(x + 1)+10

= -7x - 7 + 10

= -7x + 3

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Parameter are values ​​that represents fixed characteristics of a population.

What is a parameter?

The parameter is an important component in statistical analysis because it describes fixed characteristics of the given population. The way to conclude the population characteristics is to perform statistical analysis on a sample of the population then calculate it with the parameter formula. The most commonly used parameters are mean, median, and mode. Data distribution of a ratio can be described by mean.  The Median is used to calculate the variables of data distribution which has a few data points that are different. Mode is used to know which number appears the most in a data distribution.

Based on statistical calculations from the existing population sample, conclusions can be drawn regarding the fixed characteristics of the entire population using parameters.

Hence, a parameter represents fixed characteristics of a population.

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Answer:

i think  -12,9 and you multiply it by x,-2

Soil is often considered an abiotic factor since it is mostly made up of small particles of rock (sand and clay) mixed with decomposed plants and animals. Plants use their roots to get water and nutrients from the soil.

Also just a tip, make sure to put it in the correct category next time cause someone can report it :(

Anyways hope this helps!! :D

The total surface area of the triangular prism is 845cm².

Surface area refers to the total area of all the faces or surfaces of a three-dimensional object. It is the measure of the exposed area of an object that can be seen or touched.

The surface area of a triangular prism can be calculated by adding the areas of the six faces that make up the prism.

The surface area of a triangular prism.

SA = bh + (S₁ + S₂ + S₃)H

SA = 5×9 + ( 12 + 13 + 15 )× 20

SA = 45 + 800

SA = 845 cm²

Therefore, the surface area is 845 cm².

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The complete question is given below.

Find the total surface area of this triangular prism base=5cm 9cm line in the middle 12cm width=20cm 2 lengths on triangle 13cm and 15cm

Answer:

40000

400

Step-by-step explanation:

40000 because 4000 * 10 = 40000

400 because 1 / 10 of 4000 = 400

Answer:

ok so 1/2 is your answer 1/4 divide = 1//2 !

Step-by-step explanation:

The value of equation of circle is,

⇒ (x - 5)² + (y - 3)² = 16

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle below is centered at the point (5,3) and has a radius of length 4.

Now, We can formulate;

The value of equation of circle which has centered at the point (5,3) and has a radius of length 4 is,

⇒ (x - 5)² + (y - 3)² = 4²

⇒ (x - 5)² + (y - 3)² = 16

Thus, The value of equation of circle is,

⇒ (x - 5)² + (y - 3)² = 16

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Answer:

Everyone's action is correct except Luis

luis's equation is wrong because he flipped the inequality sign when he subtracted

true inequality ;

2.4b + 6.5 > -8.1

so Luis wrong

HAVE A NİCE DAY

Step-by-step explanation:

GOOD LUCK :D

greeetings from Turkey ツ

Answer:

(B) Luis's, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

Let's evaluate each answer choice:

"Amelia's, because the variable term must be isolated on the left side"

This answer choice is wrong! Whichever side the variable term is isolated on DOESN'T affect the answer of the problem.

"Luis's, because he flipped the inequality sign when he subtracted"

This answer choice is right! Only flip the inequality sign when dividing a NEGATIVE number.

"Shauna's, because she did not apply the subtraction property of equality properly"

This answer choice is wrong! Shauna correctly applied the subtraction proper by subtracting 6.5 from both sides.

"Clarence's, because the terms he added together were not like terms"

This answer choice is wrong! Clarence added 8.1 to both sides, so he added 8.1 to 6.5, which are like terms.

Hope it helps (●'◡'●)

Answer:

15.3 %

Step-by-step explanation:

400 / 2600 x 100 = 15.3 %

I hope im right!!

there is an increase of 3000 - 2600 = 400

400/2600 * 100 = 15.38 %

Answer:

V = 343/8 cubic inches

Step-by-step explanation:

Here, we want to find the volume of the cube given the length of its side

Mathematically, the volume of a cube is L^3

where L represents the length of one of its side.

3 1/2 = 7/2 inches

Thus we have; 7/2 * 7/2 * 7/2 = 343/8 inches cube

Answer:

february

plzz mark as a brainlist

Answer:

Step-by-step explanation:

Angelique travels 75miles Jamila travels 115kilometers show that Angelique has traveled further than Jamila

Answer:

125 cm³

Step-by-step explanation:

The volume (V) of a cube = s³ ( s is the length of the sides )

Since the shape is a cube then all sides are congruent, thus

V = 5³ = 5 × 5 × 5 = 25 × 5 = 125 cm³

Answer:

v=l×w×h 5×5×5=125cubedcm

Step-by-step explanation:

you see a cube has an equal length, width and height

Answer:

72 degrees

Step-by-step explanation:

A central angle equals the degree of the arc.

If the circumference is 20 and the arc is 4 than means the

arc is 4/20= 1/5 of the circumference.

A circles circumference is also always equal to 360 degrees.

So we need to find out what 1/5 of 360 is to find the degree of the arc.

So then 1/5*360= 72

so the Arc is equal to 72 degrees of the whole circle, which means the central angle is equal to 72  degrees as well.