In ΔDEF, the measure of ∠F=90°, EF = 2. 3 feet, and FD = 2. 9 feet. Find the measure of ∠D to the nearest tenth of a degree

Since the above question which looks at a linear relationship is incomplete, we are looking at a very similar question that has the same logic and principles. In this case, after 3 minutes, the pool now has 84 gallons of water. See the explanation below.

Note that we are already given a linear equation y = 28x. This means that

We know that the equation that models the relationship between time and volume is y = 28x, where y is the volume of water in gallons and x is the time in minutes.

We are given that when the pool has 84 gallons of water, y = 84. We can plug this into the equation and solve for x:

y = 28x

84 = 28x

x = 84/28

x = 3

Therefore, it takes 3 minutes to fill the pool with 84 gallons of water.


From the picture given, one can infer that the linear equation will be y = 25x. Thus, if the expression given is y=25x,

where y is the volume of water in gallons and

x is the time in minutes,

we can follow the same steps as before to find out how many minutes it would take to fill the pool with 84 gallons of water:

y = 25x

84 = 25x

x = 84/25

The result is x = 3.36 minutes (rounded to two decimal places).

Therefore, it would take approximately 3.36 minutes to fill the pool with 84 gallons of water if the equation that models the relationship between time and volume is y=25x.

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Full Question:

The question above is incomplete. Thus, let us look at a very similar question.

Laura is throwing a pool party to kick off the summer. Her pool is empty,

so she starts filling it with water from a garden hose. There is a proportional relationship between the time Laura has been filling up the pool (in minutes), x, and the volume of water in the pool (in gallons), y.

The equation that models this relationship is y = 28x.

After how many minutes does the pool have 84 gallons of water in it? Write your answer as a whole number or decimal.

Based on the average SAT Math score that the graduating classes got, the comparison is that this year's graduating class did better than last year's graduating class.

The average score is used to show the general trend of scores that students were able to attain.

The average score of 530 that this year's graduating class attained is higher than the average of the previous graduating year which is 520.

This means that on average, this year's graduating class did better than that of last year because their general trend was higher.

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Answer:

i had this question before

Step-by-step explanation:

c^2=a^2+b^2-2abcos(c)

c=sqrt(a^2+b^2-2abcos(c))

c=sqrt((5)^2+(12)^2-2(5)(12)cos(72))

c=sqrt(25+144-120cos(72))

c=sqrt(169-120cos(72))

c=sqrt(169-37.08)

c=sqrt(131.92)

c=11.49

Answer:

y= -\(\frac{1}{3}\)x +7

Step-by-step explanation:

         y=3x−6

1. to find the gradient of a perpendicular line we find the reciprocal of the original gradinet

so the  reciprocal of 3 is -\(\frac{1}{3}\) (we can check this by multiplying both the gradient and seeing if we get -1    -\(\frac{1}{3}\) x 3= -1 )

    so the gradient is -\(\frac{1}{3}\)

2. we sub in the gradient -\(\frac{1}{3}\) into the equation y=mx+c this give us

       y= -\(\frac{1}{3}\)x +c

3. to find the value of c we substitute in the coordinates (we then expand the brackets and then get c on its own)

       y= -\(\frac{1}{3}\)x +c

       10= -\(\frac{1}{3}\)(-9) +c

       10=3+c

       7=c

4. we sub in 7=c back to the equation y= -\(\frac{1}{3}\)x +c this gives us

     y= -\(\frac{1}{3}\)x +7

5. so our final answer is  

        y= -\(\frac{1}{3}\)x +7

The slant asymptote of the rational function f(x) = (8x³ - 6x² + 4)/(4x² + 5x - 2) is given as follows:

y = 2x + 4.

The slant asymptote of a rational function is nothing more than the result of the quotient of the function, that is, the division of the numerator of the rational function by the denominator of the rational function.

The numerator and the denominator of the rational function in this problem are given as follows:

Using a calculator, the division of the numerator of the function by the denominator is given as follows:

y = 2x + 4 + (24x - 4)/(4x² + 5x - 2.)

The remainder is disconsidered for the slant asymptote, which is then given as follows:

y = 2x + 4.

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To find the length of the radius of a circle when given the area, we can use the formula for the area of a circle: Area = π * r^2

Given that the area is 36.43 cm^2, we can set up the equation as follows:

36.43 = π * r^2

To solve for the radius (r), we need to isolate it on one side of the equation. First, divide both sides of the equation by π:

36.43 / π = r^2

Next, take the square root of both sides to solve for r:

√(36.43 / π) = r

Calculating this expression, we find:

r ≈ 3.81 cm

Rounding to two decimal places, the length of the radius is approximately 3.81 cm.

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Answer:

x > -5

Step-by-step explanation:

hope this helps :)

Answer:

x>-5

Step-by-step explanation:

X-15>-20

Add 15 to both sides;

x-15+15=>-20+15

simplify

x>-5

Hope this helped!

Helped by none other than the #QUEEN herself  aka # DrippQueenMo

Jennifer Davis will earn $910.00 in simple interest on her investment.

The principal amount is $2,600.

The interest rate is 7% per year.

The time period is 5 years.

To calculate the simple interest, we can use the following formula:

simple interest = principal * interest rate * time

Plugging in the values for the principal, interest rate, and time period, we get:

simple interest = 2600 * 0.07 * 5 = 910

Therefore, Jennifer Davis will earn $910.00 in simple interest on her investment in 5 years.

In words, the simple interest is calculated by multiplying the principal amount by the interest rate and the time period. In this case, the principal amount is $2,600, the interest rate is 7%, and the time period is 5 years. Therefore, the simple interest is $910.00.

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The difference in the total number of hours practiced in March and April is  \(24\frac{1}{2}\) hours

To find the difference in the total number of hours practiced in March and April

we need to calculate the total number of hours practiced in each month and then find the difference between the two totals.

In March:

Ballet: \(2\frac{1}{2}\) hours per week × 2 weeks = 5 hours

Jazz: \(4\frac{3}{4}\) hours per week × 2 weeks = 9 1/2 hours

Total hours practiced in March = 5 hours (ballet) + \(9\frac{1}{2}\) hours (jazz)

= \(14\frac{1}{2}\) hours

In April:

Ballet: \(3\frac{1}{4}\) hours per week × 4 weeks = 13 hours

Jazz: \(6\frac{1}{2}\) hours per week × 4 weeks = 26 hours

Total hours practiced in April = 13 hours (ballet) + 26 hours (jazz) = 39 hours

To find the difference, we subtract the total hours in March from the total hours in April:

39 hours (April) - \(14\frac{1}{2}\) hours (March) = \(24\frac{1}{2}\) hours

Therefore, the difference in the total number of hours practiced in March and April is  \(24\frac{1}{2}\) hours

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Answer:

Step-by-step explanation:

y=2/3x+4

From the triangle KLM inside the circle, the value of KM is calculated. And, the value is 1.2079.

A triangle is a polygon made up of three vertices, three angles, and three sides. First, draw a circle with a midpoint represented by O. Then, draw a triangle KLM inside a circle. Now, construct the line segments KO, MO, and LO because they form the circle's radius.

Given that KL = LM. Since two sides of the triangle KLM is equal, it is an isosceles triangle. Also, ∠K=∠M=17°. The total angle of this triangle is 180°. Then, ∠L=180°-17°-17°=146°.

Half the angle L is 73°. Then, ∠KLO=∠MLO=73°.

Consider triangle KLO, this triangle is also isosceles because KO = LO. Then, ∠KLO=∠OKL=73°.

Now, ∠KOL is calculated as follows from the triangle KLO,

\(\begin{aligned}\angle KOL&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}\)

Similarly, consider triangle MLO, this triangle is also isosceles because LO=MO. Then, ∠MLO=∠OML=73°.

Now, ∠LOM is calculated as follows from the triangle MLO,

\(\begin{aligned}\angle LOM&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}\)

Then,

\(\begin{aligned}\angle KOM&=\angle KOL+\angle LOM\\&=34^{\circ}+34^{\circ}\\&=68^{\circ}\end{aligned}\)

Using, the cosine law of the triangle KOM, we get,

\(\begin{aligned}(KM)^2&=1.08^2+1.08^2-2(1.08)(1.08)\cos 68^{\circ}\\&=2.3328-2.3328(\cos 68^{\circ})\\&=2.3328(1-\cos 68^{\circ})\\&=2.3328(0.6254)\\&=1.4589\\KM&=\sqrt{1.4589}\\&=1.2079\end{aligned}\)

Therefore, the required answer is 1.2079.

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Answer: Dilation, scale factor of 2.

Step-by-step explanation: The scale factor would be the number we multiply the 4 by 6 rectangle to get the 8 by 12 rectangle print.

Since we start with a rectangle with a length of 6 and a width of 4, and the measurements are changed to 8 and 12, we know the scale factor is 2. The scale factor is two because 4 • 2 is 8, and 6 • 2 is 12. Out of the transformations, (reflection, rotation, translation, dilation) the only one that includes a scale factor would be dilation. We also know it’s a dilation since the print is getting larger, and the pre image and image are not the same.

In a completely randomized design involving four treatments, the overall mean (the grand mean) for all treatments is: 37.3. Which is an option (B).

The grand mean (or overall mean) for all treatments can be calculated by averaging the sample means of all treatments weighted by their sample sizes. Given the following information about a completely randomized design involving four treatments: Treatment 1: Sample size = 42, Sample mean = 50

Treatment 2: Sample size = 48, Sample mean = 17

Treatment 3: Sample size = 32, Sample mean = 38

Treatment 4: Sample size = 18, Sample mean = 15

The grand mean is calculated by first multiplying each sample mean by its corresponding sample size, adding the products together, and then dividing by the total sample size of all treatments. The calculation for the grand mean is shown below:

(50*42) + (17*48) + (38*32) + (15*18) = 2100 + 816 + 1216 + 270 = 4402

Grand Mean = 4402/140 = 37.3

Therefore, the correct option is b. 37.3.

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a) \(m=\frac{-12-4}{5-(-7)}=\frac{-16}{12}=\boxed{-\frac{4}{3}}\)

b) We know the equation is \(y=-\frac{4}{3}x+b\), where b is a constant. If we substitute in the coordinates of point a, we get that:

\(4=-\frac{4}{3}(-7)+b\\4=\frac{28}{3}+b\\b=-\frac{16}{3}\)

This means the y-intercept is \(\boxed{\left(0, -\frac{16}{3} \right)}\)

To find the x-intercept, we can set the equation equal to 0 and solve for x.

\(0=-\frac{4}{3}x-\frac{16}{3}\\\frac{16}{3}=-\frac{4}{3}x\\x=-4\)

So, the x-intercept is \(\boxed{(-4, 0)}\)

c) \(\left(\frac{-7+5}{2}, \frac{4-12}{2} \right)=\boxed{(-1, -4)}\)

d) \(ab=\sqrt{(-7-5)^{2}+(-12-4)^{2}}=\boxed{20}\)

e) The perpendicular bisector must pass through the midpoint, (-1, 4), and have a slope that is the negative reciprocal (so in this case, 3/4). Substituting into point-slope form,

\(y-4=\frac{3}{4}(x+1)\\y-4=\frac{3}{4}x+\frac{3}{4}\\\boxed{y=\frac{3}{4}x+\frac{19}{4}}\)

f) If ab is a diameter of said circle, this means it is centered at the midpoint, (-1, 4), and has a radius of 20/2=10. This means the equation is

\(\boxed{(x+1)^{2}+(y-4)^{2}=100}\)

Answer: Rational

Step-by-step explanation:

3.21 is rational because it is not an infinite decimal number or a square root that is not whole.

Answer:

what could be written?

Answer:

The correct answer is 7¹⁰

Step-by-step explanation:

I think you wrote 1.7 because i wrote 1. 7¹⁰

but I meant that 1. as the first question i was answering, sorry if I wasn't clear

The probability that Stephane wins 7 games out of 10 is 0.215 or about 21.5%.

We can model the number of games Stephane wins out of 10 as a binomial distribution with parameters n = 10 (number of trials) and p = 0.6 (probability of winning). The probability mass function of a binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) = n! / (k! * (n-k)!) is the binomial coefficient.

To find the probability that Stephane wins 7 games out of 10, we can plug in k=7, n=10, and p=0.6 into the formula:

P(X=7) = (10 choose 7) * 0.6^7 * 0.4^3

= 120 * 0.0279936 * 0.064

= 0.215

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-x⁴+ 6x³- 7x²- 4x - 4

Order from least to greatest exponent (the variable, which is x in this case, is always first by the way in terms of order, then integers). This point of this problem is essentially to just rearrange the original equation.

Answer:

Yes

Step-by-step explanation:

Y in represents the following in this linear regression Y = α₀+α₁X+α₂X₂+ε: C. dependent variable.

In Mathematics and Geometry, a regression line is a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line simply refers to a line which best fits a set of data.

In Mathematics and Geometry, the general functional form of a linear regression can be modeled by this mathematical equation;

Y = α₀+α₁X+α₂X₂+ε

Where:

In conclusion, Y represent the dependent variable or response variable in a linear regression.

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A vector parallel to the line of intersection of the two planes 2y - 2x + z = -3 and 3z - 5x = 3 is u = (3, 1, -2).

To find the vector parallel to the line of intersection of the two planes 2y - 2x + z = -3 and 3z - 5x = 3, first use the two equations to find the parametric form of the line of intersection.

This can be done by solving one of the equations for one of the variables, such as by solving the first equation for z, resulting in z = 2x + 2y - 3. Substitute this expression into the second equation, 3(2x + 2y - 3) - 5x = 3, to get 6x + 6y - 9 = 5x.

Solve for x to get x = 6y - 9, and substitute this into the first equation, 2y - 2(6y - 9) + z = -3, to get z = -12y + 21.

Therefore, the parametric form of the line of intersection is x = 6y - 9, y = y, z = -12y + 21. Since this line is parallel to a vector, take a nonzero value of y, such as y = 1, to get the vector u = (3, 1, -2).

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In this utility function, the term 6X represents the utility derived from consuming good X, while the term -Y represents the disutility or loss of satisfaction from consuming good Y. By subtracting Y from 6X, Chloe's preferences reflect the substitution relationship she perceives between the two goods.

A utility function describes an individual's preferences and the satisfaction they derive from consuming different goods. In Chloe's case, she believes that 6 units of good X can fully replace the satisfaction derived from consuming 1 unit of good Y. Therefore, we can construct a utility function based on this substitution ratio.

Let's denote the quantity of good X as X and the quantity of good Y as Y. Since Chloe believes that 6 units of X perfectly substitute 1 unit of Y, we can express her utility function as:

U(X, Y) = 6X - Y

It's important to note that utility functions are subjective and specific to an individual's preferences. Chloe's utility function captures her belief that 6 units of X are equivalent to 1 unit of Y, but it may not hold true for other individuals with different preferences or perceptions of substitutability between the goods.

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The projection matrix P describes the projection of R4 onto V = span{| 1 1 0 -2 | , | 1 5 1 1 |}.

To get the projection matrix P describing the projection of R4 onto V = span{| 1 1 0 -2 | , | 1 5 1 1 |}, follow these steps:
First, create a matrix A using the given spanning vectors as columns: A = [| 1 1 0 -2 | , | 1 5 1 1 |]
Compute the matrix product A * A^T: A * A^T = [| 1 1 0 -2 | , | 1 5 1 1 |] * [| 1  1 | , | 1  5 | , | 0  1 | , |-2  1 |]
Calculate the inverse of the resulting matrix (A * A^T)^(-1): (A * A^T)^(-1) = Inverse of the matrix obtained in step 2
Compute the matrix product A^T * (A * A^T)^(-1):
A^T * (A * A^T)^(-1) = [| 1  1 | , | 1  5 | , | 0  1 | , |-2  1 |] * Inverse of the matrix from step 3
Finally, calculate the projection matrix P: P = A * A^T * (A * A^T)^(-1) * A^T
The projection matrix P describes the projection of R4 onto V = span{| 1 1 0 -2 | , | 1 5 1 1 |}.

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Answer:

FM & MG = 21

Step-by-step explanation:

Given that M is the midpoint of FG, that means it splits it into 2 congruent lengths. Therefore if \(FM=8a+1\), then the other half has the same value. I can create a equation now because both of them should add up to 42

\(8a+1+8a+1=42\\16a+2=42\\16a=40\\a=\frac{40}{16}\\ a=\frac{5}{2}\)

Now that I have a, I can plug that in to \(8a+1\) to find both values. You should get that both of them are 21.

Hope that helps!

There are 2 ice cream flavor options, 4 sauce options, and 3 topping options, which gives us a total of 2 * 4 * 3 = 24 possible combinations of ice cream flavors, sauces, and toppings for the sundaes.

Combinations are a way to count the number of ways to choose a subset of objects from a larger set, where the order of the objects does not matter.

To list the sample space of all possible combinations of ice cream flavors, sauces, and toppings for the sundaes, we can list each option for each category and pair them together systematically.

Ice cream flavors:

C - Chocolate

V - Vanilla

Sauces:

H - Hot fudge

B - Butterscotch

S - Strawberry

P - Peanut butter

Toppings:

W - Whipped cream

F - Fruit

N - Nuts

Now, we can pair each option from each category to form the possible combinations:

CCWH - Chocolate ice cream, hot fudge sauce, whipped cream topping

CCWF - Chocolate ice cream, hot fudge sauce, fruit topping

CCWN - Chocolate ice cream, hot fudge sauce, nuts topping

CCBH - Chocolate ice cream, butterscotch sauce, whipped cream topping

CCBF - Chocolate ice cream, butterscotch sauce, fruit topping

CCBN - Chocolate ice cream, butterscotch sauce, nuts topping

CCSH - Chocolate ice cream, strawberry sauce, whipped cream topping

CCSF - Chocolate ice cream, strawberry sauce, fruit topping

CCSN - Chocolate ice cream, strawberry sauce, nuts topping

CCPH - Chocolate ice cream, peanut butter sauce, whipped cream topping

CCPF - Chocolate ice cream, peanut butter sauce, fruit topping

CCPN - Chocolate ice cream, peanut butter sauce, nuts topping

Similarly, we can pair the vanilla ice cream flavor with each sauce and topping option:

VCWH, VCWF, VCWN, VCBH, VCBF, VCBN, VCSH, VCSF, VCSN, VCPH, VCPF, VCPN

In total, there are 2 ice cream flavor options, 4 sauce options, and 3 topping options, which gives us a total of 2 * 4 * 3 = 24 possible combinations of ice cream flavors, sauces, and toppings for the sundaes.

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Answer:

The first one

Step-by-step explanation:

Because the line PQ is perpendicular to line ST, the slope of line ST is -1

The points are given as

P = (1, 4)

Q = (-2, 1)

Start by calculating the slope (m) of ST using

m = (y2 - y1)/(x2 - x1)

This gives

m = (1 - 4)/(-2 - 1)

Evaluate the difference

m = -3/-3

Evaluate the quotient

m = 1

From the question, we have

Line PQ is perpendicular to line ST

This means that

Slope of ST = -1/Slope of PQ

This gives

Slope of ST = -1/1

Evaluate

Slope of ST = -1

Hence, the slope of line ST is -1

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Answer:

30 is answer bro

Step-by-step explanation:

hope it wI'll help u

Sorry dude, diagram not visible, send a clear pic so I will help uh.

The probability of being dealt a 3, 4, 5, 6, 7, all in the same suit is approximately 0.0000031.

To calculate the probability of being dealt a 3, 4, 5, 6, 7, all in the same suit, we can use the following formula:

P = (number of favorable outcomes) / (total number of possible outcomes)

the order in which the cards are chosen does not matter, so we need to divide by the number of ways we can arrange 5 cards, which is 5! (5 factorial).

Therefore, the total number of possible outcomes is (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1), which simplifies to 2,598,960.

Finally, we can calculate the probability of being dealt a 3, 4, 5, 6, 7, all in the same suit:

P = 8 / 2,598,960

P = 0.00000308 (rounded to seven decimal places)

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