A fence was installed around the edge of a rectangular garden. The length, 1, of the fence was 5 feet less than 3 times its width, w. The amount of fencing used was 90 feet. Write a system of equations or write an equation using one variable that models this situation. Determine algebraically the dimensions, in feet, of the garden.​

Answer:

1/4 of an hour is 15 minutes

Step-by-step explanation:

Answer: 1/4 of an hr

Step-by-step explanation:

15/60 is 1/4

You need 5/2 times the amounts given in the recipe, so you need:

Here we have the recipe for 16 crepes:

You want to make 5 crepes for person, for 8 persons, so you need:

8*5 = 40 crepes.

So you need to make the recipe N times:

16*N = 40

N = 40/16 = 10/4 = 5/2

So you need a fraction of 5/2 times each of the amounts in the recipes.

You will need:

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Answer:

its option B : 18x3 – 12x2 + 9x – 6

Step-by-step explanation:

[tex]12( \frac{ -2 }{3}) {}^{2} +23( \frac{ - 2}{3} )+10= \frac{16}{3} − \frac{46}{3} +10=0[/tex]

12x² + 15x + 8x + 10 has a binomial factor of (3x+2).

ax²+bx+c=0, with a not equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

We may utilize the factor theorem, which asserts that if a polynomial f(x) has a component (x - a), then f(a) = 0, to identify which polynomial has (3x + 2) as a binomial factor.

In this situation, finding a value of x that reduces 3x + 2 to zero is necessary since we are trying to discover a polynomial that contains (3x + 2) as a component. We obtain x = -2/3 by solving 3x + 2 = 0.

Let's try the polynomials one by one:

(a) 6x³ + 3x² + 4x + 2:

f(-2/3) = 6(-2/3)³ + 3(-2/3)² + 4(-2/3) + 2

= -8/3 - 4/9 - 8/3 + 2

= -32/9,

so (3x + 2) is not a factor.

(b) 12x² + 15x + 8x + 10:

f(-2/3) = 12(-2/3)₂ + 15(-2/3) + 8(-2/3) + 10

= 16/3 - 10 - 16/3 + 10

= 0,

so (3x + 2) is a factor.

(c) 18x³ - 12x² + 9x - 6:

f(-2/3) = 18(-2/3)³ - 12(-2/3)² + 9(-2/3) - 6

= -32/3 + 8/3 - 6 - 6

= -32/3,

so (3x + 2) is not a factor.

(d) 21x⁴ + 7x³ + 6x + 2:

f(-2/3) = 21(-2/3)⁴ + 7(-2/3)³ + 6(-2/3) + 2

= 64/27 - 56/27 - 4 + 2

= 2/27,

so (3x + 2) is not a factor.

Therefore, the only polynomial that has (3x + 2) as a binomial factor is 12x² + 15x + 8x + 10.

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Answer:

[tex]-8x + 6y = -180[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{5} x-\frac{3}{5}y=18[/tex]

[tex]8x + 12y = 11[/tex]

Required

Equivalent form of the first equation that eliminates x when added to the second

To do this, we simply make the coefficients of x to be opposite in both equations.

In the second equation, the coefficient of x is 8.

So, we need to make the coefficient of x -8, in the first equation.

[tex]\frac{4}{5} x-\frac{3}{5}y=18[/tex]

Multiply by -10

[tex]-10 * [\frac{4}{5} x-\frac{3}{5}y=18][/tex]

[tex]\frac{-40}{5} x+\frac{30}{5}y=-180[/tex]

[tex]-8x + 6y = -180[/tex]

When this is added to the first equation, the x terms becomes eliminated

Answer:

A, C, and F

Step-by-step explanation:

Answer:

That one

Step-by-step explanation:

It's kinda obvious if you look at the choices.

Answer:

8+14

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

half of 2/5 is 1/5 so half of 24 is 12.

since 12  is 1/5 of the number multiply 12 by 5 and you get 60.

The whole number will be 60 whose two fifths will be 24.

Given, Two fifths of a number is 24.

Writing in form of equation,

Let the whole number be x.

So, two fifth of x is 24.

[tex]\frac{2}{5} of x = 24[/tex]

[tex]\frac{2}{5} \times x = 24[/tex]

Apply cross multiplication,

[tex]x = \frac{24 \times 5}{2}[/tex]

x = 60.

Therefore the whole number is 60.

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Answer:

5) No

The actual distance between the drone and the fossil is [tex]32\dfrac{3}{4}[/tex] ft

Step-by-step explanation:

3) A. -2/9

(2/3 - 5/6)/3/4 = (-1/6)/(3/4) = (-1/6) × (4/3) = -2/9

4) d. [tex]0.\overline {90}[/tex]

10/11 = 0.9090909...

∴ 10/11 = [tex]0.\overline {90}[/tex]

5) The height of the drone is flying above the ground = [tex]25\dfrac{1}{2}[/tex] ft.

The location of the fossil below the ground = [tex]7\dfrac{1}{4}[/tex] ft.

Taking the ground level as the origin on a number line, we have;

The location of the drone relative to the ground =  + [tex]25\dfrac{1}{2}[/tex] ft. (The positive sign for a point above the origin)

The location of the fossil relative to the ground = [tex]-7\dfrac{1}{4}[/tex] ft. (The negative sign for a point below the origin)

Therefore;

The distance between the drone and the fossil = The difference between the location of the drone and the fossil

The distance between the drone and the fossil = [tex]25\dfrac{1}{2} - \left(-7\dfrac{1}{4} \right)[/tex]

[tex]25\dfrac{1}{2} - \left(-7\dfrac{1}{4} \right) = 25\dfrac{1}{2} + 7\dfrac{1}{4} = 32\dfrac{3}{4}[/tex]

The distance between the drone and the fossil = [tex]32\dfrac{3}{4}[/tex] ft.

Therefore;

The distance between the drone and the fossil > 32 ft.

Answer: C

So I was right, I guess.

Answer:

they are the same

Step-by-step explanation:

We can conclude that the volume of cylinder 1 is 3/4 times the volume of cylinder 2.

The volume of cylinder is given by -

V = πR²h

Given is to compare the volume of a cylinder with a radius of 6 inches and a height of 8 inches compare to the volume of a cylinder with a radius of 8 inches and a height of 6 inches.

Volume of cylinder 1 will be -

V(1) = πR²h = 6 x 6 x 8π = 36 x 8π = 288π

Volume of cylinder 2 will be -

V(2) = πR²h = 8 x 8 x 6π = 64 x 6π = 384π

So, we can write that -

V(1)/V(2) = (288π)/(384π)

V(1)/V(2) = (288)/(384)

V(1)/V(2) = 3/4

Therefore, we can conclude that the volume of cylinder 1 is 3/4 times the volume of cylinder 2.

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Answer:

It is called a rectangular prism

It has 8 vertices

Answer:

5ft^3

Step-by-step explanation:

The formula for volume is length × width × height.

so you multiply 1×2×2.5, which equals 5

After considering the given data we conclude that the total number of 4-element subsets that can be generated is 70.

To evaluate the number of 4-element subsets that can be formed from the set {A,B,C,D,E,F,G,H}, we can apply the combination formula:
[tex]nCr = n! / r!(n-r)![/tex]
Here,
n = maximum count of elements in the set
r = total count of elements we want to choose.
For the given case, n = 8 (since there are 8 elements in the set) and r = 4 (since we want to choose 4-element subsets).
Placing in these values, we get:
[tex]nCr = 8! / 4!(8-4)! = 8! / 4!4![/tex]
[tex]= (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70[/tex]
Hence, creation of 70, 4-element subsets that can be formed from the set {A,B,C,D,E,F,G,H}.
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a)Using the chi-square distribution table, the critical value is 12.592 using Hypothesis.

b)The value of chi-square statistic for the sample is 16.042, given that

(a)Chi-square test

The Null Hypothesis H₀ : Myers-Briggs preference type is independent of area of study.

Alternative Hypothesis H₁ : Myers-Briggs preference type is dependent of area of study.

Test statistic is χ² = ∑ ((Oi - Ei)² / Ei)

Expected frequencies:To compute the expected frequencies of the data we use the formula:

Eij = (row total i * column total j) / n where

i is the row number and j is the column number.

To find the value of chi-square statistic, the following table is necessary:

Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 66 11 19 96
EN 80 42 32 154
IS 54 30 31 115
ES 71 40 43 154
Column total 271 123 125 519

We obtain the expected frequencies by the above formula, and these are listed in the table below.

Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 51.55 23.43 21.03 96
EN 86.71 39.56 27.73 154
IS 50.14 22.88 20.97 115
ES 82.61 37.13 32.27 154
Column total 271 123 125 519

The expected frequencies are computed by multiplying the row total and column total and dividing by the grand total, n.

Here, we have four rows and three columns.

Thus, the degrees of freedom are df = (4 - 1)(3 - 1) = 6 at the 0.05 level of significance.

Since we have four rows and three columns, the number of degrees of freedom will be 6.

Using the chi-square distribution table, the critical value is 12.592.

Since 16.04 > 12.592,

we reject the null hypothesis and conclude that Myers-Briggs preference type is dependent of area of study.

(b) Value of chi-square statisticThe formula to compute the chi-square statistic is

χ² = ∑ ((Oi - Ei)² / Ei) where Oi is the observed frequency and Ei is the expected frequency.

Calculating the chi-square statistic, we have

χ² = ((66 - 51.55)² / 51.55) + ((11 - 23.43)² / 23.43) + ... + ((43 - 32.27)² / 32.27)

  = 16.042 (rounded to three decimal places).

The value of chi-square statistic for the sample is 16.042.

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Using the Chain Rule to dw/dt. w = ln [tex]\sqrt{2a}.gifx^{2} + y^{2} + z^{2}[/tex], x = 4 sin t, y = 7 cos t, z = 9 tan t the expression will give us the final result for dw/dt.

To find dw/dt using the Chain Rule,

we'll start by expressing w as a composition of functions and then differentiate it step by step.

Given:

w = ln[tex](\sqrt{} (x^2 + y^2 + z^2))[/tex], where x = 4 sin(t), y = 7 cos(t), and z = 9 tan(t).

We'll first substitute the values of x, y, and z into the expression for w:

w = ln[tex](\sqrt{} ((4 sin(t))^2[/tex] + [tex](7 cos(t))^2[/tex] + [tex](9 tan(t))^2))[/tex]

Next, we'll differentiate w with respect to t using the Chain Rule.

The Chain Rule states that if we have a composite function f(g(t)),

its derivative is given by f'(g(t)) ×g'(t).

In our case, f(u) = ln[tex](\sqrt{u}[/tex] and g(t) represents the expressions within the square root.

Applying the Chain Rule, we have:

dw/dt = [tex](1/\sqrt{} (x^2 + y^2 + z^2))[/tex] × (2xdx/dt + 2ydy/dt + 2z×dz/dt)

Substituting the expressions for x, y, and z, we get:

dw/dt = (1/[tex]\sqrt{} ((4 sin(t))^2 + (7 cos(t))^2[/tex]+[tex](9 tan(t))^2))[/tex] ×(2(4 sin(t))(cos(t)) + 2(7 cos(t))(-sin(t)) + [tex]2(9 tan(t))(sec^2(t)))[/tex]

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The correct answer is that 13 students who spend more than 12 hours a week on screens were surveyed.

The provided data represents the number of students based on their screen time and whether their grade average is above or below 80.

To find the total number of students who spend more than 12 hours a week on screens, we need to look at the "Screen Time" category that corresponds to "more than 12 hours" and sum up the corresponding counts.

Looking at the data:

Screen Time:

less than 4 hours: 6 students

4-8 hours: 15 students

8-12 hours: 9 students

more than 12 hours: 13 students

If we consider only the "more than 12 hours" category, we find that there were 13 students.

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Answer:    5x-3

Step-by-step explanation:

3x+ 2x +2-5

5x        -3

Answer:

a = 7. b = 24, c = 25. This is a Pythagorean triple

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

PowerBroker provided a solution to the security issue at ABC Co. by removing admin rights, improving application security, and addressing network security and data protection concerns.

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Cohen's d (standardized effect size): approximately 0.963

Conclusion: The difference in mean solution times between the difficult instruction group and the easy instruction group is statistically significant, with a moderate effect size.

To calculate the value of the standardized effect size, also known as Cohen's d, we can use the formula:

Cohen's d = (M1 - M2) / Sp

Where:

M1: Mean solution time for the "difficult" instruction group (given as 15.8 minutes)

M2: Mean solution time for the "easy" instruction group (given as 9.0 minutes)

Sp: Pooled standard deviation (given as 7.06)

Let's calculate the value of Cohen's d:

Cohen's d = (15.8 - 9.0) / 7.06

= 6.8 / 7.06

≈ 0.963

The value of the standardized effect size (Cohen's d) is approximately 0.963.

Now, let's provide a conclusion based on this information. A standardized effect size of 0.963 indicates a moderate effect. Since the null hypothesis was rejected, it suggests that the difference in mean solution times between the two groups (difficult instruction and easy instruction) is statistically significant.

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Answer:

50

Step-by-step explanation:

if im thinking right

im SOO sorrYYy if its wrong

Answer:

[tex](x,y) => (2.5x,2.5y)[/tex]

Step-by-step explanation:

Given

See attachment for ABCD and A'B'C'D'

Required

Determine the dilation rule

Using AB and A'B' as points of references;

[tex]AB = (-1,2)\ to\ (2,1)[/tex]

[tex]A'B' = (-2.5,5)\ to\ (5,2.5)[/tex]

The dilation factor (k) is calculated as:

[tex]k = \frac{A'B'}{AB}[/tex]

This gives:

[tex]k = \frac{(-2.5,5)}{(-1,2)} \ or\ k = \frac{(5,2.5)}{(2,1)}[/tex]

Factorize

[tex]k = \frac{2.5*(-1,2)}{(-1,2)} \ or\ k = \frac{2.5*(2,1)}{(2,1)}[/tex]

[tex]k = 2.5 \ or\ k = 2.5[/tex]

Hence, the scale factor is 2.5

The dilation rule is:

[tex](x,y) => k(x,y)[/tex]

[tex](x,y) => 2.5(x,y)[/tex]

[tex](x,y) => (2.5x,2.5y)[/tex]

Answer:

its c ^u^ and the next to it is b :D

Step-by-step explanation:

edg 21

Answer:

It’s c and the next one is b

Step-by-step explanation:

Just took edge

Answer:

arc length d = ∫ √(1 + (dy/dx)²) dx

y = 228 - x²/57

dy/dx = -2x / 57

(dy/dx)² = (2x/57)²

Upper limit for integration:

y = 0 = 228 - x²/57

yields x = 114

d = ∫ √(1 + (2x/57)²) dx for 0 ≤ x ≤ 114 = 264.9 m

Step-by-step explanation:

Answer:

Option E

Step-by-step explanation:

The two points are (1,6) and (-3,-6) . We can find the Equation of the line using two point form , as ,

[tex]\implies y - y_1 =\dfrac{y_2-y_1}{x_2-x_1}(x - x_1) \\\\\implies y - 6 = \dfrac{-6-6}{-3-1}(x-1) \\\\\implies y-6 = \dfrac{-12}{-4}(x-1) \\\\\implies \boxed{\boxed{y -6 = 3(x-1)}} [/tex]

On looking at options we see that option E is correct .