Which statement is true??

Answer:

127

Step-by-step explanation:

Answer:

  $4050

Step-by-step explanation:

You want to know how much money Lynn had left after she spent 16% and 30% of her $7500 on food and drink, respectively.

After spending a total of 16% +30% = 46% of her money, the amount remaining is 100% -46% = 54% of the original amount. That would be ...

  0.54 · $7500 = $4050

Lynn had $4050 left.

9514 1404 393

Answer:

  (x, y, z) = (8√7/105, 2√7/21, 4√7/35)

Step-by-step explanation:

The algebra is straightforward, if tedious.

We'll define X = x^2, Y = y^2, Z = z^2, -1/16 = a, -1/25 = b, -1/36 = c. Then the equations become ...

  √X = √(Y +a) +√(Z +a) . . . . [eq1]

  √Y = √(Z +b) +√(X +b) . . . . [eq2]

  √Z = √(X +c) +√(Y +c) . . . . [eq3]

__

As with any radical equation, you square both sides, isolate the remaining radical, then square both sides again. Each squaring introduces extraneous solutions.

The equations are symmetrical, so we can do the tedious stuff on the first one, then make the appropriate substitutions to see the other two equations.

  X = Y +a + 2√((Y+a)(Z+a)) +Z +a

  X - Y - Z -2a = 2√((Y+a)(Z+a)) . . . . isolate the remaining radical

  (X -Y -Z -2a)^2 = 4(Y+a)(Z+a) . . . . square both sides again

  X^2 +Y^2 +Z^2 +4a^2 -2XY -2XZ +2YZ -4aX +4aY +4aZ = 4YZ +4aY +4aZ +4a^2

Subtracting the right side gives ...

  X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4aX = 0 . . . . [eq4]

Then the remaining equations are ...

  X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4bY = 0 . . . . [eq5]

  X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4cZ = 0 . . . . [eq6]

Subtracting [eq6] from [eq5] gives a relation between Y and Z:

  -4bY +4cZ = 0

  Z = bY/c . . . . [eq7]

Substituting this into [eq4], we have ...

  X^2 +Y^2 +(bY/c)^2 -2XY -2X(bY/c) -2Y(bY/c) -4aX = 0

  X^2 +Y^2(1 -2b/c +(b/c)^2) -2XY(1 +b/c) -4aX = 0 . . . . [eq8]

Subtracting [eq5] from [eq4] gives a relation between X and Y:

  -4aX +4bY = 0

  Y = aX/b . . . . [eq9]

Substituting this into [eq8], we have ...

  X^2 +(aX/b(1 -b/c))^2 -2X(aX/b)(1 +b/c) -4aX = 0

Dividing by X* gives a linear equation in X:

  X(1 +(a/b(1 -b/c))^2 -2a/b(1+b/c)) -4a = 0

  X = 4a/(1 +(a/b(1 -b/c))^2 -2a/b(1+b/c))

Substituting the above values for a, b, c, we have ...

  X = 64/1575

  x = √X = √(64/1575) = 8/(15√7)

  Y = X(25/16)

  y = x(5/4) = 2/(3√7)

  Z = Y(36/25)

  z = y(6/5) = 4/(5√7)

The solution is ...

_____

* At this point the equation is of the form pX^2 +qX = 0 or X(pX +q) = 0. One solution is X=0, which is extraneous. The solution of interest is X = -q/p.

Explanation:

Mean of the number of new stores = (14 + 27 + 48 + 80 + 110 + 153 + 261 + 403 + 681)/9

Mean = 197.4444

Mx = 197.4444

Mean of the year = (1986 + 1987 + 1988 + 1989 + 1990 + 1991 + 1992 + 1993 + 1994)/9

Mean = 1990

My = 1990

Regression line:

Plotting the line of best fit:

The most specific name for the figure is an isosceles trapezoid

From the question, we have the following parameters that can be used in our computation:

The figure

The properties of the given figure are

Using the above as a guide, we have the following:

The figure is a trapezoid

Because the nonparallel sides are congruent, then the most specific name for the figure is an isosceles trapezoid

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When x = π/4 and dx = -0.3, dy = -2.4 and δy = 2.4. δx is an infinitesimal change in x

To find the differential of y, we differentiate y = 4tanx with respect to x. Using the derivative rules, we have dy = 4(sec^2x)dx.

To evaluate dy and δy when x = π/4 and dx = -0.3, we substitute these values into the expression for dy.

When x = π/4, sec^2(π/4) = 2, so dy = 4(2)dx = 8dx.

Given that dx = -0.3, we can calculate dy as follows: dy = 8(-0.3) = -2.4.

To evaluate δy, we use the fact that δx is an infinitesimal change in x. Therefore, δx = 0.3.

Using δy = dy = 4(sec^2x)δx, we substitute x = π/4 and δx = 0.3: δy = 4(2)(0.3) = 2.4.

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Answer:

I believe your answer is required in Rise/Run form.

Rise is -1 and Run is +2

so

-1/2

Step-by-step explanation:

Hope I helped You

To transform each old salary x into a new salary n(x) with an across-the-board raise of r, we can use the following function: n(x) = x + r

In this case, since each teacher at C.F. Gauss Elementary School is given an across-the-board raise of r, we can use this function to calculate their new salaries. For example, if a teacher's old salary is x, their new salary would be:

n(x) = x + r

So if the across-the-board raise is 10%, or r = 0.1, then a teacher with an old salary of $50,000 would have a new salary of:

n($50,000) = $50,000 + 0.1($50,000) = $55,000

Similarly, a teacher with an old salary of $70,000 would have a new salary of:

n($70,000) = $70,000 + 0.1($70,000) = $77,000

And so on for each teacher at C.F. Gauss Elementary School.

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Solution:

Given:

Cross multiplying the expression,

Therefore, the weight of 12-ft length is 248.4 lb

Answer: \(16x^4y^2a^6\)

Step-by-step explanation:

just apply to the power of 2 to every term

-4 times -4 is 16

x^2 to power of 2 is 2 times 2 so x^4

y^2 is y^2

a^3 to power of 2 is 3 x 2 = 6 so a^6

16x^4y^2a^6

Answer:

16x^4y^2a^6

Step-by-step explanation:

Do this step by step

16x^4y^2a^6

Please give brainliest!

Answer:

  7 cm, 16 cm, 19 cm

Step-by-step explanation:

Let s represent the length of the shortest side in cm. The longest side is 3s-2, and the other side is 2s+2. The perimeter is the sum of the side lengths.

  P = s + (3s -2) +(2s +2)

  42 = 6s . . . . . simplify, use the given value of perimeter

  7 = s . . . . . . . divide by 6

  2s+2 = 16

  3s -2 = 19

The side lengths are 7 cm, 16 cm, and 19 cm.

Answer:

20/4 = 5ml

Step-by-step explanation:

Answer: \(-2.2f-18\)

Step-by-step explanation:

\(-2.6f+0.4f-14-4=f(-2.6+0.4)+(-14-4)=-2.2f-18\)

The length of the beam is approximately 63.81 feet (rounded to 2 decimal places).

To find the length of the beam, we can use trigonometry. Let's consider the right triangle formed by the beam, the ground, and the building.

The angle between the ground and the beam is given as 78°, and the height of the beam from the ground to the top is 20 feet. We need to find the length of the hypotenuse, which represents the length of the beam.

Using trigonometric functions, we can relate the angle and the sides of a right triangle. In this case, we can use the sine function.

sin(78°) = opposite/hypotenuse

sin(78°) = 20/hypotenuse

To find the hypotenuse (beam length), we can rearrange the equation:

hypotenuse = 20 / sin(78°)

Calculating this value:

hypotenuse ≈ 20 / sin(78°) ≈ 63.81 feet

Therefore, the length of the beam is approximately 63.81 feet (rounded to 2 decimal places).

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Answer: -0.83

Step-by-step explanation:

A correlation coefficient(r) is used to determine the strength and direction of the relationship between two variables.

-1 ≤ r ≤1

For downward trend r is negative.

For strong correlation r should be closer to 1 or -1.

From the given correlation coefficients  -0.83 is both negative and closer to -1.

Hence, a correlation coefficient represents the strongest downward trend in a data set = -0.83

The required complete table regarding the distance traveled has been shown.

From the given condition, let y be the distance left and x be the time,
According to the question an equation model is given as,

Distance traveled = 5x
Distance remaining to travel = y = 5000 - 250x

Now,
Put x = 5
Distance traveled = 250x
                           = 250(5) = 1250

Distance remaining to travel = y
y = 5000 - 1250
y = 3750 ft

Similarly,
At
x = 20
Distance traveled = 5000

X = 10
Distance remaining = 2500

Thus, the required complete table has been shown.

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a. The two population variances are assumed to be equal

The assumption underlying the pooled t-test is that the two population variances are assumed to be equal.

The pooled t-test is used when comparing the means of two independent samples, assuming that the populations from which the samples are drawn have equal variances. This assumption allows for combining the information from both samples to obtain a more precise estimate of the common population variance.

The pooled t-test utilizes a pooled estimate of the common variance, which is calculated by combining the sample variances from both groups. By assuming equal variances, the pooled t-test takes into account the variability within each sample and provides a more accurate assessment of the difference in means.

However, it is important to note that if the assumption of equal variances is violated, the validity of the pooled t-test may be compromised. In such cases, alternative tests, such as the Welch's t-test, which does not assume equal variances, can be employed.

Therefore, the underlying assumption of the pooled t-test is that the two population variances are assumed to be equal.

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No solution

because delta ( b^2 - 4ac ) is lower than 0(zero) .

Answer:

false is the answer

Step-by-step explanation:

Answer:

12 or 13

Step-by-step explanation:

Answer:

Step-by-step explanation:

steps are below

step 1

y^3-8y^2+19y=12  equation

step 2

y^3-8y2+19y(-12)=12(-12)  minus 12 from both sides

y^3-8y^2+19y-12=0

step 3

(y-1)(y-3)(y-4)=0  add brackets

step 4

(y-1)(y-3)(y-4)=0  factor

step 5

y-1=0 or y−3=0 or y-4=0  set them equal

Answer:

y=1 or y=3 or y=4

Answer:

y=1; x=2

Step-by-step explanation:

Substitution:

x=2y

2x+5y=9

=> if x=2y, plug in the x value into other equation, so

----------------------------------------------------------------------------

2(2y)+5y=9

4y+5y=9

9y=9

y=1

You have the Y value, so now solve for X

-----------------------------------------------------------------------

plug in y value to x=2y

so x=2(1)

x=2

Answer:

8 and 5/8 miles

Step-by-step explanation:

Answer:

19.77 ft

Step-by-step explanation:

The ladder is the hypotenuse of a right triangle ....one leg is the house , the other leg is the ground.

sin 64  = opposite/hypotenuse = height /22

sin 64 = height / 22

22 * sin 64 = height = 19.77 ft

The Giapetto problem is a linear programming problem that involves maximizing profit from producing two types of wooden toys. In response to the questions:

a. The dual of the Giapetto problem can be obtained by interchanging the roles of the variables and constraints. The objective of the dual problem is to minimize the sum of the dual variables (representing the costs) subject to the constraints defined by the coefficients of the original primal problem.

b. To determine the optimal dual solution, we can examine the optimal tableau of the Giapetto problem. The dual solution is obtained by considering the dual variables associated with the constraints. These variables represent the shadow prices or the marginal values of the resources in the primal problem. By analyzing the optimal tableau, we can identify the values of the dual variables and determine the optimal dual solution.

c. In this instance, we can verify that the Dual Theorem holds. The Dual Theorem states that the optimal value of the dual problem is equal to the optimal value of the primal problem. By comparing the optimal solutions obtained in parts (a) and (b), we can confirm whether they are equal. If the optimal values match, it confirms the validity of the Dual Theorem, indicating a duality relationship between the primal and dual problems. The dual of the Giapetto problem involves minimizing costs instead of maximizing profit. By examining the optimal tableau, we can determine the optimal dual solution. Lastly, by comparing the optimal solutions of the primal and dual problems, we can verify the Dual Theorem's validity, which states that the optimal values of both problems are equal, demonstrating their duality relationship.

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Answer:

h = 440.94 feet

Step-by-step explanation:

It is given that,

An architect is standing 370 feet from the base of a building, x = 370 feet

The angle of elevation is 50°.

We need to find the approximate height of the building. let it is h. It can be calculated using trigonometry as follows :

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=370\times \tan50\\\\h=440.94\ \text{feet}\)

So, the approximate height of the building is 440.94 feet

3, -1

Step-by-step explanation:

It goes 3 to the positive side

and one down side

Answer:

Step-by-step explanation:

Given points

Midpoint formula

Midpoint is (2, 2)

The cost of the chocolate chips will be 2.75c. To find the total cost, we need to add the cost of the flour to the cost of the chocolate chips: Total cost = Cost of flour + Cost of chocolate chips Cost of flour = $3.59Cost of chocolate chips = $2.75c

To write an algebraic expression for the total amount Layla will spend at the store, we need to consider the cost of the flour and the cost of the chocolate chips. We know that she needs one bag of flour, which costs $3.59.

We also know that she needs a number of bags of chocolate chips, which we can represent using the variable c. Each bag of chocolate chips costs $2.75.

Therefore, the total cost can be represented by the following algebraic expression: Total cost = $3.59 + $2.75cThis expression gives us the total cost of all the ingredients needed to make the Double Chocolate Chocolate Chip cake.

We can use this expression to find the total cost for different values of c, depending on how many bags of chocolate chips Layla needs to buy for her recipe.

For example, if she needs 2 bags of chocolate chips, then c = 2 and the total cost will be: Total cost = $3.59 + $2.75(2) = $3.59 + $5.50 = $9.09 Similarly if she needs 3 bags of chocolate chips, then c = 3 and the total cost will be: Total cost = $3.59 + $2.75(3) = $3.59 + $8.25 = $11.84And so on.

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Step-by-step explanation:

it is geometric  

so we will use this equation:

a(n)=a1*(r)^(n-1)

and we have a(1)=75 , r=15/75=3/15=1/3

explicit formula: a(n)=75*(1/3)^(n-1)

hope this helps

Answer:

75(1/5)^n-1

Step-by-step explanation:

I just did it.