What is the length of the diagonal, d, of the rectangular prism shown below?
Round your answer to the nearest tenth.

Answer:

3

Step-by-step explanation:

Answer: 41.86 miles/hour

Step-by-step explanation:

Use Distance = Speed*Time to find the two missing values with the data that is provided for those two cases [in brackets].

MPH MILES     HOURS

 50            20      [0.4]

 [40]    70      1.75

Totals   90 miles   2.15 hours

Average = 90 miles/2.15 hours

     41.86 mph

Answer:

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tStep-by-step exrprlanation:ht

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Answer: 16

Step-by-step explanation: your welcome

Answer:

39

Step-by-step explanation:

15 students study Geography and 24 study history.

15+24=39

Answer:

a.  L = 0.5d + 34, and

b.  "Never," or "can't be determined with the information provided."

Step-by-step explanation:

a.  Write an equation for the water level, L, after d days.

L is water level, in feet.  It is rising at a rate of 0.5 ft/day.  The slope of an equation of a straight line (we know it is straight, since the rate of increase is a constant, 0.5 ft/day) would be:

y = mx + b

y = 0.5x + b

x is the number of days, which are set to "d," as per the instructions., and b is the water height at day 0, the start.  In this case, the initial height is 34 feet.  So the equation for predicting future water levels, L, is:

L = 0.5d + 34                                [L = 0.5(ft/day)d + 34(ft)]

b. In how many days will the water level be 26 feet?

The question is asking how many days it will take for the water level to reach 26 feet.  This is odd, since we are only told that the river is rising.  No information was given about timing when the river may begin falling, not the rate at which that will occur.  Based only on the way the question is written, the answer is "Never," or "can't be determined with the information provided."

If the question was phrased "In how many days will the water level reach 42 feet, we can use the equation to find d:

L = 0.5d + 34

42 = 0.5d + 34

0.5d = 8

d = 16 days  

The value of the variable 'x' and 'y' will be 6 feet and 5 feet, respectively. Then the perimeter of the small triangle will be 21 feet.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The triangles are similar triangles, then the equation is given as,

x / 15 = y / 12.5 = 10 / 25

From the last two terms,

y / 12.5 = 10 / 25

y / 12.5 = 0.40

y = 5

From the first term and last term,

x / 15 = 10 / 25

x / 15 = 0.40

x = 6

The value of the variable 'x' and 'y' will be 6 feet and 5 feet, respectively. Then the perimeter of the small triangle is given as,

P = 10 + 6 + 5

P = 21 feet

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bbbbbbbbbbbbbbb bbbbbbbbbbbbbb

Answer:

So the slope is rise over run. You need the y intercept and the slope to write an equation. To find the y intercept, use the formula : 0=4(slope)*3+b and you get 0=12+b then you subtract twelve from both sides, getting b=-12. Thats your y intercept. So your equation will be y=4x-12

The perimeter and area in hectares of the given field = 700m and 2.64 hectares respectively.

The formula that is used to calculate the perimeter here f a field = 2(l+w)

where,

Length = 240m

width = 110m

Perimeter = 2(240+110)

= 480 + 220

= 700m

The formula that is used to calculate the area of the field;

= length×width

= 240×110

= 26,400m²

To convert to hectares of land;

1 hec = 10000m²

X hec = 26,400m²

make X the subject of formula;

X= 26,400/10000

= 2.64 hectares.

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Answer: The answer is C, 1/3 cup.

Answer:

19.2 m

Step-by-step explanation:

Since this is a right triangle, we can use the pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

12^2 + 15^2 = c^2

144 + 225 = c^2

369 = c^2

Taking the square root of each side

sqrt(369) =sqrt(c^2)

19.20937271=c

To the nearest tenth

19.2 = c

Answer:

Diagonal of rectangle walk = 19.2 meter (Approx.)

Step-by-step explanation:

Given:

Length of rectangle = 12 meter

Width of rectangle = 15 meter

Find:

Diagonal of rectangle walk

Computation:

Diagonal of rectangle = √l² + b²

Diagonal of rectangle walk = √Length of rectangle² + Width of rectangle²

Diagonal of rectangle walk = √12² + 15²

Diagonal of rectangle walk = √144 + 225

Diagonal of rectangle walk = √369

Diagonal of rectangle walk = 19.2093

Diagonal of rectangle walk = 19.2 meter (Approx.)

We are given the function f(x) = x(24 − x) and asked to find and simplify the expressions for f(x + h) and f(x+h)-f(x) assuming h approaches 0.

(a) To find f(x + h), we substitute x + h into the function f(x) and simplify the expression:

f(x + h) = (x + h)(24 − (x + h))

= (x + h)(24 − x − h)

= 24x + 24h − x² − hx + 24h − h²

= 24x - x² - h² + 48h.

(b) To find f(x+h)-f(x), we substitute x + h and x into the function f(x) and simplify the expression:

f(x + h) - f(x) = [(x + h)(24 − (x + h))] - [x(24 − x)]

= (24x + 24h − x² − hx) - (24x - x²)

= 24x + 24h - x² - hx - 24x + x²

= 24h - hx.

(c) To find (f(x+h)-f(x))/h, we divide the expression f(x+h)-f(x) by h:

(f(x+h)-f(x))/h = (24h - hx)/h

= 24 - x.

Therefore, the simplified expressions are:

(a) f(x + h) = 24x - x² - h² + 48h,

(b) f(x+h)-f(x) = 24h - hx,

(c) (f(x+h)-f(x))/h = 24 - x.

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The count increase in the alien bacteria at the midnight is 31692.

Here we have to find the count of alien bacteria at midnight.

Data given:

Count of alien bacteria at 5 pm = 26,300

Percentage increase in bacteria per hour = 2.7%

increase = 1 + 2.7/100

               = 102.7

time = 12 - 5 = 7

The count of alien bacteria at midnight = 26,300 ×( 1.207 \()^{7}\)

                                                                 =  31692

Therefore the alien bacteria at midnight is 31692.

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After answering the provided question, we can state that Therefore, the equation solution for k is k = tm.

In mathematics, an equation is a proclamation stating the equality or two manifestations. An equation is made up of two sides that are separated by an analytical solution (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of equation solving is to determine the value or beliefs of the variable(s) that will allow the equation to be true. Equations can be simple or complex, normal or nonlinear, and include one or more factors. In the eqn "x2 + 2x - 3 = 0," for example, the variable x is raised to the powercell. Lines are utilized by numerous fields of mathematics, which include algebra, calculus, or geometry.

To solve for k in the equation r=tmr/k,

\(k * r = tmr\\k = tmr/r\\k = tm\)

Therefore, the solution for k is k = tm.

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Answer:

Cyclist A lives farther from the Orchard

Step-by-step explanation:

Given

\(A(x) =48.5 -21x\)

\(B(x) =42 -16.8x\)

Required:

Who lives farther from the Orchard.

To do this, we simply calculate the y intercept.

This represents the total distance traveled to get to the Orchard

To calculate y intercept, we set \(x = 0\)

So:

\(A(x) =48.5 -21x\)

\(A(0) = 48.5-21*0 =48.5-0 =48.5\)

\(B(x) =42 -16.8x\)

\(B(0) = 42 - 16.8*0 =42-0 =42\)

From the above computation:

\(A(0) > B(0) \to 48.5 > 42\)

Hence;

Cyclist A lives farther from the Orchard

Step-by-step explanation:

Use the Pythagorean theorem: a^2 + b^2 = c^2. In this case, sides a and b are each 7sqrt(3), and c is the diagonal of the square.

a^2 + b^2 = c^2

(7sqrt3)^2 + (7sqrt3)^2 = c^2

294 = c^2

c = sqrt(294) = 7sqrt(6)

\(\\ \sf \longmapsto 5x+3-2x=24\)

\(\\ \sf \longmapsto 5x-2x+3=24\)

\(\\ \sf \longmapsto 3x+3=24\)

\(\\ \sf \longmapsto 3x=24-3\)

\(\\ \sf \longmapsto 3x=21\)

\(\\ \sf \longmapsto x=\dfrac{21}{3}\)

\(\\ \sf \longmapsto x=7\)

The correct 98% confidence interval for the true proportion of graduates working in the field of study in which they obtained their degree is (0.811, 0.892).

To calculate the confidence interval, we need to use the formula for estimating proportions and the standard error of the proportion. The formula is:

Confidence interval = sample proportion ± z * standard error

Calculate the sample proportion

In this case, the sample proportion is the number of graduates working in their field of study (361) divided by the total number of graduates surveyed (424):

Sample proportion = 361/424 ≈ 0.852

Calculate the standard error

The standard error of the proportion is calculated using the formula:

Standard error = sqrt((sample proportion * (1 - sample proportion)) / sample size)

Using the given values, we have:

Standard error = sqrt((0.852 * (1 - 0.852)) / 424) ≈ 0.014

Determine the confidence interval

To find the z-value for a 98% confidence level, we look up the corresponding value in the z-table. The z-value for a 98% confidence level is approximately 2.33.

Substituting the values into the confidence interval formula, we have:

Confidence interval = 0.852 ± 2.33 * 0.014

Confidence interval ≈ (0.811, 0.892)

Therefore, the correct 98% confidence interval for the true proportion of graduates working in their field of study is (0.811, 0.892).

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Less than half of the surveyed internet users have posted photos or videos online. To determine if less than half of internet users have posted photos or videos online based on the poll, we can follow these steps:

1. Calculate the proportion of users surveyed who have posted photos or videos online.
2. Compare the proportion to 0.5 (which represents half).

Step 1: Calculate the proportion
The poll surveyed 1,765 internet users, and 865 of them posted a photo or video online. To calculate the proportion, we can divide the number of users who posted (865) by the total number of users surveyed (1,765):

Proportion = 865 / 1,765 ≈ 0.49

Step 2: Compare the proportion to 0.5
Since 0.49 is less than 0.5, it appears that less than half of the surveyed internet users have posted photos or videos online.

However, we cannot conclude that this is true for all internet users, as the poll surveyed a limited sample size of 1,765 users. A larger, more representative sample may be needed to draw a more accurate conclusion.

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Complete Question:

a poll surveyed 1765 internet users and found that 865 of them had posted a photo or video online. can you conclude that less than half of internet users have posted photos or videos online? use the ∝ = 0.01 level of significance and the P value method with the TI-84 calculator.

Answer: $23.92

Step-by-step explanation:

First, we know that 6 bagels is $2.99.

48/6=8

This means that 6 is a multiple of 48, which makes it easier to solve.

$2.99 x 8 = 23.92

= $23.92

Step-by-step explanation:

1. Degree is asking for highest exponent which is 4

2. leading coefficient is the number in front of highest degree term so 6

3. Replace x with 2 and solve

-3(2)^3 +6(2)^4 -8(2)^2 + 10(2) +16

= -24 +6(16) -32+20+16

= 76

The second option is correct. The domain of the composite function (g o f) (x) is all real numbers except x = 0.

To determine the domain of the composition (g o f)(x), we need to consider the domains of both functions, as well as any restrictions that arise from the composition.

The function f(x) = 3x is defined for all real numbers since there are no restrictions on x.

The function g(x) = 1/x, however, has a restriction. It is not defined for x = 0 because division by zero is undefined.

Thus for the composition (g o f)(x) = g(f(x)):

(g o f)(x) = g(f(x)) = g(3x) = 1/(3x)

Since the function g(x) = 1/x has a restriction at x = 0, it implies that the composition (g o f)(x) = 1/(3x) will also have the same restriction.

Therefore, the domain of the composite function (g o f)(x) is all real numbers except x = 0.

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Answer:

$1.67 per square foot

Step-by-step explanation:

First find the area of the carpet.

A=l times w

A-10(12)

A=120 square feet

Now divide 200 by 120

to find the price divide 200 by 120.

The total cost is rounded to $1.67 per square foot or round it to as many digits in your problem.

Answer:

y = 2x - 4

Step-by-step explanation:

To solve this problem, we must first calculate the slope of the line AB using the formula:

\(\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

where:

m ⇒ slope of the line

(x₁, y₁), (x₂, y₂) ⇒ coordinates of two points on the line

Therefore, for line AB with points A = (2, 5) and B = (4, 4) :

\(m_{AB} = \frac{5 - 4}{2 - 4}\)

⇒ \(m_{AB} = \frac{1}{-2}\)

⇒ \(m_{AB} = -\frac{1}{2}\)

Next, we have to calculate the slope of the line BC.

We know that the product of the slopes of two perpendicular lines is -1.

Therefore:

\(m_{BC} \times m_{AB} = -1\)      [Since BC and AB are at right angles to each other]

⇒ \(m_{BC} \times -\frac{1}{2} = -1\)

⇒ \(m_{BC} = -1 \div -\frac{1}{2}\)      [Dividing both sides of the equation by -1/2]

⇒ \(m_{BC} = \bf 2\)

Next, we have to use the following formula to find the equation of line BC:

\(\boxed{y - y_1 = m(x - x_1)}\)

where (x₁, y₁) are the coordinates of a point on the line.

Point B = (4, 4) is on line BC, and its slope is 2. Therefore:

\(y - 4 =2 (x - 4)\)

⇒ \(y - 4 = 2x - 8\)         [Distributing 2 into the brackets]

⇒ \(y = 2x-4\)

Therefore, the equation of line BC is y = 2x - 4.

Hicksian demand functions are:x1** = 2P₁x₂ ; x₂** = P₂²

Utility function: u(x1+x2) = .5ln(x1) + .25ln(x₂) .The Marshallian demand functions are: x1* = - and x₂* = P₂.

The indirect utility function is found by substituting Marshallian demand functions into the utility function and solving for v(P₁, P₂, Y).u(x1*,x2*) = v(P₁,P₂,Y) ⇒ u(-, P₂) = v(P₁,P₂,Y) ⇒ .5ln(-) + .25ln(P₂) = v(P₁,P₂,Y) ⇒ v(P₁,P₂,Y) = - ∞ (as ln(-) is not defined)

Thus the indirect utility function is undefined.

Minimum expenditure function can be derived from the Marshallian demand function and prices of goods:

Exp = P₁x1* + P₂x2* = P₁(-) + P₂P₂ = -P₁ + P₂²

Minimum expenditure function is thus:

Exp = P₁(-) + P₂²

Hicksian demand functions can be derived from the utility function and prices of goods:

H1(x1, P1, P2, U) = x1*H2(x2, P1, P2, U) = x2*

Hicksian demand functions are:

x1** = 2P₁x₂

x₂** = P₂²

If there are no restrictions on the amount of money the consumer can spend, the Hicksian demand functions for x1 and x2 coincide with Marshallian demand functions.

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Answer:

BD = 10

Step-by-step explanation:

THEY ARE EQUAL

BECAUSE LINE AB IS THE ANGLE BISECTOR

The two-column proof that the perimeter of a midsegment triangle is half the perimeter of the triangle is shown below

Below is a two-column proof that the perimeter of a midsegment triangle is half the perimeter of the triangle:

Given: us, st, and tu are midsegments of pqr.

Prove: the perimeter of stu = 1/2(pq + qr + rp).

Statement                                                                   Reason                                                                                    

us, st, and tu are midsegments of pqr                       Given  

us, st, and tu are line segments that connect           Definition of                                                                      

themidpoints of pq, qr, and rp, respectively.            midsegment

The midpoint of a line segment is the point that      Definition of

divides the line segment into two congruent            midpoint

(equal) parts

Therefore, us, st, and tu are each half the               Property of

length of pq, qr, and rp, respectively.                       midpoint

The perimeter of stu = us + st + tu                             Definition of perimeter

The perimeter of stu=(1/2)(pq) + (1/2)(qr) + (1/2)(rp)    Substitution

The perimeter of stu = 1/2(pq + qr + rp)                     Simplification

Thus, the perimeter of stu = 1/2(pq + qr + rp)             Conclusion

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Answer:

y=1/2x-4

Step-by-step explanation:

You are given the slope, 1/2. So you can plug it into the equation (y=mx+b)

You also need to plug in the x and y coordinate your given so you'll have

-3=1/2(2)+b. Then you solve for b, which is -4. You now have your answer, y=1/2x-4.

Answer:

if ur looking for the imaige of the answer:

Step-by-step explanation: