A truck can be rented from Company A for ​$130 a day plus ​$0.40 per mile. Company B charges ​$70 a day plus ​$0.80 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.

Answer:

$0.65

Step-by-step explanation:

you will divide the 12 into 7.80=7.80/12

There are 200 fishes estimated.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total. According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

captures 20 fish out of a small lake behind his college.

Now,

He again catches 20 fishes out of which 2 have markers

let the estimated fish are x.

So,

2/ 20 = 20 /x

20 x 20 = 2x

400 = 2x

x= 400/ 2

x= 200

Hence, there are 200 fishes estimated.

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Kayla would have approximately $554.93 in the account after 12 years, rounded to the nearest dollar.

Learn more about To calculate the amount Kayla would have in the account after 12 years, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = the final amount

P = the principal amount (initial deposit)

r = the annual interest rate (in decimal form)

n = the number of times interest is compounded per year

t = the number of years

In this case, Kayla deposits $380 every quarter, so the principal amount (P) is $380. The annual interest rate (r) is 3.3% or 0.033 as a decimal. The interest is compounded quarterly, so n = 4. The number of years (t) is 12.

Plugging these values into the formula:

A = $380 * (1 + 0.033/4)^(4*12)

Calculating the exponent:

A = $380 * (1 + 0.00825)^(48)

A = $380 * (1.00825)^(48)

Using a calculator, we can calculate the value of (1.00825)^(48) ≈ 1.464096

A = $380 * 1.464096

A ≈ $554.93

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Answer:

The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation. ... This is because there is truly no solution—there are no values for x that will make the equation true

Answer:

No solution

Step-by-step explanation:

The solution x = 0 means that the value 0. “No solution” means that there is no values

a. The unemployment rate is 20%.

b. The labor-force participation rate is 60%.

According to the question,

Working age population- 100,000

Labour force - 60,000

Unemployed - 12000 instructions

a) The unemployment rate is the percentage of the labor force that is unemployed and it is calculated as follows:

Unemployment Rate = \(\frac{Number of unemployed People}{Labor force}\) × 100

When an unemployed population is 12,000 and the labor force is 60,000,

the unemployment rate is  = \(\frac{12000}{60000}\) × 100 = 20%

b) labor force participation rate is the percentage of working adult population that participates in labor either by actively looking for a job, or working. It is calculated as follows:

Labor Force Participation Rate = \(\frac{Labor force}{working age population}\) × 100

When the labor force is 60,000 and the working-age population is 100,000

Labor Force Participation Rate = \(\frac{60000}{100000}\) × 100 = 60%

So, a. The unemployment rate is 20%.

b. The labor-force participation rate is 60 %.

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Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

When the equals sign (=) is used to denote equality, an algebraic theorem resembles a rule joining two statements. An algebraic equation is a factual assertion that shows the equivalence of multiple numerical variables. The values ob d + 6 and 12 are separated by an equal sign in the calculation data logger + 6 = 12. The number of syllables that correspond to each side of each letter can be expressed numerically. The message of a symbol is frequently its complete opposite.

Here,

Given :

After a few weeks, you create and calculate an equation

so determine how much money is in your bank account.

M equals -36, as you discover.

Thus,

It mean that you owe 36 amount of money to bank.

Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

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Answer:

(i) 32 cubic meters, (ii) 800

Step-by-step explanation:

(i) 1 x 4 x 0.5 = 2 m3, x 16 = 32

(ii) 1000 litre per m3 = 32,000 litres required divided by 40 = 800 bags.

Sagot:

100 cm

Hakbang-hakbang na paliwanag:

Kung ganoon :

Distansya na sakop ng Ruben = 900 centimetri

Distansya na sakop ng Jamie = 10 metro

Pagko-convert sa centimeter:

100 cm = 1 m

x cm = 10 m

Paggamit ng multiplikasyon ng krus:

x = 100 * 10

x = 1000 cm.

Dahil dito Distansya ni Jamie = 1000 cm

Distansya sa pagitan ng Jamie at Ruben;

1000 cm - 900 cm = 100 cm

Answer:

Ab and Xz are congruent, and B=X, A=Z, which proves it is with SAS

Step-by-step explanation:

Answer:

12 is the largest one number of gift bags he can make. Each will have 4 gingerbread cookies and 5 candy canes

Step-by-step explanation:

The probability that a student chosen randomly from the class passed the test or completed the homework is 20/27.

The probability that a student chosen randomly from the class passed the test or completed the homework is calculated as follows:

Let the probability that a student completed the homework be P(B).

Also, let the probability that a student passed the test be P(A)

P(A or B) = P(A) + P(B) - P(A * B)

From the data table:

The number of students who passed the test = 18

The number of students who completed the homework = 17

The number of students who both passed the test and completed the homework = 15.

Total number of students = 27

P(A) = 18/27

P(B) = 17/27

P(A*B) = 15/27

Therefore,

P(A or B) = 18/27 + 17/27 - 15/27

P(A or B) = 20/27

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The number of different pairs that will result from selecting two different brands at a time can be calculated using the formula for combinations.

The formula for combinations is nC2, where n represents the total number of items and 2 represents the number of items being selected at a time. In this case, we have 4 different brands of soft drinks. So, applying the formula, the number of different pairs will be 4C2.
Using the combination formula, 4C2 can be calculated as follows:
4C2 = 4! / (2!(4-2)!)
    = 4! / (2!2!)
    = (4 * 3 * 2 * 1) / ((2 * 1) * (2 * 1))
    = (24) / (4)
    = 6

Therefore, there will be 6 different pairs resulting from selecting two different brands at a time.There will be 6 different pairs resulting from selecting two different brands at a time.To calculate the number of different pairs, we use the formula for combinations, which is nC2. In this case, we have 4 different brands of soft drinks. So, applying the formula, 4C2 can be calculated as 4! / (2!(4-2)!), which simplifies to 24 / 4, resulting in 6. Hence, there will be 6 different pairs resulting from selecting two different brands at a time.To determine the number of different pairs resulting from selecting two different brands at a time, we can use the formula for combinations. The formula for combinations is nC2, where n represents the total number of items and 2 represents the number of items being selected at a time. In this case, we have 4 different brands of soft drinks. So, we can apply the formula as follows: 4C2 = 4! / (2!(4-2)!). Breaking down the equation, 4! (4 factorial) is calculated as 4 * 3 * 2 * 1, while 2! (2 factorial) is calculated as 2 * 1. The result is 24 / (2 * 2), which simplifies to 6. Therefore, there will be 6 different pairs resulting from selecting two different brands at a time.

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Answer:

8.74

Step-by-step explanation:

The straight line distance from the front seat to the back is approximately 69.7 feet.

Straight line distance refers to the shortest distance between two points in a straight line, as opposed to the distance that would be traveled along a curved path or following the contours of the terrain.

Let the distance from the front row to the back row be x.

Then, we can use the tangent function to find the height difference between the front and back rows:

tan(12°) = (height difference) / x

Solving for the height difference:

height difference = x * tan(12°)

The problem tells us that the height difference is 15 feet, so we can set up an equation:

15 = x * tan(12°)

Solving for x:

x = 15 / tan(12°) ≈ 69.7 feet

Therefore, the straight line distance from the front seat to the back is approximately 69.7 feet.

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The distance between the two spheres is 6 - √5 units.

To find the distance between the spheres x² + y² + z² = 4 and x² + y² + z² = 8x + 8y + 8z - 47, first rewrite the second equation:

x² - 8x + y² - 8y + z² - 8z = -43

Now, complete the squares for x, y, and z terms:

(x - 4)² - 16 + (y - 4)² - 16 + (z - 4)² - 16 = -43

Combine the constants:

(x - 4)² + (y - 4)² + (z - 4)² = 5

Now, we have two spheres with centers (0, 0, 0) and (4, 4, 4) and radii 2 (from √4) and √5 (from √5), respectively. To find the distance between the spheres, subtract their radii from the distance between their centers:

Distance = √[(4 - 0)² + (4 - 0)² + (4 - 0)²] - 2 - √5
Distance = √(64) - 2 - √5
Distance = 8 - 2 - √5

So, the distance between the two spheres is 6 - √5 units.

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Answer:

answer is explained in the image.

Step-by-step explanation:

hope this helps!

To calculate the flux of the vector field \(F = 3xy^2i + xe^zk + z^3k\)across the surface S, which is the surface of the solid bounded by the cylinder \(y^2 + z^2 = 9\)and the planes x = -3 and x = 3, we can use the Divergence Theorem.

The Divergence Theorem states that the flux of a vector field F across a closed surface S is equal to the triple integral of the divergence of F over the region enclosed by S.
First, we need to determine the divergence of F. The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by div(F) = (∂P/∂x) + (∂Q/∂y) + (∂R/∂z).
In this case, \(F = 3xy^2i + xe^zk + z^3k,\)so we have \(P(x, y, z) = 3xy^2, Q(x, y, z) = xe^z,\)and \(R(x, y, z) = z^3\). Taking the partial derivatives, we find\((∂P/∂x) = 3y^2, (∂Q/∂y) = 0\), and (∂R/∂z) = \(3z^2\).
No can, we evaluate the triple integral of the divergence of F over the region enclosed by S. The region is defined by\(-3 ≤ x ≤ 3, -√9 - z^2 ≤ y ≤ √9 - z^2,\)and -3 ≤ z ≤ 3. Integrating (∂P/∂x) + (∂Q/∂y) + (∂R/∂z) over this region will give us the flux of F across S.
Performing the integration will yield the final numerical result of the flux.

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\(\dfrac{2}{3}x=6\)

\(\dfrac{\frac{2}{3}x}{\frac{2}{3}}=\dfrac{6}{\frac{2}{3}}\\\\x=\dfrac{6}{\frac{2}{3}}\\\\x=6\div\dfrac{2}{3}\)

\(x=6\times\dfrac{3}{2}\\\\x=\dfrac{18}{2}\\\\x=9\)

x = 9

A right angle is an angle measuring exactly 90 degrees. A congruent angle is an angle that has the same measure as another angle. Therefore, for two angles to be congruent, they must have the same measure, and if they are right angles, they must each measure exactly 90 degrees.

Since both angles measure exactly 90 degrees, and any two right angles are always equal, the hypothesis that "If two angles are right angles, then they are congruent" is true. A right angle is one of the most common types of angles and is found in a variety of geometric shapes, including squares, rectangles, and triangles.

Because they always measure exactly 90 degrees, they are easy to identify and work with when solving geometry problems. In conclusion, two angles are congruent if they have the same measure, and if they are both right angles, they are also congruent because they both measure exactly 90 degrees.

The hypothesis that "If two angles are right angles, then they are congruent" is true.

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Answer:

Step-by-step explanation:

8 7/9 - 14 7/8

= 169/9 - 119/8

now you must find a common denominator

= 281/72

3 65/72 lbs

The additional information that could be used to prove that ΔXYZ ≅ ΔFEG by ASA or AAS are:

∠Z ≅ ∠G and XZ ≅ FG

∠Z ≅ ∠G and XY ≅ FE .

The AAS is a theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent angles and a pair of non-included sides.

The SAS is also another theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent sides and a pair of included congruent angles.

From the image attached below, we are only given one pair of congruent angles, which is ∠X ≅ ∠F.

Therefore, for both triangles to be congruent by AAS or SAS, the additional information needed are:

∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE .

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Answer:

5x^4y\(\sqrt{5}\)

Step-by-step explanation:

25*5=125 and 25 is a perfect square

x^4*x^4=x^8

y*y=y^2

Answer:

y- intercept = 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - \(\frac{3}{4}\) x + 5 ← is in slope- intercept form

with slope m = - \(\frac{3}{4}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{3}{4} }\) = \(\frac{4}{3}\) , then equation of perpendicular line is

y = \(\frac{4}{3}\) x + c

to find c substitute (- 3, - 3 ) into the equation

- 3 = - 4 + c ⇒ c = - 3 + 4 = 1

that is the y- intercept of the perpendicular line is c = 1

Answer:

B

Step-by-step explanation:

The equation of a line passing through the origin is

y = mx ( m is the slope )

Consider the points (0, 0 ) and (2, 100 )

slope = \(\frac{rise}{run}\) = \(\frac{100}{2}\) = 50

Then

y = 50x

There are 5 * 5 = 25 possible arrangements. Some examples include aa, bb, cc, dd, ee, ab, ac, ad, ae, ba, bb, bc, bd, be, and so on.

a. Choosing 2 objects at a time without repetition and with order counting: The ordered arrangements of 5 objects (a, b, c, d, e) taken 2 at a time without repetition and with order counting are: ab, ac, ad, ae,

ba, bc, bd, be,

ca, cb, cd, ce,

da, db, dc, de,

ea, eb, ec, ed.

b. Choosing 2 objects at a time without repetition and without order counting: The unordered arrangements of 5 objects (a, b, c, d, e) taken 2 at a time without repetition and without order counting are: ab, ac, ad, ae,

bc, bd, be,

cd, ce,

de.

c.Choosing 2 objects at a time with repetition: In this case, we can choose any of the 5 objects for the first position, and any of the 5 objects (including repetition) for the second position.

Therefore, there are 5 * 5 = 25 possible arrangements. Some examples include aa, bb, cc, dd, ee, ab, ac, ad, ae, ba, bb, bc, bd, be, and so on.

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The data suggests that training with method 1 leads to a significantly lower mean job time compared to training with method 2.

The data suggests that training with method 1 leads to a significantly lower mean job time compared to training with method 2.

Based on the data obtained from the experiment, where 10 workers were trained using both programs, it is possible to draw conclusions about the effectiveness of the training methods. The experiment employed a crossover design, where 5 workers were trained with method 1 first and then method 2, while the other 5 workers were trained with method 2 first and then method 1. After each training, the workers underwent a time-and-motion test to measure the speed of their performance in a skilled job.

The analysis of the data indicates that the mean job time is significantly lower after training with method 1 compared to method 2. This conclusion can be drawn by conducting appropriate statistical tests, such as a paired t-test or a repeated measures analysis of variance (ANOVA), to assess the significance of the observed differences in mean job time between the two training methods.

To further validate the findings and ensure the reliability of the conclusion, it is important to consider factors such as the specific nature of the skilled job being performed, the qualifications and prior experience of the workers, and the potential limitations of the experiment. These factors could influence the generalizability of the results to other contexts or populations.

Furthermore, it is crucial to evaluate the training methods themselves, including their content, delivery format, and duration, to identify potential reasons for the observed differences in mean job time. Understanding the specific aspects of method 1 that contribute to its effectiveness can provide valuable insights for optimizing industrial worker training programs and improving overall productivity.

In summary, the data from the experiment suggest that training with method 1 leads to a significantly lower mean job time compared to training with method 2. However, further research and analysis are necessary to confirm these findings, consider relevant factors, and gain a comprehensive understanding of the underlying mechanisms driving the observed results.

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