Oil flows back and forth between a small and large tank. When oil is moving into the large tank, the flow rate is
positive. When oil is moving into the small tank, the flow rate is negative.
The large tank begins with 600 gallons of oil. The flow rate is recorded as-4 gallons per minute. After a period of 32
minutes, how much oil has been moved and to which tank?
1289 into the large v tank.
After the 32 minutes, how much oil is in the large tank? gallons​

Emily can't get an A in the class, even if she gets an A on the last exam. This expectancy theory might explain.

Expectancy theory suggests that indivisuals are motivated to perform if they know that their extra performance is recognized and rewarded. Consequently companies using performance-based pay can expect improvements.

Expectancy theory explains the process of why someone chooses one behavior over another. In making this conclusion choice, there are three elements considered: expectancy, instrumentality and valence.

Expectancy is the belief that your effort will lead to better performance.

Instrumentality is the trust that if you perform well you will achieve the outcome you expect.

Valence is the how important you feel the outcome, and any related reward is to you personally.

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Thus, the cost to cover all three faces and base of the triangular prism is $12.24.

An elongated pyramid-like 3D shape is a triangular prism. It features three rectangular faces and two bases. A form must have two similar bases, at least three rectangle-shaped faces, and a consistent cross-section over its whole length in order to qualify as a prism. Your shape is a triangular prism if it is also triangular.

Area of the rectangular base A1 = length * width

A1 : 5*2 = 10 ft²

Area of two rectangles faces A2:

A2: 2*3 + 2*4 = 14 ft²

Area of the two triangles faces A3 = 1/2*base*height

Base of triangle: (x)+(x-5)

Using the Pythagorean theorem:

x²+h² = 3²  

h² = 9-x²   ...eq 1

(5-x)²+h²=4²

h²=16-(5-x)²   ...eq 2

Equating eq 1 and eq 2:

9-x² = 16-(5-x)²

9-x² = 16-25-10x-x²

on solving:

x=1.8

Then,

h²=9-(1.8)²------------ >

h=2.4 ft

Area A3 = (5*2.4)*2/2 = 12 ft²

Total Surface area A = A1+A2+A3

A = 10+14+12

A = 36 ft²

Rate of foil:

$0.34 for 1 ft²

For, A = 36 ft²

rate = 36*0.34

rate = $12.24

Thus, the cost to cover all three faces and base of the triangular prism is $12.24.

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complete question:

The figure shown is a triangular prism. How much would it cost to cover the bases and the other three faces with foil that costs $0.34 per square foot?

The value of T is 428°C.

To solve the problem, we can start by substituting the given value of R = 13946 into the equation R = 10000 + (4124 x 10^-2)T – (1779 x 10^-5)T^2 and solving for T. This gives us a quadratic equation in T which can be solved using the quadratic formula.

After simplifying, we get T = 427.67°C or T = -88.22°C. However, we know that the thermometer is only used if T ≤ 600°C, so the only valid solution is T = 427.67°C.Therefore, the temperature corresponding to a resistance of 13946 ohms is approximately 428°C.

It's important to note that this assumes the thermometer is operating within its specified range and that the resistance-temperature relationship remains linear over the given temperature range.

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Answer:

Option A is correct.

Step-by-step explanation:

Given

To determine

What is the equation in the standard form of the line that passes through the point (4, −8) and has a slope of 1/4.

Using the point-slope form of the line equation

\(y-y_1=m\left(x-x_1\right)\)

where

substituting the values m = 1/4 and the point (4, -8)

\(y-y_1=m\left(x-x_1\right)\)

\(y-\left(-8\right)=\frac{1}{4}\left(x-4\right)\)

\(y+8=\frac{1}{4}\left(x-4\right)\)

Subtract 8 from both sides

\(y+8-8=\frac{1}{4}\left(x-4\right)-8\)

\(y=\frac{1}{4}x-1-8\)

\(y=\frac{1}{4}x-9\)

Writing the equation in the standard form

As we know that the equation in the standard form is

Ax+By=C

where x and y are variables and A, B and C are constants

so

\(y=\frac{1}{4}x-9\)

\(x=4y+36\)

\(x - 4y = 36\)

Therefore, the equation in the standard form of the line that passes through the point (4, −8) and has a slope of 1/4 will be:

\(x - 4y = 36\)

Hence, option A is correct.

Answer:

25 feet per second

Step-by-step explanation:

40 yards = 120 feet

120/4.8 = 25

Answer:

25

Step-by-step explanation:

40 yards = 120 feet

120 ÷ 4.8 = 25

Answer:

$26

Step-by-step explanation:

\(25 \times \frac{4}{100} = 1\)

25+1=$26

The solution of the given system of equation is (6, 12). So the option c is correct.

In the given question, Carissa works as a babysitter during her summer vacation.

She gets paid one rate for daytime hours and a higher rate for nighttime hours.

One week, she worked 12 daytime hours and 4 nighttime hours and earned $120.

The next week, she earned $60 for a total of 4 daytime hours and 3 nighttime hours.

Let x represent the hourly daytime rate and y represent her hourly nighttime rate.

The system of equations is

12 x + 4 y = 120……………(1)

4 x + 3 y = 60……………(2)

We have to find the solution to the system of equations.

To find the solution for the system of equation we solve the given equation using elimination method.

Multiply equation by 3 on both sides, we get;

12x + 9y = 180

Subtract equation 3 and 1

12x+9y-(12x+4y)=180-120

12x+9y-12x-4y=60

5y=60

Divide by 5 on both side, we get;

y=12

Now putting the value of y in equation 2

4x+3×12=60

4x+36=60

Subtract 36 on both side, we get

4x=24

Divide by 4 on both side, we get

x=6

Hence, the solution of the given system of equation is (6, 12). So the option c is correct.

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Answer:  (6, 12)

Step-by-step explanation: did edge test

The value of x is approximately (7√3) / 3.

Given that a right triangle with base = x and the perpendicular side = 7 and the reference angle is 60°, we need to find the value of x.

To find the value of x in a right triangle with a base of x and a perpendicular side of 7, and with a reference angle of 60 degrees, we can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the side opposite the angle (in this case, 7) to the length of the side adjacent to the angle (in this case, x). So we have:

tan(60°) = 7 / x

Now, we can solve for x by multiplying both sides of the equation by x:

xtan(60°) = 7

To find the value of x, we need to know the value of tan(60°). The tangent of 60 degrees is √3. So we have:

x√3 = 7

To isolate x, we divide both sides of the equation by √3:

x = 7 / √3

To simplify the expression, we multiply both the numerator and the denominator by √3:

x = (7 / √3)(√3 / √3)

= (7√3) / 3

Therefore, the value of x is approximately (7√3) / 3.

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Angle of elevation of the ramp with a height of 27ft and a platform of 16ft is approximately 59.35°.

The ramp is 27ft long and rises to a platform, the bottom of the platform is 16ft from the foot of the ramp.

We need to find the angle of elevation of the ramp.

The angle of elevation of the ramp is the angle made by the ramp with the horizontal.

Let ABC be the ramp and D be the platform, as shown below: Let AB = 16ft and BC = 27ft.

We need to find the angle ABD.

Consider right-angled ΔABC In right-angled ΔABC,

we have:

tan⁻¹ (BC / AB)

θ  = tan⁻¹ (27 / 16)

θ ≈ 59.35°

Hence, the angle of elevation of the ramp is approximately 59.35°.

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the exact formula for X(n) is given by the sum of i from 1 to 4n + 1. The closed-form formula for X(n) is (4n + 1)(4n + 2)/2, expressed as a polynomial function. The asymptotic value of X(n) is approximately 4n^2, representing the growth rate as n approaches infinity.

(i) The exact formula for X(n) can be determined by analyzing the procedure PrintXs(n) and counting the number of times the letter "X" is printed. In this case, the outer loop runs for 4n + 1 iterations, and for each iteration, the inner loop runs i times. Thus, the total number of "X" letters printed is given by the sum of i from 1 to 4n + 1.

(ii) To express X(n) as a closed-form polynomial function, we can simplify the sum mentioned above. By using the formula for the sum of an arithmetic series, the closed-form formula for X(n) can be written as X(n) = (4n + 1)(4n + 2)/2.

(iii) The asymptotic value of X(n) can be expressed using the e-notation, which represents an estimate of the growth rate. In this case, as n approaches infinity, the dominant term in the expression (4n + 1)(4n + 2)/2 is 4n^2. Therefore, we can express the asymptotic value of X(n) as X(n) ~ 4n^2.

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The opposite side of the right triangle (x) is approximately 6.888 inches long.

To solve this problem, we can use the trigonometric ratio for the sine function, which is opposite/hypotenuse. We have the hypotenuse as 12 inches and the opposite angle as 35 degrees, so we can set up the equation:

sin(35) = opposite/12

To solve for the opposite, we can multiply both sides by 12:

opposite = 12 * sin(35)

sin(35) as approximately 0.574:

opposite = 12 * 0.574

opposite ≈ 6.888

Therefore, the opposite side of the right triangle (x) is approximately 6.888 inches long.

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Answer:

∠ B = 48° , a ≈ 18.0 , c ≈ 26.9

Step-by-step explanation:

∠ B = 180° - ( 90 + 42)° = 180° - 132° = 48°

using the tangent ratio in the right triangle

tan42° = \(\frac{opposite}{adjacent}\) = \(\frac{a}{20}\) ( multiply both sides by 20 )

20 × tan42° = a , then

a ≈ 18.0 ( to the nearest tenth )

using the cosine ratio in the right triangle

cos42° = \(\frac{20}{c}\) ( multiply both sides by c )

c × cos42° = 20 ( divide both sides by cos42° )

c = \(\frac{20}{cos42}\) ≈ 26.9 ( to the nearest tenth )

a false association between two variables that is actually due to the effect of a third variable is called a confounding variables.

In the context of a mathematical problem or experiment, a variable is anything that may be altered. Typically, a variable is denoted by a single letter. Common generic symbols used for variables include the letters x, y, and z. An attribute that can be measured and have a wide range of values is called a variable. Size, age, wealth, place of birth, academic standing, and kind of housing are a few examples of factors. Both categorically and numerically can be used to categorise variables into two primary groups.

Third factors that affect both the independent and dependent variables are referred to be confounding variables. You risk overestimating the correlation between your independent and dependent variables if you don't take confounding factors into account.

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Answer:

all you have to do is Just divided the numbers

Step-by-step explanation:

÷

The probability that atleast one ball is red is 14/15.

Given that:-

Number of red balls = 4

Number of black balls = 2

One ball is randomly selected, without replacement, the second ball is selected.

We have to find the probability that atleast one ball is red.

There are four ways in which this can happen:-

RR, BR, RB, BB

Where R stands for Red ball and,

B stands for Black ball.

We know that,

Probability that no ball is red + Probability that atleast one ball is red = 1

Hence, we can write,

Probability that atleast one ball is red = 1 - Probability that no ball is red

P(BB) = (2/6)*(1/5) = 1/15

Hence,

Probability that atleast one ball is red = 1 - (1/15) = 14/15

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RMSE =  (nΣt=1 (At-Ft)²/n is the formula .

What is Root Mean Square Error (RMSE)?

What makes a good RMSE?

Identify the formula used to calculate the root mean square error over a range of forecasted values, if the actual value of the time series at time t and the forecast value for time t are denoted by A t and F t respectively.

RMSE = [ (nΣt=1 (At-Ft)2) / n ]0.5

MSE = (nΣt=1 (At-Ft)²/n

RMSE = Root of MSE

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a) Hypothesis test:

Null hypothesis (H0): The percentage of graduate students looking for housing on campus is equal to 15%.

Alternative hypothesis (Ha): The percentage of graduate students looking for housing on campus is greater than 15%.

To test the hypothesis, we can use a one-sample proportion test. We will calculate the test statistic and compare it to the critical value or p-value to make a decision.

The observed proportion of graduate students looking for housing on campus is 78/433 = 0.1804.

Using a significance level (α) of 0.05, we will conduct the test and calculate the test statistic and p-value.

Plan:

Test statistic: z = (p - p) / sqrt(p(1-p)/n)

where p is the observed proportion, p is the hypothesized proportion (0.15), and n is the sample size (433).

Do:

Calculating the test statistic:

z = (0.1804 - 0.15) / sqrt(0.15 * 0.85 / 433)

z ≈ 2.07

Conclude:

Since the test statistic is 2.07, we compare it to the critical value or calculate the p-value.

The critical value for a one-sided test with a significance level of 0.05 is approximately 1.645. Since 2.07 > 1.645, the test statistic falls in the rejection region.

The p-value associated with the test statistic of 2.07 is less than 0.05. Therefore, we reject the null hypothesis.

Based on the survey data, there is evidence to suggest that the percentage of graduate students looking for housing on campus is greater than 15%. The housing office should consider increasing the amount of housing available to graduate students.

b) The p-value obtained in part a) represents the probability of obtaining a test statistic as extreme as the one observed (or more extreme), assuming the null hypothesis is true.

In this case, the p-value is less than 0.05, which suggests strong evidence against the null hypothesis. It indicates that the observed proportion of graduate students looking for housing on campus is significantly higher than the hypothesized proportion of 15%.

c) Including the 21 non-respondents would change the sample size and potentially affect the estimated proportion. If these additional respondents had similar characteristics to the 433 who responded, it is possible that the recommendation might still remain the same.

However, the exact impact depends on the responses of the non-respondents, so it is difficult to determine the precise effect without their data.

d) Type II error in this study would occur if the housing office fails to increase the amount of housing on campus when it is actually necessary (i.e., the percentage of graduate students looking for housing on campus is higher than 15%).

This means the null hypothesis would not be rejected when it should have been. A consequence of this type of error would be the unmet demand for housing, potentially causing dissatisfaction among graduate students and a shortage of available housing options.

e) Type I error in this study would occur if the housing office increases the amount of housing on campus when it is not necessary (i.e., the percentage of graduate students looking for housing on campus is not higher than 15%). This means the null hypothesis would be rejected incorrectly.

A consequence of this type of error would be allocating resources and efforts towards increasing housing capacity unnecessarily, which could result in wastage of resources and potentially impact other areas of the university's operations.

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Answer:

its true

Step-by-step explanation:

Answer:

see below!

Step-by-step explanation:

A) \(\frac{.15x + 25 + 48(.15)}{x + 48}\) which can be simplified to \(\frac{32.2 + .15x}{x + 48}\) = f(x)

B)

plug in 952 to x because x is the number of cookies left that you need to bake since 48 has been taken out already for the samples

\(\frac{32.2 + .15(952)}{952 + 48}\) -----> \(\frac{32.2 + 142.8}{1000}\)------> \(\frac{175}{1000}\) ------> $0.175 or 17.5 cents

hope this helps.......

Answer:

Additive

-2 = 2

18 = -18

-30 = 30

2/5 = -2/5

Multiplicative

8/9 = 9/8

12/15 = 15/12

-6 = -1/6

10 = 1/10

Step-by-step explanation:

an additive inverse is a number you must add to another number to get 0

(think of it as the negative version of the number)

{but WHY? In math, you can imagine comparing numbers on a number line. If we are finding the opposite of a number, we want to find the same distance from 0, but on the opposite side of 0. So, 2 would be two to the right of 0, -2 would be two to the left of 0}

-2 + 2 = 0

18 - 18 = 0

-30 + 30 = 0

2/5 - 2/5 = 0

a multiplicative inverse is a number that you multiply by another number to get 1.

We are finding the "reciprocal" of a number; you are essentially flipping it as a fraction

(reciprocal of 2 = 1/2  {remember, 2 is the same thing as 2/1 }   ; reciprocal of 1 / 8 = 8)

note: reciprocal is being used interchangeably with multiplicative inverse here

8/9 · 9/8 = 1

12/15 · 15/12 = 1

-6 · -1/6 = 1                     {-6  = -6/1}

10 · 1/10 = 1                    {10 = 10/1}

hope this helps!! have a lovely day :)

Answer:

Additive: number that you add to get 0

2

-18

30

-2/5

Multiplicative: number that you multiply to get 1

9/8

15/12

-1/6

1/10

hope this is helpful!!  ^u^

Answer:

Step-by-step explanation:

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     3

                     B   =    -2

                     C   =  -10

 B2  -  4AC   =

       4 - (-120) =

             =  124

Applying the quadratic formula :

              2 ± √ 124

  x  =    —————

                   6

 √ 124 simplified

 The prime factorization of  124   is

  2•2•31

To be able to remove something from under the radical, there have to be  2  instances of it

√ 124   =  √ 2•2•31   =

               ±  2 • √ 31

 √ 31, rounded to 4 decimal digits, is   5.5678

So now we are looking at:

          x  =  ( 2 ± 2 •  5.568 ) / 6

Two real solutions:

x =(2+√124)/6=(1+√ 31 )/3= 2.189

or:

x =(2-√124)/6=(1-√ 31 )/3= -1.523

Answer:

Step-by-step explanation:

3x^2-2x-10=0

This is a quadratic equation that can be solved using the quadratic formula where

a = 3, b = -2, and c = -10

x=−b±(b^2−4ac)^(1/2)/2a

x=−(−2)±((−2)2−4(3)(−10)^(1/2)/2(3))

x=2±(124)^(1/2)/6

Simplify the Radical:

x=((2/6) ±2(31)^(1/2))/6

x=26±231−−√6

Simplify fractions and/or signs:

x=1/3±√31/3

which becomes

x=2.18925

See the attached image for a more clear display of solving using the quadratic equation.

x=−1.52259

Answer:

come here if you want to see

The length of the other parallel side is 10 cm.

Trapezium is a quadrilateral (has four sides and four angles) with a pair of parallel sides. The area (A) of a trapezium is given by:

A = (1/2)(a + b)h

where a and b are the length of the parallel sides, h is the height of the trapezium

Given A = 54, a = 8 cm, h = 6 cm, hence:

54 = (1/2)(8 + b)6

8 + b = 18

b = 10 cm

The length of the other parallel side is 10 cm.

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The length of AB which is a diameter of the circle is equal 52 m using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

The hypotenuse of the right triangle ADC is a radius and twice the length of the radius is that of the diameter so;

radius = √(10² + 24²)

radius = √(100 + 576)

radius = √676

radius = 26

diameter AB = 2 × 26 = 52m

Therefore, the length of AB which is a diameter of the circle is equal 52 m using the Pythagoras rule.

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Answer:

ok, so the answer would be 27 hot dogs and 53 tacos salads

Step-by-step explanation:

Answer:

28-4x

Step-by-step explanation:

Step 1: Open most inner bracket and simplify

=18-2(x+x-5)

=18-2(2x-5)

Step 2: Expand brackets by multiplying 2 in and simplify

=18-2(2x)-2(-5)

=18-4x+10

=28-4x

Therefore the answer is 28-4x

Answer: 15 units

Step-by-step explanation:

Given

The endpoints of the line segment are \((-7,10)\ \text{and}\ (-6,-5)\)

The length of the line segment is given by the distance formula i.e.  

\(d=\sqrt{\left( x_2-x_1\right)^2+\left( y_2-y_1\right)^2}\)

Insert the values,

\(\Rightarrow d=\sqrt{\left( -6+7\right)^2+\left( -5-10\right)^2}\\\Rightarrow d=\sqrt{1^2+\left( -15\right)^2}\\\Rightarrow d=\sqrt{1+225}\\\Rightarrow d=15.0\ \text{units}\)

Therefore, the length of line segment TU is 15 units

Answer:

Step-by-step explanation: Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(8, 5)=1. In the next intermediate step the fraction result cannot be further simplified by cancelling. In words - four multiplied by two fifths=eight fifths.

The formula or equation used to determine the slope of a straight line is as follows:

m = (Y₂-Y₁)/(X₂-X₁)

An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.

Equations can be graphed, they are used to model many problems and theories.

The straight lines are characterized by a finite succession of points, when they have an inclination they adopt a slope value different from 0, and to determine that slope it is necessary to know two points of the line and use the following equation:

m = (Y₂-Y₁)/(X₂-X₁)

Where the points are:

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