Tina bought 7.1 pounds of fruit for a class party. The class ate 0.74 pounds of the fruit. How much fruit is left?

The oven is approximately 10°C hotter than the initial reading of 22°C, indicating an estimated oven temperature of 32°C based on the recorded thermometer readings after 39 and 78 seconds.

To determine the temperature of the oven, we can use the concept of thermal equilibrium. When the thermometer is placed in the oven, it gradually adjusts to the oven's temperature. In this scenario, the thermometer initially reads 22°C and then increases to 31°C after 39 seconds and 32°C after 78 seconds.

Since the thermometer reaches a higher temperature over time, it can be inferred that the oven is hotter than the initial reading of 22°C. The difference between the final temperature and the initial temperature is 31°C - 22°C = 9°C after 39 seconds and 32°C - 22°C = 10°C after 78 seconds.

By observing the increase in temperature over a consistent time interval, we can conclude that the oven's temperature increases by 1°C per 39 seconds. Therefore, to find the temperature of the oven, we can calculate the increase per second: 1°C/39 seconds = 0.0256°C/second.

Since the oven reaches a temperature of 10°C above the initial reading in 78 seconds, we multiply the increase per second by 78: 0.0256°C/second * 78 seconds = 2°C.

Adding the 2°C increase to the initial reading of 22°C, we find that the oven's temperature is 22°C + 2°C = 24°C.

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The data set can be said to be continuous because it represents a range of possible values that can be obtained by players in the English Premier League.

Mohamed Salah is a prolific striker for Liverpool F.C. with an impressive record in the English Premier League (EPL).

The number of assists a player can achieve ranges from 0 to infinity mathematically, and it is not possible to achieve negative assists while it is not feasible for a player to score 1000 goals.

Likewise, the number of goals a player can score ranges from 0 to infinity,

and it is not mathematically feasible to achieve negative goals while it is highly unlikely for a player to score 1000 goals. The data set can be best classified as continuous data because it can take any value within a given range.

Continuous data is data that can take any value within a given range, which means that it is not possible to list all the possible values in a set. Therefore, the data set can be said to be continuous because it represents a range of possible values that can be obtained by players in the English Premier League.

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Answer:

The slope is 7.

Step-by-step explanation:

(-1, 2) and (1, 16)

Slope is found using the following formula:

(y₂ - y₁) / (x₂ - x₁)

First, let's label the coordinates (these can be in any order, as long as the second numbers in each coordinate are in the y slots and the first numbers are in the x slots:

y₂: 16

y₁: 2

x₂: 1

x₁: -1

Now, substitute into the original formula:

(y₂ - y₁) / (x₂ - x₁)

(16 - 2) / (1 - (-1))

Simplify

(14)/(2)

7

The slope is 7.

Hope this helps :)

The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

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Step-by-step explanation:

1/sin10-√3/cos10

= (cos10 - √3sin10)/cos10sin10

multiplying 1/2 in denominator and numerator

= {(cos10/2) - (√3sin10/2)}/(cos10sin10/2)

= (cos60cos10 - sin60sin10)/(cos10sin10/2)

= cos(60 + 10)/(cos10sin10/2)

= cos70/(cos10sin10/2)

= 2cos70/cos10sin10

multiplying 2 on numerator and denominator

= 4cos70/2sin10cos10

=4cos70/sin20

=4cos70/cos70

= 4  proved

Answer:

D 280

Step-by-step explanation:

Answer:

adjacent

Step-by-step explanation:

Answer:

adjacent angles

Step-by-step explanation:

Hope this Helps! :)

9514 1404 393

Answer:

   f•g(-2) = -160

Step-by-step explanation:

f(-2) = (-2)^2 -6(-2) = 4 + 12 = 16

g(-2) = -2 -8 = -10

f•g(-2) =  f(-2)•g(-2) = 16•(-10)

f•g(-2) = -160

Answer:

hope this pic helps.enjoy

The total electric potential at point a is the sum of the electric potentials due to q1 and q2 is 0, the total electric potential at point b is the sum of the electric potentials due to q1 and q2 is 84.5 and the work done on q3 by the electric forces exerted by q1 and q2 is -0.42 J.

The electric potential at point a due to q1 and q2 can be calculated using the formula for electric potential due to a point charge,

V=kq/r, where k=9×10^9 N.

m²/C² is the Coulomb constant,

q is the point charge,

and r is the distance from the point charge to the point where the potential is being measured.

Using this formula, the electric potential due to q1 at point a is:

V1=kq1/r1

where q1=+2.00μC is the charge on q1 and r1 is the distance from q1 to point a.

Since q1 is at one of the corners of the square and a is at the center, the distance r1 is half the length of the diagonal of the square:

r1=√(12+12)=0.75 cm

Substituting the values in the formula, we get:

V1 = 9×10^9×2.00×10^-6/0.75×10^-2V1

     = 240 V

The electric potential due to q2 at point a can be calculated similarly.

Since q2 is at the opposite corner of the square, the distance r2 is the length of a side of the square:

r2=1.50 cm

Substituting the values in the formula, we get:

V2 = 9×10^9×(-2.00)×10^-6/1.50×10^-2V2

     = -240 V

The total electric potential at point a is the sum of the electric potentials due to q1 and q2:

V = V1+V2V=240 - 240V

   = 0

Since point b is at the empty corner closest to q2, the electric potential at point b due to q2 is zero.

The electric potential at point b due to q1 can be calculated using the same formula we used for point a:

V1=kq1/r1

where q1=+2.00μC is the charge on q1 and r1 is the distance from q1 to point b.

Since q1 is at one of the corners of the square and b is at the opposite corner, the distance r1 is the length of a diagonal of the square:

r1=√(1.5²+1.5²)=2.12 cm

Substituting the values in the formula, we get:

V1 = 9×10^9×2.00×10^-6/2.12×10^-2V1

     = 84.5 V

The total electric potential at point b is the sum of the electric potentials due to q1 and q2:

V = V1+V2V

   = 84.5 + 0V

    = 84.5 V

The electric force exerted on a point charge by another point charge is given by Coulomb's law:

F=kq1q2/r²

where F is the force,

           q1 and q2 are the point charges,

           r is the distance between the charges,

           and k is the Coulomb constant.

Since q3 is negatively charged, it will experience a force in the direction opposite to the force experienced by a positive charge at the same location.

Thus, the total work done by the electric forces exerted by q1 and q2 on q3 can be calculated as the negative of the change in electric potential energy of q3 from point a to point b:

W=-ΔPE

where ΔPE is the change in potential energy of q3 from point a to point b.

Substituting the values, we get:

W=-q3(Vb - Va)

where q3=-5.00μC is the charge on q3,

           Va=0 is the electric potential at point a,

            and Vb=84.5 V is

the electric potential at point b:

W = -5.00×10^-6(84.5 - 0)W

   = -0.42 J

Therefore, the work done on q3 by the electric forces exerted by q1 and q2 is -0.42 J.

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Therefore,  subscript indices must be either positive integers or logical. True

Explanation: The statement "subscript indices must be either positive integers or logicals" is true. Subscript indices are used to identify elements in an array. A positive integer subscript identifies a particular element in an array, while a logical subscript identifies a subset of elements based on a logical condition. For example, if we have an array A, then A(1) would identify the first element of the array, while A(A > 0) would identify all elements in the array that are greater than zero. Subscript indices cannot be negative or non-integer values.

Therefore,  subscript indices must be either positive integers or logical. True

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The score that separates the top 59% from the bottom 41% is 39.3.

To solve this problem, we need to find the z-score that separates the top 59% from the bottom 41%, and then use the z-score formula to find the corresponding raw score.

The z-score for the top 59% is the z-score that corresponds to a cumulative area of 0.59 to the left of it. We can find this using a standard normal table or a calculator:

z = invNorm(0.59) = 0.24

The z-score for the bottom 41% is the z-score that corresponds to a cumulative area of 0.41 to the left of it:

z = invNorm(0.41) = -0.24

The score that separates these two z-scores can be found using the z-score formula:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation. Solving for x, we get:

x = z * σ + μ

Plugging in the values we found earlier, we get:

x = 0.24 * 7.6 + 37.6 = 39.3

Therefore, the score that separates the top 59% from the bottom 41% is 39.3.

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Answer:

1,691

Step-by-step explanation:

This is correct 100%.

Have a great day

The equation to represent a, the Area in square feet, as a function of w, the width in feet is:a = (80w - 3w²)/2.

A school is constructing a rectangular play area against an exterior wall of the school building. It uses 80 feet of fencing to enclose three sides of the play area1.

The equationn to represent l, the length of the play area in feet, as a function of w, the width in feet:

We need to find an equation to represent l, the length of the play area in feet, as a function of w, the width in feet. The given information in the question is that it uses 80 feet of fencing to enclose three sides of the play area.

One side of the play area is the exterior wall of the school building.

Hence, there are three sides of the play area that require fencing .Let us assume that the width of the rectangular play area is w.

Therefore, the length of the play area will be l. We can obtain the equation to represent l, the length of the play area in feet, as a function of w, the width in feet as follows:

We know that the perimeter of a rectangle is given by the formula, Perimeter = 2(l + w)

Therefore, for the given problem, we have 80 feet of fencing. This 80 feet fencing has to be used to enclose three sides of the play area.

Therefore, we can say that the perimeter of the play area is given by:80 feet = 2(l + w) + Since we are asked to find an equation to represent l, the length of the play area in feet, as a function of w, the width in feet, we need to solve the above equation for l.2(l + w) + w = 80 2l + 2w + w = 80 2l + 3w = 80 2l = 80 - 3w l = (80 - 3w)/2

Therefore, the equation to represent l, the length of the play area in feet, as a function of w, the width in feet is:l = (80 - 3w)/2.2. The equation to represent a, the area in square feet, as a function of w, the width in feet:

We need to find an equation to represent a, the area in square feet, as a function of w, the width in feet. The area of a rectangle is given by the formula, Area = length × width

Therefore, for the given problem, we can say that the area of the play area is given by:Area = l × w We know that the length of the play area is given by l = (80 - 3w)/2.

Therefore, we can substitute this value in the above equation to obtain an equation to represent a, the area in square feet, as a function of w, the width in feet.Area = l × w = [(80 - 3w)/2] × w = (80w - 3w²)/2

Therefore, the equation to represent a, the area in square feet, as a function of w, the width in feet is:a = (80w - 3w²)/2.

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Answer:

1.5 units squared

Step-by-step explanation:

Area of a Triangle formula: A = 1/2bh

Pythagorean Theorem: a² + b² = c²

Since you are missing the h to find the area of the triangle, you must use Pythagorean to find the 3rd missing side (it is a right triangle so you can use Pythagorean).

Step 1: Use Pythagorean

2.5² = 1.5² + b²

4 = b²

b = 2

Step 2: Switch variables

b (from Pythagorean) = h (height for Area)

Step 3: Solve for Area

A = 1/2(1.5)(2)

A = 1.5

And you have your final answer.

The predetermined overhead rate is the estimated manufacturing overhead cost per unit of a specific allocation base.

In the options, there are four different rates:

1. $10.00 / MH (MH stands for machine hour): This means that the estimated manufacturing overhead cost per machine hour is $10.00.

2. $17.50 / MH: This indicates that the estimated manufacturing overhead cost per machine hour is $17.50.

3. $20.00 / MH: This implies that the estimated manufacturing overhead cost per machine hour is $20.00.

4. $32.86 / MH: This shows that the estimated manufacturing overhead cost per machine hour is $32.86.

Each rate represents the estimated cost of manufacturing overhead per unit of the allocation base (machine hour) and is used to allocate overhead costs to products or services based on their usage of the allocation base.

The specific rate chosen depends on the nature of the business, its cost structure, and the accuracy of the estimated overhead costs.

The correct question is ''What is the predetermined overhead rate?\(\( \$ 10.00 / \mathrm{MH} \) \( \$ 17.50 / \mathrm{MH} \) \( \$ 20.00 \) / MH \( \$ 32.86 / \mathrm{MH} \)\).''

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68% of IQ scores are found to be between 90 and 120

The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation from the mean, 95% of the data falls within two standard deviation from the mean and 99.7% of the data falls within three standard deviation from the mean.

Given mean of 105 and a standard deviation of 15.

68% of data falls within one standard deviation from the mean = mean ± standard deviation = 105 ± 15 = (90, 120)

68% of IQ scores are between 90 and 120

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This formula is the same as the formula we obtained for the definite integral of a linear function.

If f is a linear function with slope m and y-intercept b, then its equation can be written as:

f(x) = mx + b

To evaluate the integral of f(x) from a to b, we can use the formula for the definite integral of a linear function:

∫[a, b] f(x) dx = [(mx + b) * x]_a^b = (mb + bm) / 2 = mb + (b-a) * m / 2

Therefore, the integral of the linear function f(x) from a to b is:

∫[a, b] f(x) dx = mb + (b-a) * m / 2

Note that if we integrate a linear function over its entire domain, we get the area of the trapezoid formed by the function's graph, the x-axis, and the vertical lines at x = a and x = b. The formula for the area of a trapezoid is:

A = (b-a) * (f(a) + f(b)) / 2 = (b-a) * (ma + b + mb + b) / 2 = (b-a) * (ma + mb + 2b) / 2 = mb + (b-a) * m / 2

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The constraint(s) to ensure that the ratio of 3 bedroom rentals to 2 bedroom rentals is no more than 4 to 1 is:

3X3 <= 4X2

This constraint states that the number of 3 bedroom rentals (X3) must be less than or equal to four times the number of 2 bedroom rentals (X2). This ensures that the ratio of 3 bedroom rentals to 2 bedroom rentals does not exceed 4 to 1.

For example, if there are 10 2 bedroom rentals (X2), the constraint would be:

3X3 <= 4(10)
3X3 <= 40

This means that the number of 3 bedroom rentals (X3) cannot exceed 40.

The constraint to ensure the ratio of 3 bedroom rentals to 2 bedroom rentals is no more than 4 to 1 is 3X3 <= 4X2.

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Answer:

D. Testing the null hypothesis that the mean difference equals 0 is not equivalent to determining whether the confidence interval includes 0

Step-by-step explanation:

Dependent samples are samples that are related to one another.

In a hypothesis test, the hypothesis test and the confidence interval are equivalent in the sense that they result in the same conclusion.

However, in an hypothesis test , we fail to reject the null hypothesis if the rejection region is greater than the t-test statistics. It is therefore crucial to understand that if the true mean is zero. the confidence interval level for the mean of differences within the lower limit and the upper limits must contain zero , which implies the mean difference and the confidence interval  are equivalent.

Answer:

Arithmetic

Step-by-step explanation:

A sequence is a set of numbers, called terms, arranged in some particular order. An arithmetic sequence is a sequence with the difference between two consecutive terms constant

Answer: y=x-4

Step-by-step explanation:

Answer: y= x-4

Step-by-step explanation:

The point estimate that can be used to estimate the true mean population is 11.97 inches.

To find the point estimate that can be used to estimate the true population mean, we need to take the sample mean of the given observations. The formula for the sample mean is:

Mod(X)= (Σx) / n

where Mod(X)  is the sample mean, Σx is the sum of all the observations, and n is the size.

Using the given observations, we can calculate the sample mean as follows:

Mod(X) = (11.3 + 10.7 + 12.4 + 15.2 + 10.1 + 12.1 + 16.2 + 10.5 + 11.4 + 11.0 + 10.7 + 12.0) / 12

Mod(X) = 11.97

Therefore, the point estimate that can be used to estimate the true mean population is 11.97 inches.

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9514 1404 393

Answer:

  5

Step-by-step explanation:

The degree of the polynomial is the degree of the highest-degree term. The degrees of the terms are ...

  4, 5, 1

The highest degree is 5, so the degree of the polynomial is 5.

(a) 0.0516 is the standard form for 5.16×10^-2. (b) 9.912×10^4 is the correct answer for the computation (2.36×10^2)×(4.2×10^3).

The standard form for 5.16×10^-2 is option (a) 0.0516. In standard form, a number is expressed as a decimal between 1 and 10 multiplied by a power of 10. Here, 5.16 is the decimal part, and 10^-2 represents the power of 10. Therefore, the standard form is 0.0516.

For the computation (2.36×10^2)×(4.2×10^3), the correct answer is option (b) 9.912×10^4. To multiply numbers in scientific notation, we multiply the decimal parts and add the exponents of 10. In this case, 2.36 multiplied by 4.2 gives 9.912, and the exponents 2 and 3 are added to give 5. Therefore, the product is 9.912×10^5.

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Answer:

B

Step-by-step explanation:

Fip numbers and change both signs when reflecting over y=-x

Answer:

C

Step-by-step explanation:

Answer: I may not be much of a help, but....

Step-by-step explanation: Count up each year by 2%, and then do the rounding! I really do hope this helps!

Answer:

Step-by-step explanation:

So basically ur adding  2 % every year.

The average GPA of students in MATHS146 and historical GPA of students in MATH&146 is compared by t-test and chi-test.

Hypothesis testing is a statistical method that compares two datasets and uses the test results to determine whether the differences observed are significant or due to chance alone. This method is used in a variety of fields, including medicine, psychology, and engineering. To investigate the success of the new class, two hypotheses need to be tested:

1. Does the proportion of students who pass (get a 2.0 GPA or above) in corequisite MATHS146 differ from the proportion of students who have historically passed regular MATH&146?

2.Does the average GPA of students in MATHS146 differ from the historical GPA of students in MATH&146?

The null hypothesis (H0) for each of these hypotheses is that there is no difference between the two datasets,

while the alternative hypothesis (Ha) is that there is a difference. To test these hypotheses, statistical tests such as the t-test or chi-square test can be used, depending on the nature of the data. The level of significance (α) should also be chosen beforehand, usually at 0.05 or 0.01, to determine whether the results are significant enough to reject the null hypothesis.

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The number of ways to replace all the -1s in the array is zero.

The array can be represented as a wave if and only if the number of -1s is even. This is because each -1 must be replaced with a positive integer in order to create a wave, and replacing one -1 with a positive integer will create a new -1 on the opposite side of the wave. Therefore, if there are an odd number of -1s, it is impossible to create a wave.

In the given array, there are 7 -1s, which is an odd number. Therefore, it is impossible to replace the -1s with positive integers in such a way that the resulting array can be represented as a wave.

The number of ways to replace the -1s with positive integers in the range 1 to m is:

(m^7) mod (10^9) = (m^7)

However, since it is impossible to create a wave with this array, the final answer is 0.

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