Tayshia mailed two birthday presents in a box weighing 14 pound. One present weighed 15 pound. The other present weighed 12 pound. What was the total weight of the box and the presents.





Group of answer choices



311 lb



1911 lb



1140lb



320lb

Option (B) x + 6 < 10 and (C) 5x < 20 have same graph.

From the given set of inequalities;

(A) x < 2 represents x ∈ (-∞, 2)

(B) X + 6 < 10 ⇒ x < 4

    represents x ∈ (-∞, 4)

(C) 5x < 20 ⇒ x < 4

     represents x ∈ (-∞, 4)

(D) x - 2 > 2 ⇒ x > 4

     represents x ∈ (4, ∞)

(E) x < 4 represents x ∈ (-∞, 8)

We can see that inequalities (B) and (C) both represents x ∈ (-∞, 4)

Thus, the graph of both inequalities are same.

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A vertical translation (5 units up) is applied on quadratic function f(x) = x².

In this problem we find the representation of quadratic function and its image on Cartesian plane. The image is the consequence of using a vertical translation, whose definition is now introduced:

g(x) = f(x) + k

Where k is the y-coordinate of the quadratic function.

If we know that f(x) = x² and k = 5, then the image of the function is:

g(x) = x² + 5

The image is the result of a vertical translation (5 units up).

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The experimental probability of weather causing school to be canceled in at least three of the next four school years is (3+1)/24, which simplifies to 1/6 or approximately 0.1667.

To find the experimental probability of weather causing school to be canceled in at least three of the next four school years, we need to count the number of times there were three or more cancellations in each set of four years and divide that by the total number of sets of four years.

According to the table of simulated values, there are 24 sets of four years. Out of these, there were three or more cancellations in three sets of four years, and there were four cancellations in one set of four years.  Therefore, the experimental probability of weather causing school to be canceled in at least three of the next four school years is 20%.

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a. The area of Priya's scalp is ≈ [tex]615.75 cm^2[/tex]. b. Priya has approximately 92,363 strands of hair on her head.

a. The area of Priya's scalp can be estimated using the formula for the area of a circle, which is A = π[tex]r^2[/tex] ,where r is the radius (half the diameter) of the circle. Since Priya's diameter is 28cm, her radius would be 14cm. So, the area of her scalp would be:

A = π[tex](14cm)^2[/tex]
A ≈[tex]615.75 cm^2[/tex]

b. To estimate how many strands of hair Priya has on her head, we can multiply the number of hairs per square cm by the total area of her scalp. So, if Priya has approximately 150 hairs per square cm and her scalp has an estimated area of 615.75 cm^2, then:

Total number of hairs ≈ [tex]150 hairs/cm^2 * 615.75 cm^2[/tex]
Total number of hairs ≈ 92,362.5 hairs

Therefore, we can estimate that Priya has approximately 92,363 strands of hair on her head.

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The statement that  describes how the graph of h is different from the graph of g is: B. The graph of h is the graph of g vertically shifted up 1 unit.

The function h(x) = g(x) + 1 is obtained by adding a constant (1) to the output of the function g(x) = x^2. This means that the graph of h(x) will be the same as the graph of g(x), except that every point on the graph of h(x) will be shifted vertically upward by 1 unit.

Therefore, the correct statement is: B. The graph of h is the graph of g vertically shifted up 1 unit.

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The worth of the computer after depreciating for 3 years is $749.77, under the condition that a rate of 16% per year was applied.

Then the derived formula for evaluating depreciation
Depreciation = (Asset Cost – Residual Value) / Life-Time Production × Units Produced
Then,
Asset Cost = $1,495
Residual Value = 0 (assuming the computer has no resale value after 3 years)
Life-Time Production = 3 years
Units Produced = 1

Hence, the depreciation rate
[tex]Depreciation Rate = (1 - (Residual Value / Asset Cost)) ^{ (1 / Life-Time Production) - 1}[/tex]

[tex]Depreciation Rate = (1 - (0 / 1495))^{(1/3-1)}[/tex]

Depreciation Rate = 16%

Now to evaluate  the value of the computer after three years of depreciation at a rate of 16% per year, we can apply the derived formula
Value of Asset After Depreciation = Asset Cost × (1 - Depreciation Rate) ^ Life-Time Production

Value of Asset After Depreciation = $1,495 × (1 - 0.16)³

Value of Asset After Depreciation = $749.77

Hence, the computer is worth $749.77 after three years of depreciation at a rate of 16% per year.


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The complete question is
Cleo bought a computer for $1,495. What is it worth after depreciating for 3 years at a rate of 16% per year?

Assuming the population of times is normally distributed, and using the 0. 01 level of significance, we can conclude that the new booklet is effective.

To determine if the new instructional booklet is effective in reducing the assembly time for novices, we will perform a one-sample t-test using the given information.

1. State the null hypothesis (H0) and the alternative hypothesis (H1):

H0: There is no difference in the mean assembly time with the new booklet (µ = 3.15 hours).

H1: The mean assembly time with the new booklet is less than 3.15 hours (µ < 3.15 hours).

2. Identify the level of significance, sample size, sample mean, and sample standard deviation:

α = 0.01

n = 25

x = 2.98 hours

s = 0.23 hours

3. Calculate the test statistic:

t = (x - µ) / (s / √n) = (2.98 - 3.15) / (0.23 / √25) = -0.17 / 0.046 = -3.70

4. Find the p-value for the test:

Using a t-distribution table or calculator, the p-value for a one-tailed test with t = -3.70 and degrees of freedom (df) = 24 is approximately 0.0005.

5. Compare the p-value with the level of significance:

Since the p-value (0.0005) is less than α (0.01), we reject the null hypothesis.

Based on the p-value, we have enough evidence to conclude that the new instructional booklet is effective in reducing the assembly time for novices at the 0.01 level of significance.

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Mr. Mensah's total earnings at the end of the fifteenth year of service is €1920.00 + €2520.00 = €4440.00.

To calculate Mr. Mensah's salary in the fifteenth year of service, we need to determine the pattern of salary increase over the years.

We know that Mr. Mensah's salary starts at €6400.00 and increases by €240.00 every year for the first eight years. After that, he is promoted to a new post with an annual salary of €9500.00, which increases by €360.00 every year.

Let's break it down:

For the first eight years, the salary increases by €240.00 per year:

After 1 year: €6400.00 + €240.00 = €6640.00

After 2 years: €6640.00 + €240.00 = €6880.00

...

After 8 years: €6400.00 + (8 * €240.00) = €6400.00 + €1920.00 = €8320.00

From the ninth year onwards, the salary increases by €360.00 per year:

After 9 years: €9500.00 + €360.00 = €9860.00

After 10 years: €9860.00 + €360.00 = €10220.00

...

After 15 years: €9500.00 + (7 * €360.00) = €9500.00 + €2520.00 = €12020.00

Therefore, Mr. Mensah's salary in the fifteenth year of service is €12,020.00.

To calculate Mr. Mensah's total earnings at the end of the fifteenth year of service, we need to sum up his salaries from year 1 to year 15.

For the first eight years, the total earnings can be calculated as follows:

Total earnings = (Salary in year 1 + Salary in year 2 + ... + Salary in year 8) = 8 * €240.00 = €1920.00

From the ninth year onwards, the total earnings can be calculated as follows:

Total earnings = (Salary in year 9 + Salary in year 10 + ... + Salary in year 15) = 7 * €360.00 = €2520.00

Therefore, Mr. Mensah's total earnings at the end of the fifteenth year of service is €1920.00 + €2520.00 = €4440.00.

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Answer:

15 cubic centimeters

Step-by-step explanation:

The figure is in the shape of a rectangular and the formula for volume of such a rectangular box is

V=lwh, where V is the volume, l is the length, and h is the height.

Since each cube is 1 cm, we see that the length is 5 cm (1 cm cube * 5 = 5 cm), the width is 3 cm (1 cm cube * 3 = 3 cm), and the height is 1 cm (1 cm cube * 1 = 1 cm).

Thus, we the product of our length, width, and height will give us the volume of the figure:

V = 5 * 3 * 1

V = 15 cubic centimeters

x² + 10x + 25 is the expression of (x+5)^2 in trinomial in standard form

A trinomial is a polynomial that consists of three terms. It is a type of algebraic expression that contains three algebraic terms separated by either plus or minus signs.

For example, the expression 2x^2 + 5x - 3 is a trinomial because it has three terms: 2x^2, 5x, and -3. Similarly, the expression 4a^3 - 7a^2 + 2a is also a trinomial because it has three terms: 4a^3, -7a^2, and 2a.

We have to expand this

x² + 2(x)(5) + 5²

= x² + 10x + 25

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The mean score for the test Phyllis scored 84, exactly one standard deviation above the mean is  78.

One of the statistics used in the generalised Cochran-Mantel-Haenszel tests is the mean score statistic. When the answer levels (columns) are assessed using an ordinal scale, it is applicable.

The chi-square distribution with (R-1) degrees of freedom, where R is the number of treatment groups, serves as the asymptotic distribution of the mean score statistic if the two variables are independent of one another in all strata (rows).

If the mean scores of the response differ between the treatment groups in at least one stratum, the mean score statistic tends to have larger values. The term "nonparametric ANOVA statistic" also applies to this statistic.

x = 84

[tex]\sigma=6[/tex]

since, x is 1 standard deviation above mean so,

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]1=\frac{84-\mu}{6}\\ \\[/tex]

[tex]\mu[/tex] = 84-6

[tex]\mu[/tex] =78.

therefore, mean = 78.

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The effective utilization for the XYZ medical facility provides medical services to patients in Russellville is 81.63%, option B.

The percentage of your available resources that are now being used is known as resource utilization. To make sure your business is as productive as possible, it might assist to plan how to use your resources more wisely.

Employers and workers may both benefit from efficient resource management. On one side of the spectrum, it may also avoid overworking and burnout, resulting in a more balanced work life overall. On the other, it makes sure that workers have enough work to keep their position sustainable and lucrative.

Design capacity = 40 patients per hour,

Effective capacity is 35 patients per hour

Actual capacity is given by,

200/7 patients per hour

Effective utilization is given by = 200 x 100 /7 x 35

= 20000/245

= 81.63%.

Therefore, the effective utilization is 81.63%.

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The quadratic equation where the squares had been completed is:

(x + 2)² = 27/5

Remember the perfect square trinomial:

(a + b)² = a² + 2ab + b²

now we have the quadratic equation:

5x² + 20x - 7 = 0

If we divide it all by 5, we will get.

x² + 4x - 7/5 = 0

Now we can rewrite this as:

(x² + 2*2*x )  - 7/5 = 0

Now we need to add 2² in both sides, we will get:

(x² + 2*2x + 2²) - 7/5 = 2²

(x + 2)² = 4 + 7/5

(x + 2)² = 27/5

There the square is completed.

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The student from the first class performs better when comparing their scores using z-scores.

To compare the students' performances, we will calculate their z-scores, which show how many standard deviations away their scores are from the mean of their respective classes.

For the student from the first class:
z-score = (Score - Mean) / Standard Deviation
z-score = (62 - 56) / 9
z-score ≈ 0.67

For the student from the second class:
z-score = (83 - 75) / 15
z-score ≈ 0.53

The student from the first class has a higher z-score (0.67) compared to the student from the second class (0.53). This means the student from the first class performed better relative to their classmates.

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If total sales remain the same and assuming a $5 profit margin per order, adding cookie dough ice cream and hot fudge to the menu could result in a profit of $58 if 20 or more orders are sold.

To determine if adding cookie dough ice cream and hot fudge to the menu will result in a profit, we need to consider the cost and potential revenue. If the cost of adding these items is $42, we need to calculate how many orders of cookie dough ice cream with hot fudge we need to sell to cover that cost and make a profit.

Assuming the profit margin on each order of cookie dough ice cream with hot fudge is $5 (for example), we would need to sell at least 9 orders (rounding up from 8.4) to cover the $42 cost and break even. If we sell more than 9 orders, we would make a profit.

Assuming we sell 20 orders of cookie dough ice cream with hot fudge, the total revenue generated would be $100 ($5 profit per order x 20 orders). Subtracting the $42 cost of adding these items, the net profit would be $58.

Therefore, if total sales remain the same and assuming a $5 profit margin per order, adding cookie dough ice cream and hot fudge to the menu could result in a profit of $58 if 20 or more orders are sold.

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If the area of the hallway is 250 square feet, it would cost $625 to carpet the hallway with $2.50 per square foot carpet.

To find the cost of carpeting the hallway, we need to know the area of the hallway first. Let's assume that the length of the hallway is 50 feet and the width is 5 feet.

The area of the hallway = length x width
= 50 feet x 5 feet
= 250 square feet

Now that we know  we can find the cost of carpeting it.

Cost of carpeting = area x cost per square foot
= 250 square feet x $2.50 per square foot
= $625

Therefore, it would cost $625 to carpet the hallway with $2.50 per square foot carpet.

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To show that the quadrilateral on the tile floor is a parallelogram, you can use the opposite sides theorem, opposite angles theorem, consecutive angles theorem, and Diagonal bisector theorem.

1. Opposite sides theorem: If both pairs of opposite sides of the quadrilateral are congruent (equal in length), then it is a parallelogram.

2. Opposite angles theorem: If both pairs of opposite angles of the quadrilateral are congruent (equal in measure), then it is a parallelogram.

3. Consecutive angles theorem: If the consecutive angles of the quadrilateral are supplementary (their sum is 180 degrees), then it is a parallelogram.

4. Diagonal bisector theorem: If the diagonals of the quadrilateral bisect each other (divide each other into two equal parts), then it is a parallelogram.

Choose the most appropriate theorem based on the given information and apply it to prove that the quadrilateral is a parallelogram.

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Step-by-step explanation:

[tex]6x + 26 = 16x\\ 16x - 6x = 26 \\ 10x = 26 \\ x = 2.6[/tex]

The formula for the function h(x) is given as follows:

h(x) = g(x + 5).

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The function h(x) is a translation left 5 units of the function g(x), hence it is defined as follows:

h(x) = g(x + 5).

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Answer:

[tex]f(x)=x^3+11x^2+43x+65[/tex]

Step-by-step explanation:

If a polynomial function has a complex zero, then the conjugate of that complex zero is also a zero of the polynomial.

So, if (-3 - 2i) is a zero of the polynomial, then its conjugate (-3 + 2i) is also a zero of the polynomial.

Therefore, the three zeros of the polynomial function are:

The zero of a polynomial f(x) is the x-value when f(x) = 0.

According to the factor theorem, if f(a) = 0 then (x - a) is a factor of the polynomial f(x).

Therefore, the polynomial function in factored form is:

[tex]\begin{aligned}f(x) &= (x - (-5))(x-(-3-2i))(x-(-3+2i))\\&= (x +5)(x+3+2i)(x+3-2i)\end{aligned}[/tex]

Expand the brackets to write the polynomial in standard form.

[tex]\begin{aligned}f(x) &=(x +5)(x+3+2i)(x+3-2i)\\&=(x+5)(x^2+3x-2xi+3x+9-6i+2ix+6i-4i^2)\\&=(x+5)(x^2+6x+9-4i^2)\\&=(x+5)(x^2+6x+9-4(-1))\\&=(x+5)(x^2+6x+9+4)\\&=(x+5)(x^2+6x+13)\\&=x^3+6x^2+13x+5x^2+30x+65\\&=x^3+11x^2+43x+65\end{aligned}[/tex]

Therefore, the polynomial function of least degree with integral coefficients that has the given zeros -5 and (-3 - 2i) is:

[tex]f(x)=x^3+11x^2+43x+65[/tex]

f(x)=x3+11x²+43x+65

Answer:

g(-2) = 4.

Step-by-step explanation:

To find g(-2), we simply need to substitute -2 for x in the function g(x) and simplify:

g(-2) = -4(-2) - 4

g(-2) = 8 - 4

g(-2) = 4

Therefore, g(-2) = 4.

To calculate the cost for Design A and Design B, we need to know the size of each design in square inches. Once we have that information, we can multiply the size of each design by the cost per square inch of wood to determine the total cost.

Let's say Design A is 10 inches by 10 inches, which is a total of 100 square inches. To calculate the cost for Design A, we would multiply 100 by 0.15, which gives us a total cost of $15.

Similarly, let's say Design B is 8 inches by 12 inches, which is a total of 96 square inches. To calculate the cost for Design B, we would multiply 96 by 0.15, which gives us a total cost of $14.40.

Therefore, the cost for Design A is $15 and the cost for Design B is $14.40.

In summary, the cost of a wooden design can be calculated by multiplying the size of the design in square inches by the cost per square inch of wood. In this case, we used a cost of 0.15 per square inch and calculated the cost for Design A and Design B. It is important to know the size of the design before calculating the cost.

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A customer will save $117 by purchasing the annual subscription over paying per month. So the (d) $117 is the right answer.

To determine how much a customer will save by purchasing the annual subscription over paying per month, follow these steps:
Calculate the discounted annual subscription cost:
Option A: 25% off an annual subscription of $308.00
Discount = 25% of $308 = 0.25 * $308 = $77
Discounted Annual Subscription = $308 - $77 = $231
Calculate the total cost of the monthly subscription for one year:
Option B: Pay $29 per month
Total Monthly Subscription Cost = $29 * 12 months = $348
Calculate the savings:
Savings = Total Monthly Subscription Cost - Discounted Annual Subscription
Savings = $348 - $231 = $117
So, a customer will save $117 by purchasing the annual subscription over paying per month. Your answer is d. $117.

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Answer:

Sure, here are ten ordered pairs with the country as the first element and the capital as the second element:

1. (France, Paris)

2. (United States, Washington D.C.)

3. (China, Beijing)

4. (Mexico, Mexico City)

5. (Brazil, Brasília)

6. (Japan, Tokyo)

7. (Canada, Ottawa)

8. (Germany, Berlin)

9. (Australia, Canberra)

10. (India, New Delhi)

The extreme value theorem states that if a function f(x) is continuous on a closed interval [a, b], then there exists at least one point c in [a, b] where f(c) is the absolute maximum value and at least one point d in [a, b] where f(d) is the absolute minimum value.

A. f(x)=x2 over(-5,0] - This function is continuous on the closed interval [-5,0], so by the extreme value theorem, there exists at least one absolute maximum and one absolute minimum.

B. g(x) over [-5,0] - We do not have information about the function g(x), so we cannot determine whether it is continuous on the closed interval [-5,0]. Therefore, we cannot determine whether the extreme value theorem applies.

C. h(x)=1x-1 lover [-5.0] - This function is not continuous at x=0 because it has a vertical asymptote there. Therefore, the extreme value theorem does not apply.

D. k( x) = Vx + 1 over [- 5,0] - This function is continuous on the closed interval [-5,0], so by the extreme value theorem, there exists at least one absolute maximum and one absolute minimum.

E. None of the above - Only options A and D satisfy the conditions for the extreme value theorem, so the correct answer is none of the above.

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The initial condition y(5) = 4 tells us that we should use the positive square root.

To find the particular solution to the given differential equation, we can use separation of variables. First, we rearrange the equation to get:

y dy = 2x dx

Next, we integrate both sides with respect to their respective variables:

∫y dy = ∫2x dx

This gives us:

y^2/2 = x^2 + C

where C is the constant of integration. To find the value of C, we use the initial condition y(5) = 4:

4^2/2 = 5^2 + C

8 = 25 + C

C = -17

So the particular solution to the differential equation dy/dx = 2x/y with the initial condition y(5) = 4 is:

y^2/2 = x^2 - 17

or

y = ±√(2x^2 - 34)

Note that there are two possible solutions, one with a positive square root and one with a negative square root, but the initial condition y(5) = 4 tells us that we should use the positive square root.

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To compare Ralph's and Frank's t-shirt companies, let's calculate the total cost of buying a certain number of t-shirts from each company.

1. Ralph's t-shirt company:

- Price per t-shirt: $5.00

- Shipping and design fee: $20.00

Total cost for Ralph's t-shirts = (number of t-shirts * $5.00) + $20.00

2. Frank's t-shirt company:

- Price per t-shirt: $10.00

- No additional fees

Total cost for Frank's t-shirts = number of t-shirts * $10.00

Now you can compare the total costs for each company depending on the number of t-shirts you want to buy.

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This means that in the population represented by the formula, someone with a femur length of 27.4 centimeters would be expected to have a height of 128 centimeters

When h is 128, we can use the formula h = 2.46f + 60.6 to solve for the corresponding value of f.

128 = 2.46f + 60.6

Subtracting 60.6 from both sides:

67.4 = 2.46f

Dividing both sides by 2.46:

f ≈ 27.4

Therefore, when h is 128, the f-value (length of the femur) is approximately 27.4 centimeters. This means that in the population represented by the formula, someone with a femur length of 27.4 centimeters would be expected to have a height of 128 centimeters.

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The probability that a given voicemail is between 20 and 50 seconds is 0.8185, or 81.85%.

To find the probability that a voicemail is between 20 and 50 seconds, we need to standardize the values and use a standard normal distribution table.

First, we find the z-scores for 20 seconds and 50 seconds:

z1 = (20 - 40) / 10 = -2

z2 = (50 - 40) / 10 = 1

Using a standard normal distribution table, we can find the area to the left of each z-score:

Area to the left of z1 = 0.0228

Area to the left of z2 = 0.8413

To find the probability between 20 and 50 seconds, we subtract the area to the left of z1 from the area to the left of z2:

P(20 < x < 50) = P(-2 < z < 1)

= 0.8413 - 0.0228

= 0.8185

Therefore, the probability that a given voicemail is between 20 and 50 seconds is 0.8185, or 81.85%.

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