The simplified exponential expression in the context of this problem is given as follows:
[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]
How to simplify the exponential expression?The exponential expression in the context of the problem is defined as follows:
[tex](6m^5g^5)^2[/tex]
The power of a power rule is used when a single base is elevated to multiple exponents, and states that simplified expression is obtained keeping the base, while the exponents are multiplied.
Applying the exponent of 2, we have that:
6² = 36.5 x 2 = 10.Hence the simplified exponential expression in the context of this problem is given as follows:
[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]
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The function f(x)=√x is shown on the graph.
4
3+
2+
--5-4-3-2-1₁
-2+
-3+
4
1 2 3 4
Which statement is correct?
O The range of the graph is all real numbers less than
or equal to 0.
O The domain of the graph is all real numbers less
than or equal to 0.
O The domain and range of the graph are the same.
O The range of the graph is all real numbers.
Answer:
The domain and range of the graph are the same
Step-by-step explanation:
The domain and range of the graph are both [tex][0,\infty)[/tex] because you cannot take the square root of a negative number to produce a real result, and you cannot square a real number to get a negative number.
An investment banking house conducted a survey to determine how two of its proposed investment plans for three different age categories are used. This table shows the responses they received. Plan I Plan II Neither Ages 26–35 19 14 17 Ages 36–45 14 28 8 Ages 46–55 27 21 2 What percentage of people preferring plan I are from the 36–45 age group, and what percentage of people from the 46–55 age group prefer plan II? Round your answers to the nearest whole number. A. 23% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II. B. 28% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II. C. 23% of people who prefer plan I are from the 36–45 age group, and 33% of people from the 46–55 age group prefer plan II. D. 28% of people who prefer plan I are from the 36–45 age group, and 33% of people from the 46–55 age group prefer plan II. E. 32% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II.
The Percentage of people from the 46-55 age group preferring Plan II is 42%.
The percentages, we need to calculate the ratio of people preferring Plan I in the 36-45 age group and the ratio of people preferring Plan II in the 46-55 age group.
Let's start with the first part of the question:
Percentage of people preferring Plan I from the 36-45 age group:
To calculate this percentage, we need to divide the number of people preferring Plan I in the 36-45 age group by the total number of people preferring Plan I, and then multiply by 100 to express it as a percentage.
Number of people preferring Plan I in the 36-45 age group = 14
Total number of people preferring Plan I = 14 + 28 + 21 = 63
Percentage = (14 / 63) * 100 ≈ 22.22 ≈ 22% (rounded to the nearest whole number)
So, the percentage of people preferring Plan I from the 36-45 age group is approximately 22%.
Now, let's move on to the second part of the question:
Percentage of people from the 46-55 age group preferring Plan II:
To calculate this percentage, we need to divide the number of people preferring Plan II in the 46-55 age group by the total number of people from the 46-55 age group, and then multiply by 100 to express it as a percentage.
Number of people preferring Plan II in the 46-55 age group = 21
Total number of people in the 46-55 age group = 27 + 21 + 2 = 50
Percentage = (21 / 50) * 100 = 42%
So, the percentage of people from the 46-55 age group preferring Plan II is 42%.
Based on the calculations, the correct answer is:
A. 23% of people who prefer Plan I are from the 36-45 age group, and 42% of people from the 46-55 age group prefer Plan II.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
[tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
Step-by-step explanation:
The equation of a circle with a center at (h, k) and radius r is given by:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
We are given that the points G(5,-2) and H(1, −2) lie on the circle. We can use the distance formula to find the distance between these two points.
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]d = \sqrt{(5 - 1)^2 + ((-2) - (-2))^2} = \sqrt{16} = 4[/tex]
Therefore, the radius of the circle is 4.
We can now find the center of the circle by taking the average of the x-coordinates and y-coordinates of the points G and H.
[tex](h, k) = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) = \left(\frac{5 + 1}{2}, \frac{-2 - 2}{2}\right) = (3, -2)[/tex]
Therefore, the equation of the circle is:
[tex](x - 3)^2 + (y + 2)^2 = 4^2[/tex]
Simplifying the equation, we get:
[tex]\bold{(x - 3)^2 + (y + 2)^2 = 16}[/tex] is a required equation.
Check out this square pyramid: Find the surface area of the square pyramid (above) using its net (below).
The surface area of a square pyramid attached is
40 square units
How to find the surface area of a square pyramidThe surface area of a square pyramid is solved using the formula
= a² + 2 * a * l
where
a = side of the square
l = slant height
In the problem
a = 4
l = 3
plugging in the values
surface area of a square pyramid = 4² + 2 * 4 * 3
surface area of a square pyramid = 16 + 24
surface area of a square pyramid = 40 square units
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Johnson Industries purchased a metal-working lathe for $38,000. This item will be used for business 90% of the time. Accountants elected to take a $18,000 section 179 deduction and utilize the special depreciation allowance of 50%.
Prepare a depreciation schedule (in $) using MACRS.
Round all dollar amounts to the nearest cent.
The depreciation schedule (in dollars) using MACRS for the metal-working lathe is as follows:
Year 1: $1,429.00
Year 2: $2,449.00
Year 3: $1,749.00
Year 4: $1,249.00
Year 5: $893.00
Year 6: $892.00
Year 7: $893.00
What is the MACRS depreciation schedule?The depreciation schedule using the Modified Accelerated Cost Recovery System (MACRS) is prepared as follows:
Given data:
Purchase cost of the metal-working lathe: $38,000
Business use percentage: 90%
Section 179 deduction: $18,000
Special depreciation allowance: 50%
Depreciable basis = Purchase cost - Section 179 deduction
Depreciable basis = $38,000 - $18,000 = $20,000
Special depreciation allowance = $20,000 * 50%
Special depreciation allowance = $10,000
Adjusted depreciable basis = $20,000 - $10,000
Adjusted depreciable basis = $10,000
The recovery period for a metal-working lathe is 7 years.
Using MACRS, the depreciation rates for a 7-year recovery period are as follows:
Year 1: 14.29%
Year 2: 24.49%
Year 3: 17.49%
Year 4: 12.49%
Year 5: 8.93%
Year 6: 8.92%
Year 7: 8.93%
Annual depreciation expense = Adjusted depreciable basis * Depreciation rateYear 1:
Depreciation expense = $10,000 * 14.29% = $1,429.00
Year 2:
Depreciation expense = $10,000 * 24.49% = $2,449.00
Year 3:
Depreciation expense = $10,000 * 17.49% = $1,749.00
Year 4:
Depreciation expense = $10,000 * 12.49% = $1,249.00
Year 5:
Depreciation expense = $10,000 * 8.93% = $893.00
Year 6:
Depreciation expense = $10,000 * 8.92% = $892.00
Year 7:
Depreciation expense = $10,000 * 8.93% = $893.00
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
A)19.0
B)10.0
Step-by-step explanation:
Using [tex]\frac{1}{2} * absin(C)[/tex]
This is used when you have an angle between two sides
Kindly check the attached image for the solution
The entire graph of the function h is shown in the figure below. Write the domain and range of h as intervals or unions of intervals.
The domain and the range of the graph are Domain = (-5, -1) U (2, 5] and Range = (-4, 5]
Calculating the domain and range of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The above graph can be represented as a list of ordered pairs
The rule of a graph is that
The domain is the x valuesThe range is the f(x) valuesUsing the above as a guide, we have the following:
Domain = (-5, -1) U (2, 5]
Range = (-4, 5]
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Inputs: People at concession stand Outputs: Cost of their order
this relation a function?
it a constant function?
it a 1-1 function?
People at the concession stand as input Cost of their order's output.
(1) The relation in question is a function.
(II) This function is not constant. (Each category of concession has a different order cost.)
Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)
A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.
The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.
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Graph shows two triangles plotted on a coordinate plane. One triangle is at A (minus 4, 4), B (minus 8, 2), and C (minus 6, minus 6). Another triangle is at A prime (4, minus 2), B prime (2, 2), and C prime (6, 0). A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a followed by a .
The sequence of transformations that maps triangle ABC onto triangle A'B'C' is a translation by (+8, -6) followed by a reflection across the y-axis.
To determine the sequence of transformations that maps triangle ABC onto triangle A'B'C', let's analyze the given coordinate points.
Triangle ABC:
A (-4, 4)
B (-8, 2)
C (-6, -6)
Triangle A'B'C':
A' (4, -2)
B' (2, 2)
C' (6, 0)
By comparing the corresponding vertices, we can identify the transformations:
Translation:
To transform A to A', we can observe that A' is obtained by moving 8 units to the right and 6 units downwards from A. Therefore, the first transformation is a translation by (+8, -6).
Reflection:
Next, we notice that B' is the reflection of B across the y-axis. Thus, the second transformation is a reflection about the y-axis.
Therefore, the sequence of transformations that maps triangle ABC onto triangle A'B'C' is a translation by (+8, -6) followed by a reflection across the y-axis.
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7. For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating re
A, Part B, and Part C.
in.
Part A: Determine the value of the diameter of the circle shown above.
Part B: Determine the value of the radius of the circle shown above.
Part C: Explain your reasoning for Part A and Part B of this problem.
- AA- A
B
U Font Family
FE E
C
1
D
1+
4
Answer:
A: The diameter is 6in.
B: The radius is 3in.
C: The diameter is given to us in the problem. A line is drawn out that strikes through the center point. of the circle, and it is labeled 6in in the middle, so we can deduce that it is the diameter. The radius of a circle is 1/2 the length of the diameter, so 6/2 = 3in. If the 6in was on either side of the line, then that would be labeling the radius.
Using digits 1to 9 fill in the boxes once write largest and smallest absolute value. Then find the decimal equivalent.
The decimal equivalent of the largest Absolute value, 987654321, is 987,654,321. the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.
The largest and smallest absolute values using the digits 1 to 9, we need to arrange them in a way that maximizes or minimizes the resulting number. Let's consider the boxes as placeholders for the digits.
To determine the largest absolute value:
We place the digit 9 in the leftmost box, as it is the largest digit among 1 to 9. Then we arrange the remaining digits, 8, 7, 6, 5, 4, 3, 2, and 1, from largest to smallest in the remaining boxes. This gives us the number 987654321, which is the largest possible number using the given digits. Therefore, the largest absolute value is 987654321.
To determine the smallest absolute value:
We place the digit 1 in the leftmost box, as it is the smallest digit among 1 to 9. Then we arrange the remaining digits, 2, 3, 4, 5, 6, 7, 8, and 9, from smallest to largest in the remaining boxes. This gives us the number 123456789, which is the smallest possible number using the given digits. Therefore, the smallest absolute value is 123456789.
To find the decimal equivalent of these numbers, we simply read the digits from left to right. The decimal equivalent of the largest absolute value, 987654321, is 987,654,321. The decimal equivalent of the smallest absolute value, 123456789, is 123,456,789.
Thus, the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.
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2
5. Many people believe that criminals who plead guilty tend to get lighter sentences than those
who are convicted in trials. The accompanying table summarizes randomly selected sample
data for defendants in burglary cases in a specific city. All of the subjects had prior prison
sentences. Use a 0.05 significance level to find the critical value needed to test the claim that
the sentence (sent to prison or not sent to prison) is independent of the plea.
Sent to prison
Not sent to prison
Guilty Plea
392
564
Not-Guilty Plea
58
14
(1 point)09.488
03.841
042.557
05.991
Answer:
Is 03.841
Step-by-step explanation:
To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.
In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.
To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.
The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.
Therefore, the correct answer is 03.841.
ہے
8. A randomized controlled trial was designed to compare the effectiveness of splinting versus
surgery in the treatment of carpal tunnel syndrome. Results are given in the table. The results
are based on evaluations made one year after the treatment. Using a 0.01 significance level,
find the test statistic and critical value needed to test the claim that the success is independent
of the type of treatment.
Splint treatment
Surgery treatment
Successful
Treatment
60
67
Otest statistic = 0.848, critical value = 6.635
statistic 9 750 critical value = 6.635
Unsuccessful
Treatment
23
6
The test statistic and critical value needed to test the claim that the success is independent of the type of treatment are 9.750 and critical value is 6.635.
How to calculate the valueThe expected value for each cell is calculated as follows:
E = row total * column total / grand total
The grand total is 150.
The row totals are 83 and 67.
The column totals are 86 and 64.
The expected values are as follows:
Successful: 60 * 86 / 150 = 36.4
Unsuccessful: 60 * 64 / 150 = 29.6
Surgery treatment
Successful: 67 * 86 / 150 = 49.6
Unsuccessful: 67 * 64 / 150 = 27.4
The test statistic is calculated as 9.750
The critical value is calculated as follows:
α = 0.01
df = (r-1)(c-1) = (2-1)(2-1) = 1
x²(α, df) = 6.635
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Triangle FGH is inscribed in circle O, the length of radius OH is 6, and maFGH-20. What is the area of the sector formed by angle FOH, in terms of pi 1) 2k 2) 3/2 (3) 4
PLEASE HELP ME, NO FAKE ANSWERS (sorry that it's blurry)
Triangle FGH is inscribed in circle O, the length of radius OH is 6, and ma FGH-20. The area of the sector formed by angle FOH, in terms of pi is 6π. Hence, it is neither of the options.
Given that triangle FGH is inscribed in circle O, the length of radius OH is 6, and m∠FGH = 20.
We have to find the area of the sector formed by angle FOH, in terms of pi.
Using the central angle, we know that the measure of ∠FOH is twice that of ∠FGH, which is 40°.
Therefore, the measure of the central angle FOH is 2 * 40 = 80°.
The area of the sector formed by angle FOH, in terms of pi is given by, A = r²θ/2 where A = Area of the sector, r = radius of the circle and θ = central angle in radians.
To calculate the value of A in terms of pi, we have to convert the central angle from degrees to radians.
1 radian = 180°/π radians
Therefore, 80° = 80° * (π/180°) = 4π/9 radians.
Now we can plug in the given values of r and θ to find the area of the sector.
A = (6)² * (4π/9) / 2 = 18π/3 = 6π
Thus, the area of the sector formed by angle FOH, in terms of pi is 6π.
Hence, option 1) 2k is incorrect. Option 2) 3/2 (3) is incorrect. Option 3) 4 is incorrect. Answer: 6π.
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A number b increased by 2 is less than -30 as an inequality
Answer:
b + 2 < -30
Step-by-step explanation:
But if it needs to be simplified the answer is b < -32
O+O+O=30
1-3 -5 -7
9 -11 -
15
To solve the equations:
O + O + O = 30
1 - 3 - 5 - 7
9 - 11 -
15
We can start by simplifying the second equation:
1 - 3 - 5 - 7 = -14
9 - 11 - x = -14
To find the value of x, we can solve the equation:
-11 - x = -14
Adding 11 to both sides of the equation:
-11 + 11 - x = -14 + 11
Simplifying:
-x = -3
Multiplying both sides by -1:
(-1) * (-x) = (-1) * (-3)
x = 3
Now, substituting the value of x back into the second equation:
9 - 11 - 3 = -14
-5 - 3 = -14
-8 = -14
This is not a true statement. Therefore, the values provided do not satisfy the equations given.
A student was given the following diagram and asked to prove that AX= XC.
What would be the reason for the fourth step in the proof?
Given: AB- BC and ZABX 2CBX
Prove: AX XC
Statements
1. AB BC and ZABXZCBX
2. BX BX
3. AABXACBX
4. AXEXC
B
X
Reasons
Given
Reflexive Property of Equality
SAS Triangle Congruence Theorem
A. Definition of perpendicular bisector
B. Substitution property of equality
C. Corresponding parts of congruent triangles are congruent
(CPCTC)
D. Definition of midpoint
K
The reason for the fourth step to prove the congruence of [tex]\overline{AX}[/tex] and [tex]\overline{XC}[/tex], based on the congruence of the triangles ΔABX and ΔCBX is the option C.
C. Corresponding parts of congruent triangles are congruent (CPCTC)
What are congruent triangles?Congruent triangles are triangles that have the same shape and size.
The completed two column table to prove the congruence of the segment [tex]\overline{AX}[/tex] and [tex]\overline{XC}[/tex] can be presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{AB}[/tex] ≅ [tex]\overline{BC}[/tex] and ∠ABX ≅ ∠CBX [tex]{}[/tex] Given
2. [tex]\overline{BX}[/tex] ≅ [tex]\ovderline{BX}[/tex] [tex]{}[/tex] Reflexive property of Equality
3. ΔABX ≅ ΔCBX [tex]{}[/tex] SAS Triangle Congruence Theorem
4. [tex]\overline{AX}[/tex] ≅ [tex]\overline{XC}[/tex] [tex]{}[/tex] CPCTC
The reason for the fourth step can be presented as follows;
CPCTC is an acronym for corresponding parts of congruent triangles are congruent. The triangles ΔABX and ΔCBX are congruent, therefore, CPCTC indicates that the segments [tex]\overline{AX}[/tex] and [tex]\overline{XC}[/tex] which are corresponding parts are therefore congruent.
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What is the area of the figure? In Units
Answer:
Area = 40
Perimeter = 26
Step-by-step explanation:
length = 8
width = 5
Area = 8 x 5 = 40
Perimeter = 2(8 + 5) = 26
Which expressions are equivalent to the expression 3x2 - 5a3+2y4?
Answer: There are several expressions that are equivalent to the given expression 3x^2 - 5a^3 + 2y^4. Here are a few examples:
2y^4 - 5a^3 + 3x^2-5a^3 + 3x^2 + 2y^43x^2 + 2y^4 - 5a^32y^4 + 3x^2 - 5a^3
These expressions have the same terms but may differ in the order in which the terms are written. It's important to note that the coefficients and exponents of the variables remain unchanged in each expression.
By definition, theoretical probability is equal to:
A. No. of favorable outcomes/ total no. of possible outcomes ✅️
B. No. of total outcomes/ total no. of impossible outcomes
C. No. of possible outcomes/ total no. of favorable outcomes
D. No. of total outcomes/ total no. of possible outcomes
Theoretical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, making option A the correct answer.
The correct answer is A. Theoretical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. It represents the likelihood of an event occurring based on mathematical calculations and assumptions.
To provide a detailed explanation, let's break down the components of the definition:
Favorable outcomes: These are the outcomes that meet the desired criteria or event you are interested in. For example, if you are rolling a fair six-sided die and you want to find the probability of rolling a 3, the favorable outcome would be a single outcome where the die shows a 3.
Total number of possible outcomes: This refers to the complete set of all possible outcomes in the given situation. In the case of the fair six-sided die, there are six possible outcomes (numbers 1 to 6) since each face of the die represents a different number.
Theoretical probability is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This ratio provides an estimate of the probability of the event occurring under ideal, theoretical conditions. It assumes that each outcome is equally likely to occur.
It's worth noting that theoretical probability is based on mathematical calculations and assumptions, and it may not always reflect the actual probability observed in real-world scenarios. However, it serves as a foundation for understanding and analyzing probabilities in various contexts, such as in mathematics, statistics, and decision-making processes.
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Ethan and Calvin meet daily in the elevator. One morning they found that if they multiply their current ages, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Ethan and Calvin.
The sum of Ethan and Calvin's current ages is approximately 45.65.
Let's assume Ethan's current age is represented by 'E', and Calvin's current age is represented by 'C'.
From the given information, we can establish the following equations:
The product of their current ages is 238:
E × C = 238
The product of their ages after four years is 378:
(E + 4) × (C + 4) = 378
We can solve this system of equations to determine the values of E and C, and then calculate their sum.
From equation 1, we can express E in terms of C:
E = 238 / C
Substituting this value of E into equation 2:
(238 / C + 4) × (C + 4) = 378
Expanding and simplifying the equation:
(238 + 4C) × (C + 4) = 378
[tex]238C + 952 + 4C^2 + 16C - 378 = 0\\4C^2 + 254C + 574 = 0[/tex]
Now, we can solve this quadratic equation for C using the quadratic formula:
C = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
a = 4, b = 254, c = 574
C = (-254 ± √([tex]254^2[/tex]- 4 × 4 × 574)) / (2× 4)
After solving, we find two possible values for C: C ≈ -73.85 and C ≈ -39.65
Since age cannot be negative, we discard the negative value. Thus, C ≈ 39.65.
Plugging this value of C back into equation 1:
E × 39.65 = 238
E ≈ 238 / 39.65
E ≈ 6
Therefore, Ethan's current age (E) is approximately 6 and Calvin's current age (C) is approximately 39.65.
The sum of their current ages is:
6 + 39.65 ≈ 45.65
Hence, the sum of Ethan and Calvin's current ages is approximately 45.65.
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an online store begins selling a new kind of baskelballshoe. At week zero, 30 pairs of shoes were sold.
In week 3, the store sold 240 pairs of shoes. Write an exponential model that relates the number of shoes sold to the week number, and use the model to predict how many shoes will be sold during week 7.
Answer:
3840 pairs of shoes
Step-by-step explanation:
To write an exponential model that relates the number of shoes sold to the week number, we can use the general form of an exponential function:
y = a * b^x
where:
y is the number of shoes sold,
x is the week number, and
a and b are constants to be determined.
Given the information:
In week 0, 30 pairs of shoes were sold.
In week 3, 240 pairs of shoes were sold.
We can use these two data points to determine the values of a and b.
Using the data point for week 0:
30 = a * b^0
30 = a
Using the data point for week 3:
240 = 30 * b^3
8 = b^3
b = 2 (taking the cube root of both sides)
Therefore, the exponential model that relates the number of shoes sold to the week number is:
y = 30 * 2^x
To predict the number of shoes sold during week 7, we substitute x = 7 into the model:
y = 30 * 2^7
y = 30 * 128
y = 3840
Therefore, the model predicts that 3840 pairs of shoes will be sold during week 7.
Beth and Kelly spent the same total amount of money for dog sitting while on vacation. Beth took her dog, Pockets, to Rover Sleepover and was charged $24.50 per day and a fee of $90.50 for food and cleaning. Kelly took her dog, Monty, to Pet Palace and was charged $32 per day and a $45.50 cleaning fee.
How many days were Beth and Kelly on vacation?
Beth and Kelly were on vacation for 6 days. both spent same amount of money for dog sitting while on vacation.
Let's assume the number of days Beth and Kelly were on vacation is represented by 'd.'
For Beth:
Total cost for dog sitting = (Cost per day * Number of days) + Cleaning and food fee
24.50d + 90.50
For Kelly:
Total cost for dog sitting = (Cost per day * Number of days) + Cleaning fee
32d + 45.50
Since both Beth and Kelly spent the same amount, we can set their total costs equal to each other and solve for 'd':
24.50d + 90.50 = 32d + 45.50
Rearranging the equation:
24.50d - 32d = 45.50 - 90.50
-7.50d = -45
Dividing both sides by -7.50:
d = -45 / -7.50
d = 6
Therefore, both Beth and Kelly were on vacation for 6 days.
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total population = 8,000,000
civilian labor force = 4,000,000
number of unemployed individuals who are actively seeking jobs = 400,000
number of unemployed individuals who are not seeking work 100,000.
This information indicates that country y's unemployment rate equals.
The given information indicates that country y's unemployment rate equals 10 %.
How to find the unemployment ?The formula to calculate the unemployment rate is:
Unemployment Rate = ( Number of Unemployed Individuals / Civilian Labor Force ) × 100
In this case, the number of unemployed individuals actively seeking jobs is 400,000, and the civilian labor force is 4,000,000.
Unemployment Rate = ( 400, 000 / 4, 000, 000) × 100
Simplifying the calculation :
= 0. 1 x 100
= 10 %
In conclusion, the unemployment rate in Country Y is 10%.
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Here, S.P. = . 1,61, 680 D%= 6%. M.P. = ?
The marked price (M.P.) is 1,72,000 when the selling price is 1,61,680 with discount of 6%.
To find the marked price (M.P.), we can use the formula:
M.P. = S.P. / (1 - D%)
Given:
S.P. = 1,61,680
D% = 6%
First, we need to convert the discount percentage to decimal form by dividing it by 100:
D% = 6/100 = 0.06
Now, we can substitute the values into the formula:
M.P. = 1,61,680 / (1 - 0.06)
M.P. = 1,61,680 / 0.94
M.P. = 1,72,000
Therefore, the marked price (M.P.) is approximately 1,72,000.
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______
36 | 8,325
is it
203 R17 or 231 R9 or 231 R11 or 234 R1
The quotient is 231, and the remainder is 9 or 231 R9.
To perform long division to find the quotient and remainder of 8,325 divided by 36, you would proceed as follows:
______
36 | 8,325
- 7,200 (36 x 200)1,125
1,080 (36 x 30)45
and, 36 (36 x 1)
9
The quotient is 231, and the remainder is 9.
Therefore, the correct answer is 231 R9.
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round 3666042 to the nearest hundred thousand
3666042 to the nearest hundred thousand is 3,700,000
7x 2/9 what the answer
Answer:
1.55
Step-by-step explanation:
2/9=0.22 x 7 =1.55
i hope this helps!
The radius of a circular play ground is 77m. Calculate the distance covered by a runner is 5 complete rounds around the ground. ( ans2420) how ?
Step-by-step explanation:
To solve this problem, we need to find the circumference of the circular playground and then multiply it by the number of rounds the runner completes.
The circumference of a circle can be calculated using the formula:
Circumference = 2 * π * radius
Given that the radius of the playground is 77m, we can substitute this value into the formula to find the circumference:
Circumference = 2 * π * 77
Now, we need to calculate the distance covered by the runner in 5 complete rounds. Since one round is equal to the circumference, the distance covered in 5 rounds would be:
Distance = 5 * Circumference
Substituting the value of the circumference, we have:
Distance = 5 * (2 * π * 77)
To simplify, we can use an approximation of π as 3.14:
Distance ≈ 5 * (2 * 3.14 * 77)
Calculating further:
Distance ≈ 5 * (6.28 * 77)
Distance ≈ 5 * 483.56
Distance ≈ 2417.8
Therefore, the distance covered by the runner in 5 complete rounds around the circular playground is approximately 2417.8 meters, which can be rounded to 2420 meters (as given in the answer).
Hope this helps!
Answer:
2420
Step-by-step explanation:
Circumference = 2πr
One complete round will be equal to the circumference = 2πr
Five rounds will be five times the circumference
= 5*2πr
= 10πr
[tex]= 10 *\frac{22}{7}*77 \\\\= 10* 22* 11\\\\= 2420[/tex]
i need the whole problem done plus the steps to it please, im stressed and its due soon
Total Surface Area of the Triangular prism = 30 ft².
Here, we have,
The triangular prism is attached.
The triangular prism shown has 2 triangular faces and 3 lateral faces.
here, we have,
Base of the triangle =2 ft
Height of the Triangle =3 ft
Area of one Triangular Face is:
A = 1/2 * 2 * 3 = 3 ft²
The dimensions of the lateral rectangles are:
2 ft by 3 ft
3 ft by height 3 ft
3 ft by height 3 ft
Therefore, total surface area of the triangular prism
=2(Area of one Triangular Face)+Area of 3 rectangular faces
= 2 *3 + ( 2*3 + 3*3 + 3*3)
= 6 + 24
= 30 ft²
Total Surface Area of the Triangular prism = 30 ft².
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