Answer:
1. -30
2. 3
3. 40
4. 70
5. 90
6. 90
7. 80
The profit at each level of bicycle production is One bike: -$30
Two bikes: $3
Three bikes: $240
Four bikes: -$70
Five bikes: -$90
Six bikes: -$90
Seven bikes: $270
What is Algebra?
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
The table of bikes produced per day, total cost, total revenue
Now,
To calculate the profit at each level of bicycle production, we need to subtract the total cost from the total revenue.
One bike: Total revenue - Total cost = $50 - $80 = -$30
Two bikes: Total revenue - Total cost = $100 - $97 = $3
Three bikes: Total revenue - Total cost = $350 - $110 = $240
Four bikes: Total revenue - Total cost = $130 - $200 = -$70
Five bikes: Total revenue - Total cost = $160 - $250 = -$90
Six bikes: Total revenue - Total cost = $210 - $300 = -$90
Seven bikes: Total revenue - Total cost = $270 - $0 = $270
Therefore, by algebra the profit at each level of bicycle production will be
One bike: -$30
Two bikes: $3
Three bikes: $240
Four bikes: -$70
Five bikes: -$90
Six bikes: -$90
Seven bikes: $270
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Classify these two lines y=4x+5 and -4x+y=-13
Answer:
Parallel
Step-by-step explanation:
The book fair had a sale where 5 books were $25.85. If you wanted to buy 6 books, how much money would you need?
Answer:
$31.02
Step-by-step explanation:
5 books = $25.85
1 book= $5.17
6 books= $5.17*6
6 books= $31.02
What is the sum?
8+(-12)
О-20
0-4
020
Answer: -4
Work: So, to get -4, we need to simplify the equation. If you see any equation with +(- that's subtraction. So, with the rule, this equation is basically 8-12, and that's -4.
Answer:
-4
Step-by-step explanation:
8+(-12)
= 8-12
12-8=4
the answer is -4
2. 20% of what number is 15
Answer:
75
20 percent (calculated percentage %) of what number equals 15? Answer: 75
If y= 5x 61, find dxdy at x=−1 The value of dxdy at x=−1 is
We can use this formula for finding dxdy: dxdy = d/dy(dx/dx), the derivative of x to y. The value of dx dy at x = −1 is 5.
The value of dxdy at x = −1 is 5.
We can use the formula for finding dxdy:
dxdy = d/dy(dx/dx), which is the derivative of x to y.
Given that y = 5x + 61, we can first find dx/dy and then evaluate it at x = −1.
Using the Chain Rule:
d/dy(5x + 61) = 5
(d/dy(x)) = 5(dx/dy)
Then,
dx/dy = (1/5)
d/dy(5x + 61).
Differentiating w.r.t y:
d/dy(5x + 61) = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 5
(d/dy(x)) = 5(dx/dy)
Substituting x = −1, we get:
dx/dy = (1/5)(5) = 1
Therefore, dx dy at x = −1 is 5
We can use the formula for finding dxdy: dxdy = d/dy(dx/dx), the derivative of x to y.
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9 marbles your draw one what is the probability of drawing a red pen? You have 2 yellow 3 black and 4 reds
Answer:
4 / 9
Step-by-step explanation:
There are 4 reds out of 9 so the probability would be 4 out of 9 or 4 / 9.
Answer:
None
Step-by-step explanation:
Notice how it says red pens, not red marbles. There is no red pen
4. For data at the interval level, you cannot calculate meaningful differences between data entries.
For data at the interval level, we cannot calculate meaningful differences between data entries. The statement is false.
Interval:
The interval of a numerical value generally represents the maximum and minimum value between which the numerical value belongs, it is the amount of time that has passed between the beginning and end of the event which is also known as elapsed time.
The various ways of showing intervals are Inequalities, interval notations, and number lines, the amount of time between two given times is known as the time interval.
Data at the ordinal level can be qualitative or quantitative. A true statement is "For data at the interval level, you can calculate meaningful differences between data entries."
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Evaluate the expression when b=2
12-b
Answer:
10 \(\huge\checkmark\)
Step-by-step explanation:
Hi there, hope you are having a nice day!
All we should do is plug in the value of b:
12-2
10 (Answer)
Hope you find it helpful.
Feel free to ask if you have any questions.
\(\bf{-MistySparkles^**^*\)
Answer:
10
Step-by-step explanation:
If b = 2,
12 - b equals 12 - 2,
thus the result is 10.
a cube has an edge of 5 feet. the edge is increasing at the rate of 3 feet per minute. express the volume of the cube as a function of m, the number of minutes elapsed.
The volume of a cube is given by the formula V = s^3, where s represents the length of one side of the cube. In this case, the length of one side is given as 5 feet.
To express the volume of the cube as a function of m, the number of minutes elapsed, we need to consider that the edge of the cube is increasing at a rate of 3 feet per minute.
Since the length of one side of the cube is increasing by 3 feet every minute, after m minutes, the length of one side will be 5 + 3m feet.
Therefore, the volume of the cube, as a function of m, can be expressed as:
V(m) = (5 + 3m)^3
To simplify this expression, we can expand the cube:
V(m) = (5 + 3m)(5 + 3m)(5 + 3m)
Using the distributive property, we can multiply each term:
V(m) = (25 + 15m + 15m + 9m^2)(5 + 3m)
Simplifying further:
V(m) = (25 + 30m + 9m^2)(5 + 3m)
Now, we can multiply each term:
V(m) = 25(5 + 3m) + 30m(5 + 3m) + 9m^2(5 + 3m)
V(m) = 125 + 75m + 150m + 90m^2 + 45m^2 + 27m^3
Combining like terms:
V(m) = 125 + 225m + 135m^2 + 27m^3
So, the volume of the cube, as a function of m, is V(m) = 27m^3 + 135m^2 + 225m + 125.
This function represents how the volume of the cube changes as time passes, considering the increasing length of one side at a rate of 3 feet per minute.
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what type of function helps the data
QUESTION 6 · 1 POINT
It takes George 16 minutes to sew one pillowcase. If he sews 6 pillowcases, how many minutes will
he have spent sewing? Do not include any units in your answer.
Answer: The answer is 96 minutes (or 1 hr 36 minutes)
Step-by-step explanation:
Since it takes George 16 minutes to sew one pillowcase, it would take him 96 minutes/1 hr 36 minutes to sew 6 pillowcases (16x6 or 16+16+16+16+16+16/6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6)
A tank has a height of 10 feet. The area of the horizontal cross section of the tank at height h feet is given by the function A, where A(h) is measured in square feet. The function A is continuous and decreases as h increases. Selected values for A(h) are given in the table above. (a) Use a left Riemann sum with the three subintervals indicated by the data in the table to approximate the
volume of the tank. Indicate units of measure.
To approximate the volume of the tank using a left Riemann sum, we can use the provided data in the table. The left Riemann sum is obtained by multiplying the width of each subinterval by the corresponding height value of the function A.
Given that the height of the tank is 10 feet and the function A is decreasing as the height increases, we can divide the height interval into three subintervals: [0, 2], [2, 6], and [6, 10].
Using the left endpoint of each subinterval, we can calculate the approximate volume as follows:
Volume ≈ (width of subinterval 1) * (A(0)) + (width of subinterval 2) * (A(2)) + (width of subinterval 3) * (A(6))
Let's assume the width of each subinterval is 2 feet based on the given data. Using the values from the table, we can substitute the corresponding height values:
Volume ≈ (2) * (8) + (2) * (6) + (2) * (4)
Simplifying the expression, we get:
Volume ≈ 16 + 12 + 8 = 36 cubic feet
Therefore, the approximate volume of the tank using the left Riemann sum with the given three subintervals is 36 cubic feet.
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f(x) = 2x; translate up 5 units, reflect in x-axis.
After f(x) = 2x translated up 5 units, then it reflect in x-axis is g(x) = f(2x)+5.
What does a graphing translation mean?
A graph can be vertically translated by moving the base graph up or down in the y-axis direction. Each point on a graph is moved k units vertically to translate the graph by that many units.The rules for transforming a function f(x) into g(x):
g(x) = a·f(b(x-c)) + d
a = vertical dilation (stretch); reflects across x-axis if negativeb = horizontal dilation (stretch); reflects across y-axis if negativec = horizontal translation (shift); shift right if c is positive, left if c is negatived = vertical translation; up if d is positive, down if d is negativeHence, After f(x) = 2x translated up 5 units, then it reflect in x-axis is g(x) = f(2x) + 5.
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Lines A || B find the value of x then the value of both angles
Answer:
x = 5, each angle is 100 degrees
Step-by-step explanation:
Because of some angle rule (I don't remember sorry) the two angles are gonna be equal to each other.
2x+90=x+95 Solve for x
2x=x+5
x=5
Plug x in both of the equations
2(5) + 90 = 100
(5) + 95 = 100
The graph of a linear function is shown
Which word describes the slope of the line?
positive
negative
zero
undefined
Answer:
the answer is b
Step-by-step explanation:
plz give me a Brainliest
A word that describes the slope of the line is negative. The correct answer is option B.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data. It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
For this case the first thing you should know is that we have an equation of the form:
y = mx + b
Where,
m: The slope of the line
b: Cutting point with the vertical axis.
For this case, we observe that the values of y decrease when the values of x increase. Therefore, the function decreases.
This means that it is true that:
m < 0
Therefore, the slope of the line is negative.
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Find the length of the third side. If necessary, write in simplest radical form.
IMAGE DOWN BELOW!
SOMEONE PLEASE HELP ME!! ILL GIVE YOU BRAINLIST ANSWER
Answer:
Step-by-step explanation:
6^2+B^2=3^2X5
36+b^2=9x5
b^2=9
b=3
Find the partial derivatives of the function f(x,y)=∫ y
x
cos(1t 2
+6t−8)dt f x
(x,y)
f y
(x,y)=
The partial derivative \(\(f_x(x, y)\)\) of the function \(\(f(x, y)\) is \(y \cdot F'(yx)\),\) and the partial derivative \(\(f_y(x, y)\) is \(x \cdot F'(yx)\),\) where \(\(F'(t)\)\) is the derivative of an antiderivative of \(\(\cos(1t^2 + 6t - 8)\).\)
To find the partial derivatives of the function \(\(f(x, y) = \int_{0}^{yx} \cos(1t^2 + 6t - 8) \, dt\),\) we need to differentiate with respect to each variable separately. The partial derivative \(\(f_x\)\) represents the rate of change of \(\(f\)\) with respect to \(\(x\), and \(f_y\)\) represents the rate of change of \(\(f\) with respect to \(y\).\)
To find \(\(f_x(x, y)\),\) we differentiate \(\(f\)\) with respect to \(\(x\)\) while treating \(\(y\)\) as a constant. Similarly, to find \(\(f_y(x, y)\),\) we differentiate \(\(f\)\) with respect to \(\(y\)\) while treating \(\(x\)\) as a constant.
Since the function \(\(f\)\) involves an integral, we will need to apply the Fundamental Theorem of Calculus to find its partial derivatives. According to the theorem, if \(\(F(t)\)\) is an antiderivative of \(\(\cos(1t^2 + 6t - 8)\),\) then
\(\[f(x, y) = \int_{0}^{yx} \cos(1t^2 + 6t - 8) \, dt = F(yx) - F(0).\]\)
Now, let's find the partial derivatives \(\(f_x(x, y)\) and \(f_y(x, y)\)\) using the Fundamental Theorem of Calculus. Taking the derivative of \(\(f\)\) with respect to \(\(x\)\) gives us:
\(\[f_x(x, y) = \frac{\partial}{\partial x} \left[F(yx) - F(0)\right].\]\)
By applying the chain rule, we have:
\(\[f_x(x, y) = y \cdot F'(yx).\]\)
Similarly, taking the derivative of \(\(f\) with respect to \(y\)\) gives us:
\(\[f_y(x, y) = \frac{\partial}{\partial y} \left[F(yx) - F(0)\right].\]\)
Again, using the chain rule, we have:
\(\[f_y(x, y) = x \cdot F'(yx).\]\)
So, the partial derivatives of \(\(f(x, y)\) are \(f_x(x, y) = y \cdot F'(yx)\)\) and \(\(f_y(x, y) = x \cdot F'(yx)\), where \(F'(t)\)\) is the derivative of an antiderivative of \(\(\cos(1t^2 + 6t - 8)\).\)
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A6-Sequences and Series
Q1. Below are the first few terms of some important mathematical sequences. State the 7th term
of each sequence:
a) 2, 4, 6, 8, .......
b) 1, 4, 9, 16, ....
c) 1, 8, 27, 64, ....
d) 2, 3, 5, 7, 11, ....
7th term is.
7th term
7th term is .............. (1)
7th term is ........…….…….. (1)
(Total 4 marks)
Answer:
Step-by-step explanation:
7th term of the first sequence is 14
first we need to find out the nth term so,
tn=Ti+(n-1)d
2(n-1)2
2+2n-2
2n+2-2
2n+0
Now we need to find out the 7th term
n=7
2(7)-0
14-0=0
Second sequences 7th term is 33
first we need to find the nth term
1(n-1)3
1+3n-3
3n+1-3
3n-2
so now we need to find 7th term
3(7)-2
35-3
33
the 4th sequence 7th term is 20
Identify the values of coefficients a, b, and c in the quadratic equation 5x^2=4x+7
The values of a, b and c in the given quadratic equation; 5x² = 4x + 7 are; 5, -4 and -7 respectively.
What are the values of a, b and c in the given quadratic equation?It follows from the task content that the values of a, b and c be determined in the quadratic equation; 5x² = 4x + 7.
Recall, the standard form of a quadratic equation takes the form; ax² + bx + c = 0.
Therefore, for the given equation; 5x² = 4x + 7; we have that;
5x² - 4x - 7 = 0.
Ultimately, the value of a is 5, b is -4 and c is -7.
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If Maggie’s snow cone maker can make 800 cubic inches of ice, how many snow cones can she make with the dimensions shown below (those being 6.5 inches, and 5 inches)
The volume of the snow cone is 42.54 cubic in. Then the number of the snow cone will be 18.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
If Maggie’s snow cone maker can make 800 cubic inches of ice.
Then the number of the snow cones can she make with the dimensions 6.5 in. height and 5 in. diameter.
The volume of the cone will be
\(\rm Volume = \dfrac{1}{3} \times \dfrac{\pi}{4} \times d^2 \times h\\\\Volume = \dfrac{1}{3} \times \dfrac{\pi}{4} \times 5^2 \times 6.5 \\\\Volume = 42.54 \ in ^3\)
Then the number of the cone will be
\(\rm \rightarrow \dfrac{800}{42.54}\\\\\rightarrow 18.805 \approx 18 \ cones\)
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Evaluate the expression for the given value of the variables.
0.7g - 1.7h
g= 17, h = 3
0.7g - 1.7h =
To evaluate the expression 0.7g - 1.7h when g = 17 and h = 3, we substitute these values into the expression and perform the necessary calculations. The expression 0.7g - 1.7h, when evaluated for g = 17 and h = 3, equals 6.8.
Substituting g = 17 and h = 3 into the expression 0.7g - 1.7h, we have:
0.7(17) - 1.7(3)
Now we perform the calculations:
0.7(17) = 11.9
1.7(3) = 5.1
Substituting the calculated values back into the expression, we have:
11.9 - 5.1
Performing the subtraction, we get the final result:
11.9 - 5.1 = 6.8
Therefore, the expression 0.7g - 1.7h, when evaluated for g = 17 and h = 3, equals 6.8.
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2. The following set of count readings was made in a gradient-free γ-ray field, using a suitable detector for repetitive time periods of one minute: 18,500;18,410; 18,250;18,760;18,600;18,220;18,540;18,270;18,670;18,540. (a) What is the mean value of the number of counts? (b) What is its standard deviation (S.D.)? (c) What is the theoretical minimum S.D. of the mean? (d) What is the actual S.D. of a single reading? (e) What is the theoretical minimum S.D. of a single reading?
The inflection point of f(t) is approximately t = 3.73.
(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.
Taking the derivative of f(t), we have:
f'(t) = -1.275t^2 + 9.516t + 6.741
To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:
-1.275t^2 + 9.516t + 6.741 = 0
Using the quadratic formula, we find two possible values for t:
t ≈ 0.94 and t ≈ 6.02
Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).
For t < 0.94, choose t = 0:
f'(0) = 6.741 > 0
For 0.94 < t < 6.02, choose t = 1:
f'(1) ≈ 14.982 > 0
For t > 6.02, choose t = 7:
f'(7) ≈ -5.325 < 0
From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).
(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.
Taking the second derivative of f(t), we have:
f''(t) = -2.55t + 9.516
Setting f''(t) = 0 and solving for t, we find:
-2.55t + 9.516 = 0
t ≈ 3.73
Therefore, The inflection point of f(t) is approximately t = 3.73.
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What are the coordinates of the point of intersection in the graph?
Answer: (2,6)
Step-by-step explanation:
Which of the following best explains why the mean is NOT an appropriate indicator of how much time Mary spends exercising on a typical day?
A. There is more than one mean.
B. The mean is not an integer value.
C. The mean is skewed by the days Mary did not exercise.
D. The set of data points is too small.
Answer:
C. The mean is skewed by the days Mary did not exercise.
Step-by-step explanation:
If Mary does not exercise for, say, a month then the mean will be very low and is not an indicator of how much time Mary spends exercising on an average
6.
2x + 5y = -7
7x + y = -8
Answer:
(- 1, - 1 )
Step-by-step explanation:
2x + 5y = - 7 → (1)
7x + y = - 8 → (2)
multiplying (2) by - 5 and adding to (1) will eliminate y
- 35x - 5y = 40 → (3)
add (1) and (3) term by term to eliminate y
(- 35x + 2y) + (5y - 5y) = - 7 + 40
- 33x + 0 = 33
- 33x = 33 ( divide both sides by - 33 )
x = - 1
substitute x = - 1 into either of the 2 equations and solve for y
substituting into (1)
2(- 1) + 5y = - 7
- 2 + 5y = - 7 ( add 2 to both sides )
5y = - 5 ( divide both sides by 5 )
y = - 1
solution is (- 1, - 1 )
4-3
Write a program that prompts the user to input an integer between 0 and 35. The prompt should say Enter an integer between 0 and 35:.
If the number is less than or equal to 9, the program should output the number; otherwise, it should output:
A for 10
B for 11
C for 12
. . .
and Z for 35.
(Hint: For numbers >= 10, calculate the ACSII value for the corresponding letter and convert it to a char using the cast operator, static_cast().)
Here's a sample program in C++ that satisfies your requirements:
```
#include
using namespace std;
int main() {
int num;
cout << "Enter an integer between 0 and 35: ";
cin >> num;
if (num <= 9) {
cout << num << endl;
} else if (num >= 10 && num <= 35) {
char letter = static_cast('A' + num - 10);
cout << letter << endl;
} else {
cout << "Invalid input." << endl;
}
return 0;
}
```
- The program prompts the user to input an integer between 0 and 35 using the `cout` and `cin` statements.
- The `if` statement checks whether the number is less than or equal to 9. If it is, it outputs the number using the `cout` statement.
- The `else if` statement checks whether the number is between 10 and 35 (inclusive). If it is, it calculates the corresponding letter using the ASCII value for 'A' and the given number. The `static_cast` statement converts the calculated value to a character. Finally, the program outputs the letter using the `cout` statement.
- The `else` statement handles the case when the input is outside the range of 0 to 35. It outputs an error message using the `cout` statement.
- The program ends with the `return 0` statement.
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what does it mean when the second derivative equals zero
When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.
The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.
Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.
Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.
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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.
The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.
To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.
Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.
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The diagram shows an open rectangular box ABCDEFGH.
A straight stick AGM rests against A and G and extends outside the box to M.
a. Calculate the angle between the stick and the base of the box.
b. AM= 30 cm.
Show that GM= 4.8 cm, correct
to 1 decimal place.
The angle between the stick and the base of the box is 77. 9 degrees
How to determine the angleTo determine the angle between the stick and the base, we have to know the trigonometric identities.
These identities are;
sinecosinecotangenttangentsecantcosecantFrom the information given, we have;
sin A = FB/AB
Given that;
GB = 14.5cm
AB = 18. 6cm
substitute for the length of the sides, we have;
sin A = 14.5/18. 6
Divide the values, we have;
sin A = 0. 7796
Find the inverse sine
A = 77. 9 degrees
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If I used the distributive property on this expression, what would it become?
12(x+3)
Answer:
It would become 12x+36
Answer:
12x+36
Step-by-step explanation:
Multiply the parts in parentheses by 12
which choice is equivalent to the expression below 2^7 times 19
The expression 2^7 times 19 can be simplified by first evaluating the exponential term, 2^7, which is equal to 128. Therefore:2^7 times 19 = 128 * 19We can then evaluate the product of 128 and 19 using multiplication. When we do that, we get:2^7 times 19 = 2432Therefore, the choice that is equivalent to the expression 2^7 times 19 is 2432