100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

The 9th arrangement will have 36 dots, the 10th arrangement will have 45 dots, and when adding the number of dots in any two consecutive arrangements, the result will be the number of dots in the next arrangement.

To determine the number of dots in the 9th and 10th arrangements, we need to understand the pattern in the given sequence: 1, 3, 6, 10, 15, ...

To find the pattern, we can observe the differences between consecutive terms: 2, 3, 4, 5, ...

We notice that these differences increase by 1 each time. This indicates that the sequence is formed by adding consecutive positive integers to the previous term.

Using this pattern, we can determine the 9th and 10th arrangements as follows:

9th arrangement:

Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.

Therefore, the 9th arrangement will have 36 dots.

10th arrangement:

Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.

Therefore, the 10th arrangement will have 45 dots.

Now, let's address the observation when we take any two consecutive arrangements and add the number of dots.

If we take the nth arrangement and the (n+1)th arrangement, we can observe that the number of dots in the (n+1)th arrangement will be the sum of the number of dots in the nth arrangement and the number of dots added in the (n+1)th step.

For example, let's consider the 2nd and 3rd arrangements:

2nd arrangement: 3 dots

3rd arrangement: 3 + 3 (adding 2, the next positive integer) = 6 dots

This pattern holds true for any two consecutive arrangements in the sequence.

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The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

[tex]y = 96(0.5)^x[/tex]

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

The height of the upper end of the handrail above the floor is approximately 3.467726 meters.

To calculate the height of the upper end of the handrail above the floor, we can use trigonometry and the given information about the length of the handrail and the angle of inclination.

Let's break down the problem into two right triangles:

The first right triangle is formed by the handrail, the floor, and a vertical line connecting the lower end of the handrail to the floor. The vertical line represents the height of the lower end above the floor, which is given as 0.7m.

The second right triangle is formed by the handrail, the floor, and a horizontal line parallel to the floor, connecting the upper end of the handrail to the floor. This horizontal line represents the height we need to calculate.

Now, let's apply trigonometric ratios to find the height of the upper end of the handrail above the floor.

In the first right triangle:

Opposite side = height of the lower end = 0.7m

Hypotenuse = length of the handrail = 5.4m

Using the sine function:

sin(angle) = Opposite / Hypotenuse

sin(40°) = 0.7 / 5.4

Now, let's solve for the sin(40°):

sin(40°) ≈ 0.64279

Multiplying both sides of the equation by 5.4:

0.64279 * 5.4 ≈ 3.467726

So, the length of the vertical line in the second right triangle (representing the height of the upper end of the handrail above the floor) is approximately 3.467726 meters.

Therefore, the height of the upper end of the handrail above the floor is approximately 3.467726 meters.

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The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

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Answer:

  A, D

Step-by-step explanation:

You want to identify the tables that represent inverse functions.

For every ordered pair (x, y) of a function, there is an ordered pair (y, x) of its inverse function.

The first table shown has an ordered pair (x, y) = (4, -14). That means its inverse function must have the ordered pair (-14, 4). The two tables with that characteristic are shown in the attachment.

<95141404393>

The amount of inches that the plant grows in 14 days is given as follows:

420 inches.

The proportional relationship that models the situation is given as follows:

i = 30d.

This means that the plant grows by 30 inches every day.

After 14 days, we have that d = 14, hence the size of the plant after 14 days is given as follows:

i = 30 x 14

i = 420 inches.

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Indianapolis: Ratio as decimal: 0.006939, Owners per 100: 0.7

New York: Ratio as decimal: 0.049018, Owners per 100: 4.9

Cairo: Ratio as decimal: 0.000554, Owners per 100: 0.1

Beijing: Ratio as decimal: 0.045336, Owners per 100: 4.5

Tokyo: Ratio as decimal: 0.064198, Owners per 100: 6.4

To calculate the ratio as a decimal and the owners per 100 for each city, we need to divide the number of owners by the total population and perform some additional calculations.

Let's calculate the ratio as a decimal for each city:

For Indianapolis:

Number of Owners: 6,245

Total Population: 0.90 million

Ratio as decimal: 6,245 / 0.90 million

= 6,245 / 900,000

= 0.006939

For New York:

Number of Owners: 911,216

Total Population: 18.6 million

Ratio as decimal: 911,216 / 18.6 million

= 911,216 / 18,600,000

= 0.049018

For Cairo:

Number of Owners: 10,598

Total Population: 19.1 million

Ratio as decimal: 10,598 / 19.1 million

= 10,598 / 19,100,000

= 0.000554

For Beijing:

Number of Owners: 959,611

Total Population: 21.2 million

Ratio as decimal: 959,611 / 21.2 million

= 959,611 / 21,200,000

= 0.045336

For Tokyo:

Number of Owners: 1,700,510

Total Population: 26.5 million

Ratio as decimal: 1,700,510 / 26.5 million

= 1,700,510 / 26,500,000

= 0.064198

Now, let's calculate the owners per 100 for each city by multiplying the ratio as a decimal by 100:

Owners per 100 for Indianapolis: 0.006939 * 100 = 0.6939

Owners per 100 for New York: 0.049018 * 100 = 4.9018

Owners per 100 for Cairo: 0.000554 * 100 = 0.0554

Owners per 100 for Beijing: 0.045336 * 100 = 4.5336

Owners per 100 for Tokyo: 0.064198 * 100 = 6.4198

Therefore, rounding the ratio as a decimal to 6 places, and the owners per 100 to one decimal, we have:

Indianapolis: Ratio as decimal: 0.006939, Owners per 100: 0.7

New York: Ratio as decimal: 0.049018, Owners per 100: 4.9

Cairo: Ratio as decimal: 0.000554, Owners per 100: 0.1

Beijing: Ratio as decimal: 0.045336, Owners per 100: 4.5

Tokyo: Ratio as decimal: 0.064198, Owners per 100: 6.4

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Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Answer: $2.21

Step-by-step explanation:

To calculate the cost per pound of mushrooms, we need to use the yield factor given in the question. The yield factor tells us the percentage of the total weight of the mushrooms that can be used for cooking or sale. Here, the yield factor is 90%, which means that 90% of the weight of the mushrooms can be used. Let's begin with the calculation:

First, we need to find out how much of the weight of the mushrooms is usable: 90% of 15 pounds = 0.9 x 15 = 13.5 pounds

Now, we can find out the cost per pound of the mushrooms:

Cost per pound = Total cost / Total usable weight

Total cost = $29.85

Total usable weight = 13.5 pounds

Therefore, the cost per pound of mushrooms = $29.85 / 13.5 pounds ≈ $2.21 per pound

Therefore, the cost per pound of mushrooms is $2.21 per pound.

The amount that can be withdrawn immediately after the last deposit is approximately $8,876.80.

We can use the formula for the future value of an ordinary annuity. The formula is given by:

[tex]FV = P * [(1 + r/n)^(^n^t^) - 1] / (r/n)[/tex]

Where

Given:

Plugging in the values, we have:

[tex]FV = 480 * [(1 + 0.045/2)^(^2*^8^) - 1] / (0.045/2)[/tex]

Calculating the expression inside the brackets

[tex](1 + 0.045/2)^(^2^*^8^) = 1.0225^1^6[/tex]≈ 1.4197

Substituting this value back into the formula:

FV = 480 * (1.4197 - 1) / (0.045/2)

FV = 480 * 0.4197 / 0.0225

FV ≈ $8,876.80

So, the amount that can be withdrawn immediately after the last deposit is approximately $8,876.80.

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The transformation of g(x) to f(x) is g(x) is shifted up 15 units and shifted left by 16 units

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

Where, we have

f(x) = 1/(x + 16) + 15

g(x) = 1/x

From the above, we have

Horizontal difference = 16 - 0 = 16

Vertical difference = 15 - 0 = 15

This means that the transformation of g(x) to f(x) is g(x) is shifted up 15 units and shifted left by 16 units

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The equation of the line in the graph that passes through (0,1) and (4,0) is  [tex]y = -\frac{1}{4}x + 1[/tex].

The equation of line is expressed as:

y = mx + b

Where m is slope and b is the y-intercept.

From the image, the graph passes through points (0,1) and (4,0).

First, we calculate the slope (m) using the formula:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = \frac{0 - 1 }{4 - 0} \\\\m = -\frac{1 }{4 }[/tex]

Next, plug the slope m = -1/4 and one point (0,1) into the point-slope form and simplify:

( y - y₁ ) = m( x - x₁ )

[tex]y - 1 = -\frac{1}{4}( x - 0 ) \\\\y - 1 = -\frac{1}{4}x\\\\y = -\frac{1}{4}x + 1[/tex]

Therefore, the equation of the line is [tex]y = -\frac{1}{4}x + 1[/tex].

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Answer: x=2, y=4

Step-by-step explanation:

Since the lines are parallel, we can say that the larger triangle and the smaller triangle are similar. Thus. x+3/(2y-1) = (3/2x+2)/(3y-5). Also, note that there are hash lines, telling us that 2y-1 and 3y-5 are equal. Thus 2y-1=3y-5, and y=4. Plugging y=4 into the first equation yields: (x+3)/(7)=(3/2x+2)/(7), or x+3=3/2x+2. Then 1/2x=1, x=2.

Thus: x=2, and y=4

Answer:

x = 2

y = 4

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

As the line bisects the side of the triangle with the y-variables, then the line is the midsegment of the triangle. This means that the line also bisects the side of the triangle with the x-variables.

Therefore, the two expressions with the x-variable are equal.

Similarly, the two expressions with the y-variable are equal.

Solving for x:

[tex]\boxed{\begin{aligned}\dfrac{3}{2}x+2&=x+3\\\\\dfrac{3}{2}x+2-x&=x+3-x\\\\\dfrac{1}{2}x+2&=3\\\\\dfrac{1}{2}x+2-2&=3-2\\\\\dfrac{1}{2}x&=1\\\\2 \cdot \dfrac{1}{2}x&=2 \cdot 1\\\\x&=2\end{aligned}}[/tex]

Solving for y:

[tex]\boxed{\begin{aligned}3y-5&=2y-1\\\\3y-5-2y&=2y-1-2y\\\\y-5&=-1\\\\y-5+5&=-1+5\\\\y&=4\end{aligned}}[/tex]

Answer:

polynomial; left 3 right 1

Step-by-step explanation:

The type of function is a polynomial.

The parent function is translated by moving -2x^3 to the left 3 and right 1.

Answer:

The function is a quadratic function.

Series of transformations:

Step-by-step explanation:

A quadratic function is a polynomial function of degree 2 (the highest exponent of the variable is 2).

Therefore, the given equation, y = -2(x + 3)² + 1, represents a quadratic function as the term (x + 3)² indicates that the highest power of the x-variable is 2.

[tex]\hrulefill[/tex]

The parent function of a quadratic function is y = x².

To translate the parent function to produce the given equation, we need to apply this series of transformations:

1. Horizontal translation

When "a" is added to the x-variable, the graph is shifted "a" units to the left. Therefore, the addition of 3 inside the parentheses shifts the graph horizontally to the left by 3 units.

2. Vertical Stretch

The coefficient in front of the squared term (x + 3)² indicates a vertical stretch or compression. In this case, since the coefficient greater than 1, it stretches the graph vertically, making it narrower compared to the parent function.

3. Reflection

As the stretch coefficient is negative, the graph is reflected across the x-axis, meaning the parabola opens downwards.

4. Vertical translation

When "a" is added to the function, the graph is shifted "a" units up. Therefore, the addition of 1 to the function shifts the graph vertically up by 1 unit.

In summary, the series of transformations that maps the parent function to the given function is:

The equation of the line that passes through the points (1,0) and (3,6) is y = 3x - 3.

The formula for equation of line is expressed as:

y = mx + b

Where m is slope and b is the y-intercept.

Given that, the line passes through points  (1,0) and (3,6).

First, we determine the slope:

[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{6 - 0}{3 - 1} \\\\Slope\ m = \frac{6}{2} \\\\Slope\ m = 3[/tex]

Now we plug the  slope m = 3 and one point (1,0)into the point-slope form to find the equation:

( y - y₁ ) = m( x - x₁ )

( y - 0 ) = 3( x - 1 )

y = 3x - 3

Therefore, the equation of the line is y = 3x - 3.

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Identify the matrix A: C. A is a 3 × 3 square matrix.

The negative (additive inverse) of A is: -A =  [tex]\left[\begin{array}{ccc}1&0&-5\\-3&-6&1\\4&7&-1\end{array}\right][/tex]

In Mathematics and Geometry, a square matrix can be defined as a type of matrix that is composed of an equal number of both rows and columns. Generally speaking, m × m matrix is typically referred to as a square matrix of order m.

In this context, we can reasonably infer and logically deduce that the number of rows in matrix A is the same as the number of columns in matrix A;

3 rows = 3 columns;

m × m = 3 × 3

From additive inverse postulate, we have the following:

A + (-A) = 0

[tex]\left[\begin{array}{ccc}-1&0&5\\3&6&-1\\-4&-7&1\end{array}\right]+\left[\begin{array}{ccc}1&0&-5\\-3&-6&1\\4&7&-1\end{array}\right]=0[/tex]

-A =  [tex]\left[\begin{array}{ccc}1&0&-5\\-3&-6&1\\4&7&-1\end{array}\right][/tex]

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Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

The transformation T maps the unit square to a figure with an area of 24 and a vertex at (5,3) which gives: T(x, y) = (6x + 5, 8y + 3).

To find a transformation T that maps the unit square to a figure with an area of 24 and a vertex at (5,3), we can use a combination of scaling and translation.

Let's denote the unit square as S, and the transformed figure as F.

To obtain a rectangle with an area of 48 and a vertex at (5,3), we can scale the unit square by multiplying the x-coordinates by 6 and the y-coordinates by 8, and then translate the scaled rectangle by adding (5,3) to the coordinates of each point.

Therefore, the transformation T can be expressed as:

T(x, y) = (6x + 5, 8y + 3)

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The system of equations that is represented by the graph include:

D. y = x - 4

   [tex]y=\frac{x-4}{x+2}[/tex]

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of the red line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 + 5)/(4 + 1)

Slope (m) = 5/5

Slope (m) = 1

At point (4, 0) and a slope of 1, a linear equation for C can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 1(x - 4)

y = x - 4

Since the rational function has a y-intercept of (0, -2), it would have a vertical asymptote and the denominator would be undefined at x = 2;

[tex]y=\frac{x-4}{x+2}[/tex]

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

To prepare a July 31 Balance Sheet for Academic Learning Services, you would need access to the financial statements and records provided in the class, as well as the information from Practical Exercise

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To the nearest hundredth, the third side of the triangle is 62.74.

To find the length of the third side of the triangle, we can use the Law of Cosines, which relates the lengths of the sides and the cosine of an angle in a triangle. The formula is as follows:

[tex]c^2[/tex] = [tex]a^2[/tex] + [tex]b^2[/tex] - 2ab*cos(C)

Where:

c = length of the third side,

a and b = lengths of the other two sides, and

C = included angle.

Given that the lengths of the two sides are 43 and 67, and the included angle is 27 degrees, we can substitute these values into the formula:

[tex]c^2[/tex] = [tex]43^2[/tex] + [tex]67^2[/tex] - 2 * 43 * 67 * cos(27°)

Now we can calculate the value of c:

[tex]c^2[/tex] ≈ 1849 + 4489 - 2 * 43 * 67 * 0.8910065242

[tex]c^2[/tex] ≈ 1849 + 4489 - 5946.654213618

[tex]c^2[/tex] ≈ 3931.345786382

Taking the square root of both sides to isolate c, we get:

c ≈ √3931.345786382

c ≈ 62.74

Therefore, to the nearest hundredth, the length of the third side of the triangle is approximately 62.74.

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Answer:

11 yards and 3 feet

Answer:

24 u jus gotta multiply by 3 cuz it is 1 out of 3

Step-by-step explanation: hi :)

If the total height between two floors is 9'0 1/2" and 14 risers are to be used in a set of stairs, the height of each riser would be approximately 7.75 inches.

To find the height of each riser in a set of stairs given the total height between two floors, we need to divide the total height by the number of risers.

First, let's convert the total height to a consistent unit. The distance between two floors is given as 9'0 1/2". We can convert this to inches by multiplying the feet by 12 and adding the remaining inches:

9 feet = 9 * 12 = 108 inches

0 1/2 inch = 0.5 inch

Total height = 108 + 0.5 = 108.5 inches

Next, we divide the total height by the number of risers (14) to find the height of each riser:

Height of each riser = Total height / Number of risers

Height of each riser = 108.5 inches / 14

Using a calculator, we can compute:

Height of each riser ≈ 7.75 inches

Therefore, the height of each riser in the set of stairs would be approximately 7.75 inches.

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Answer:

total age = 84 years

Step-by-step explanation:

mean is calculated as

mean = [tex]\frac{total}{count}[/tex]

here count = 7 and mean = 12 , then

[tex]\frac{total}{7}[/tex] = 12 ( multiply both sides by 7 )

total = 7 × 12 = 84 years

The area of the trapezium with bases 20cm and 10cm and a height of 16cm is 240 square centimeters.

A trapezium is simply a two-dimensional quadrilateral that has one pair of parallel sides.

The area of a trapezium is expressed as:

Area = 1/2 × ( a + b ) × h

Where a and b are the base measure and h is the height.

From the diagram:

Base a = 20 cm

Base b = 10 cm

Height h 16 cm

Area = ?

Plug the values into the above formula and solve for the area:

Area = 1/2 × ( a + b ) × h

Area = 1/2 × ( 20 + 10 ) × 16

Area = 1/2 × ( 30 ) × 16

Area = 15 × 16

Area = 240 cm²

Therefore, the area of the trapezium is 240 square centimeters.

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Step-by-step explanation:

I am going to assume that = sign should be the ≅.

For the Statements :

1. AB=DC

AB ll DC

2. Line AC is the transversal of AB and CD

3. Angle BAC ≅ Angle DCA

4. Angle BCA ≅ Angle DAC

5. Line AC=Line AC

6. Triangle ABC ≅ Triangle CDA

For the Reasons:

1. Given

2. Definition of a transversal

3. Alternate Interior Angles

4. Alternate Interior Angles

5. Reflexive Property

6. ASA

The set intersection X' ∩ Y' is expressed as; {e, 24}

We are given the sets as;

U = {a, b, c, d, e, f, 19, 20, 21, 22, 23, 24}

X = {a, b, c, 20, 21, 22}

Y = {b, d, f, 19, 21, 23}

Union of the sets A and B , denoted A ∪ B , is the defined as the set of all objects that are a member of A , or B , or both. The union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4} . Intersection of the sets A and B , denoted A ∩ B , is the set of all objects that are members of both A and B

Thus:

X' ∩ Y' is as follows;

X' = {d, e, 19, 23, 24}

Y' = {a, c, e, 20, 22, 24}

X' ∩ Y' = {e, 24}

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The number of subsets for the set in this problem is given as follows:

16 subsets.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

[tex]2^n[/tex]

The set in this problem is given as follows:

{C, D, E, F}.

Hence the cardinality of the set is given as follows:

n = 4.

Then the number of subsets is given as follows:

[tex]2^4 = 16[/tex]

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Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.