The solution in the equation is x = 12.
We have,
To solve the logarithmic equation log (x − 2) = 1,
We can use the definition of logarithm which states that log base b of x equals y if and only if b to the power of y equals x, where b is the base of the logarithm.
In this case, the base is not specified, so we assume it is 10, which is the common base used in most calculators and mathematical applications
Using the exponential form, we have:
log (x - 2) = 1
10^1 = x - 2
10 = x - 2
x = 12
Therefore,
The solution is x = 12.
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The picture below shows a large square with side lengths equal to 1 yd. The
square is divided into smaller squares that are all of equal size. Some of the
smaller squares are shaded, forming a shaded rectangular region.
Step-by-step explanation:
so, the 1 yard is split into 6 equal parts.
each small square has therefore an area of 1/6 × 1/6 yard² = 1/36 yard²
the shaded area is 4×3 = 12 small squares large.
is area is therefore
12 × 1/36 = 1/3 yard²
since 1 yard = 3 ft, 1 × 1 = 1 yard² = 3 × 3 ft² = 9 ft².
and 1/3 yard² = 1/3 × 9 ft² = 3 ft²
so, whatever dimension you need.
the area is
1/3 yard² = 3 ft²
1.2 grams is how many grains
Direct Materials Purchases Budget Anticipated sales for Solid Grip Company were 66,000 passenger car tires and 20,000 truck tires. Rubber and steel belts are used in producing passenger car and truck tires as follows: Passenger Car Truck Rubber 33 lb. per unit 77 lb. per unit Steel belts 5 lb. per unit 13 lb. per unit The purchase prices of rubber and steel are $2.90 and $3.80 per pound, respectively. The desired ending inventories of rubber and steel belts are 62,000 and 13,000 pounds, respectively. The estimated beginning inventories for rubber and steel belts are 73,000 and 11,000 pounds, respectively. Prepare a direct materials purchases budget for Solid Grip Company for the year ended December 31, 20Y8. When required, enter unit prices to the nearest cent.
Direct Materials Purchases Budget is given by,
Rubber Steel
Expected production 3,718,000 lb. 590,000 lb.
Desired ending inventory 62,000 lb. 13,000 lb.
Total required 3,780,000 lb. 603,000 lb.
Less: Beginning inventory (73,000 lb.) (11,000 lb.)
Total to be purchased 3,707,000 lb. 592,000 lb.
Unit price $2.90/lb. $3.80/lb.
Total cost $10,749,300 $2,249,600
To prepare a direct materials purchases budget for Solid Grip Company,
The amount of rubber and steel belts needed for the production of 66,000 passenger car tires and 20,000 truck tires.
The desired ending inventories and estimated beginning inventories for each material.
First, let us calculate the amount of rubber and steel belts required for the production of passenger car and truck tires.
Passenger car tires,
Rubber,
66,000 tires x 33 lb. per unit = 2,178,000 lb.
Steel belts,
66,000 tires x 5 lb. per unit = 330,000 lb.
Truck tires,
Rubber,
20,000 tires x 77 lb. per unit = 1,540,000 lb.
Steel belts,
20,000 tires x 13 lb. per unit = 260,000 lb.
Next, let us calculate the total amount of rubber and steel belts needed for production.
Rubber,
2,178,000 lb. + 1,540,000 lb. = 3,718,000 lb.
Steel belts,
330,000 lb. + 260,000 lb. = 590,000 lb.
To calculate the total amount of rubber and steel belts required for purchase,
Add the desired ending inventories and subtract the estimated beginning inventories,
Rubber,
3,718,000 lb. + 62,000 lb. - 73,000 lb. = 3,707,000 lb.
Steel belts,
590,000 lb. + 13,000 lb. - 11,000 lb. = 592,000 lb.
Finally, calculate the total cost of rubber and steel belt purchases.
Rubber,
3,707,000 lb. x $2.90 per pound = $10,749,300
Steel belts,
592,000 lb. x $3.80 per pound = $2,249,600
Therefore, the direct materials purchases budget for Solid Grip Company for the year ended December 31, 20Y8 is as follows,
Direct Materials Purchases Budget
Rubber Steel
Expected production 3,718,000 lb. 590,000 lb.
Desired ending inventory 62,000 lb. 13,000 lb.
Total required 3,780,000 lb. 603,000 lb.
Less: Beginning inventory (73,000 lb.) (11,000 lb.)
Total to be purchased 3,707,000 lb. 592,000 lb.
Unit price $2.90/lb. $3.80/lb.
Total cost $10,749,300 $2,249,600
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Please help
A line with a slope of 1/5 passes through the point (-4,-3). What is its equation in point slope form?
A line that includes the point (1,3) has a slope of nine. What is its equation in point slope form?
A line with a slope of -10 passes through the point (-4,-1) what is this equation in point slope form?
There is a line that includes the point (9,3) and has a slope of -1/6 what is its equation in point slope form?
A line passes through the points (1,2) and (2,10). What is its equation in point slope form?
When answering all these questions, you specific points in the equation
Can someone help…………..zzz.
Answer:
(2,0)
Step-by-step explanation:
Vertex is the top or bottom of the graph, depending on if the graph is upside down or not.
In this case, the graph is upside down, so the vertex will be at the top. We see that the vertex is located at (2,0) in this graph. So, the vertex is (2,0).
3.14+24 is the sum rational or irrational?
It is the sum of rational numbers.
What are rational numbers?Any given number which can be expressed in form of fraction where its denominator is not zero, is said to be a rational number. Examples are: 2, 10, 3.14 etc.
While irrational numbers are numbers that can not be expressed as a fraction. Examples are: π, [tex]\sqrt{10}[/tex] etc.
To determine if the given number are rational or irrational numbers, then;
3.14 = 314/ 100
and
24 = 24/ 1
Therefore, both numbers are rational.
So that;
3.14 + 24 = 27.14
Then,
27.14 = 2714/ 100
Thus we can conclude that the sum is rational.
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need help pls quick.. algebra here is screenshot right answer only
The value that would help Charlie find out how long it takes his basketball to reach the highest point is "x at the vertex". The correct option is A.
When the basketball reaches the highest point, its vertical velocity is zero. The time taken to reach this point can be found using the equation:
t = -b / (2a)
where a is the acceleration due to gravity (-9.8 m/s²) and b is the initial vertical velocity of the basketball.
The vertex of the parabolic path that the basketball follows is the point where the basketball reaches its maximum height. This point occurs at the halfway point of the ball's total flight time. The horizontal distance the basketball travels during this time is called "Ox at the vertex".
Therefore, by finding the "x at the vertex", Charlie can calculate the total flight time of the basketball, and then use the equation above to find the time it takes to reach the highest point.
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Which is the same length as 65 km
Answer:
65000 metres
Step-by-step explanation:
65*1000=65000
Someone pls help me with this
The value of the angle a is 38⁰
The value of the angle b is 52⁰
The value of the angle c is 104⁰
The value of the angle d is 90⁰
What are the value of the angles?The value of the angles is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
a = ¹/₂ x arc 76⁰
a = 38⁰
Since the chord passed through the center, arc c is calculated as;
arc c = 180 - 76 (sum of angles of a semicircle)
arc c = 104⁰
b = ¹/₂ x 104⁰
b = 52⁰
d = 180 - (a + b) (sum of angles in a triangle)
d = 180 - (38 + 52)
d = 90⁰
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what base could be written in the blank to make the exponential function model 15% decay ? y= (____) ^t\12 what answer would I put in the blank?
The exponential function model is y = (0.85[tex])^{t/12[/tex].
We know, The form of the function should be
y= a bˣ
Where, A should be the initial amount and b decrease rate.
Now, y = [tex]b^{t/12}[/tex]
So, the value of base be
= (100 - 15) / 100
= 0.85
Then, the function should be y = (0.85[tex])^{t/12[/tex]
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Lia prepared 35 kilograms of dough after working 7 hours. How much dough did Lia prepare if she worked for 9 hours?
Just write the number for your answer please.
Answer:
We can use the proportion method to solve this problem.
Let's define the rate of dough preparation as the amount of dough Lia can prepare per hour. We can write:
rate = amount of dough / time
We are given that Lia prepared 35 kg of dough in 7 hours. We can use this information to find her rate of dough preparation:
rate = 35 kg / 7 hours = 5 kg/hour
Now we can use this rate to find how much dough Lia will prepare if she works for 9 hours:
amount of dough = rate x time
amount of dough = 5 kg/hour x 9 hours = 45 kg
Therefore, if Lia works for 9 hours, she will prepare 45 kilograms of dough.
PLS HELP ASAP!!!!!!!!!
Answer: 4m^5-3m^2+2m+21
Step-by-step explanation: you just have to put the exponents int he right order which we always put the highest first so you put 4m^5-3m^2+2m+21 which is the answer
The credit card with the transactions described on the right uses the average daily balance method to calculate interest. The monthly interest rate is 2.5% of the average daily balance. Calculate parts a-d using the statement on the right.
a. Find the average daily balance for the billing period. Round to the nearest cent.
The average daily balance for the billing period is $
(Round to the nearest cent as needed.)
b. Find the interest to be paid on April 1, the next billing date. Round to the nearest cent.
The interest to be paid on April 1 is $
(Use the answer from part a to find this answer. Round to the nearest cent as needed.)
c. Find the balance due on April 1.
The balance due on April 1 is $ .
(Use the answer from part b to find this answer.)
d. This credit card requires a $10 minimum monthly payment if the balance due at the end of the billing period is less than $360. Otherwise,
1
the minimum monthly payment is
36 of the balance due at the end of the billing period, rounded up to the nearest whole dollar. What is the
minimum monthly payment due by April 9?
The minimum monthly payment is $ .
(Use the answer from part c to find this answer. Round up to the nearest
The Average Daily Balance is 6106.77
The interest to be paid on 1st April April is 152.67
Balance Due on April 1 is 6412.67
How to calculate the valueAverage Daily Balance = Total of (Number of days * Balance) / 31 days
= 189310 / 31
= 6106.77
(b.) The Interest to be paid on 1st April April = Average Daily Balance * 2.5%
= 6106.77 * 2.5%
= 152.67
(c.) Balance Due on April 1 = 6260 + Interest for April
= 6260 + 152.67
= 6412.67
(d.) In case of Minimum Due = 6412.64 / 36 = 178.13
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what is the relationship between the area of a rectangle and a parallelogram
Answer: The relationship between the area of rectangle and area of parallelogram is that they both are equal in area.
Step-by-step explanation:
parallelogram is formed when two parallel lines intersects other two parallel lines and rectangle is a type of parallelogram in which the intersecting lines intersects at right angle.
rectangle and parallelogram shares the same property and If we consider same base and same parallel lines then the area of parallelograms formed is always equal and as I mentioned above rectangle is also a parallelogram.
hence area of rectangle is equal to the area of parallelogram in same base and same parallel lines.
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Anyone else have this question figured out
The equation of line is,
⇒ y = 1/2x + 2
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (- 4, 0) and (0, 2).
Now,
Since, The equation of line passes through the points (- 4, 0) and (0, 2).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (2 - 0) / (0 + 4)
m = 2 / 4
m = 1/2
Thus, The equation of line with slope 1/2 is,
⇒ y - 0 = 1/2 (x + 4)
⇒ y = 1/2x + 2
Therefore, The equation of line is,
⇒ y = 1/2x + 2
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What is the total perimeter of this figure?
34.71 ft
31.71 ft
39.42 ft
36.42 ft
The rectangle's circumference is 27+ (3/2) fee and one of its sides is a semicircle.
We can start by finding the perimeter of the rectangle, which is simply the sum of the lengths of all four sides:
Perimeter of rectangle = 2(length + width) = 2(12 + 3) = 30 feet
Next, we need to find the perimeter of the semicircle.
The diameter of the semicircle is equal to the width of the rectangle, which is 3 feet. The formula for the perimeter of a semicircle is:
Perimeter of semicircle = (π/2) x diameter + diameter
Plugging in the values, we get:
Perimeter of semicircle = (π/2) x 3 + 3 = (3/2)π + 3
Now, we can add the perimeter of the semicircle to the perimeter of the rectangle to get the total perimeter:
Total perimeter = Perimeter of rectangle + Perimeter of the semicircle- 2*diameter of the semicircle
= 30 + (3/2)π + 3 - 3*2
= 27+ (3/2)π
Therefore, the perimeter of the rectangle with a semicircle on one side is 27+ (3/2)π feet, or approximately 31.71 feet (rounded to two decimal places).
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Which of the
�
nn-values satisfy the following inequality?
3
�
−
7
<
26
3n−7<263, n, minus, 7, is less than, 26
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
�
=
10
n=10n, equals, 10
A
�
=
10
n=10n, equals, 10
(Choice B)
�
=
11
n=11n, equals, 11
B
�
=
11
n=11n, equals, 11
(Choice C)
�
=
12
n=12n, equals, 12
C
�
=
12
n=12n, equals, 12
All values of n must be smaller than 11 in order to meet the inequality. The answer may be expressed as follows in interval notation: n (-∞, 10)
To solve the inequality 3n - 7 < 26, you can follow these steps:
Add 7 to both sides of the inequality to isolate the n variable on one side:
3n - 7 + 7 < 26 + 7
3n < 33
Divide both sides of the inequality by 3 to get n by itself:
3n/3 < 33/3
n < 11
Therefore, the values of n that satisfy the inequality are all values less than 11. In interval notation, you can write the solution as:
n ∈ (-∞, 10)
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Please help 100 points
The surface area of the triangular prism is 184 metres².
How to find the surface area of a triangular prism?The surface area of the triangular base prism can be found as follows:
surface area of the prism = (s₁ + s₂ + s₃)l + bh
where
b =base
h = height
l = height of the prism
s₁, s₂ and s₃ are side length of the prism.
Therefore,
b = 6 units
h = 4 units
s₁ = 5 units
s₂ = 5 units
s₃ = 6 units
l = 10 units
Hence,
surface area of the prism = (5 + 5 + 6)10 + 6(4)
surface area of the prism = 160 + 24
Therefore,
surface area of the prism = 184 metres²
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Robert had 2 2/5 cups of chocolate syrup left in his freezer he used 1/4 cup of Chocolate syrup when he makes a milkshake what is the maximum number of milkshakes that Robert can make with the chocolate syrup
Robert can make a maximum of 8 milkshakes with the remaining chocolate syrup.
How to find the maximum number of milkshakes that Robert can make with the chocolate syrupConverting the mixed number 2 2/5 to an improper fraction: 2 2/5 = 12/5
Subtracting the amount of chocolate syrup used per milkshake from the total amount of chocolate syrup:
12/5 - 1/4 = (48 - 5) / 20 = 43/20
Therefore, Robert has 43/20 cups of chocolate syrup left, which is the maximum amount he can use to make milkshakes.
For maximum number of milkshakes:
(43/20) / (1/4) = (43/20) x (4/1) = 172/20 = 8.6
Since Robert cannot make a fraction of a milkshake, he can make a maximum of 8 milkshakes with the remaining chocolate syrup.
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One quarter has a mass of 5.67 grams. Which is the mass of 50 quarters?
The mass of 50 quarters is 283.5 grams.
A quarter could be a unit of currency utilized in a few nations, including the United States and Canada.
Mass could be a fundamental physical quantity that measures the sum of matter in an object. It is as a rule measured in kilograms (kg) or grams (g).
In the given question,
One quarter has a mass of [tex]5.67[/tex] grams.
Mass of 50 quarters =?
To find out the mass of 50 quarters we have to multiply by the mass of one quarter.
Mass of 50 Quarter = [tex]5.67[/tex] ×[tex]50[/tex]
Mass of 50 Quarter = [tex]283.5 grams[/tex]
Therefore, the mass of 50 quarters is 283.5 grams.
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HELP PPPSKSKFJSJSJSJSJSHDHDDH
Answer:D
Step-by-step explanation:
got it right
Differentiate y=3xcosx+sinx
Answer:
Step-by-step explanation:
To differentiate y = 3x cos(x) + sin(x), we can use the product rule and the chain rule.
Let's start by differentiating the first term, 3x cos(x), using the product rule:
d/dx (3x cos(x)) = 3 cos(x) - 3x sin(x)
Next, we can differentiate the second term, sin(x), using the chain rule:
d/dx (sin(x)) = cos(x)
Putting it all together, we get:
dy/dx = 3 cos(x) - 3x sin(x) + cos(x)
Simplifying the expression, we get:
dy/dx = (4cos(x)) - (3xsin(x))
Therefore, the derivative of y = 3x cos(x) + sin(x) is dy/dx = 4cos(x) - 3xsin(x).
Find the total surface area of this cylinder. Give your answer to 1 decimal place. 18 cm 24 cm
The total surface area of the cylinder is 2260.8 cm².
How to find the total surface area of a cylinder?The height of the cylinder is 18 centimetres and the diameter of the cylinder is 24 centimetres.
Therefore, the total surface area of the cylinder can be calculated as follows:
total surface area = 2πr(r + h)
where
r = radiush = heightTherefore,
r = 24 / 2 = 12 cm
h = 18 cm
total surface area = 2 × 3.14 × 12(12 + 18)
total surface area = 75.36(30)
total surface area = 2260.8 cm²
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A child’s pool is in the shape of a rectangular prism with a height of 2 ft and a base that is 4 ft wide by 5 ft long. During the course of the summer, the child’s pool needed to be filled 3 times. How many cubic feet of water were needed to fill the pool during the summer? Responses 40 ft³ 40 ft³ 80 ft³ 80 ft³ 120 ft³ 120 ft³ 160 ft³ 160 ft³
The requried, 120 ft³ of water was needed to fill the pool during the summer.
The volume of the child's pool is given by multiplying its length, width, and height.
The volume of the pool = Length x Width x Height
= 5 ft x 4 ft x 2 ft
= 40 cubic feet
Since the pool was filled 3 times during the summer, the total amount of water needed is:
The total volume of water = Volume of pool x Number of times filled
= 40 ft³ x 3
= 120 ft³
Therefore, 120 ft³ of water was needed to fill the pool during the summer.
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Find y.
I will give Brainliest to correct answer !
Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: [tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]
What is a square root function?In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;
f(x) = √x
g(x) = -√9(x - 1) + 2
[tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]
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finding the inverse of [tex]-(1/2)-log_{3}\sqrt{9-x}[/tex]
The inverse function of the function f(x) is [tex]g(y) = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]
To find the inverse of the given function f(x) = -(1/2) - log₃√(9-x)
we need to solve for x in terms of y, where y = f(x).
Replace f(x) with y
Function y = -(1/2) - log₃√(9-x)
Solve for x
First, isolate the logarithmic term on one side of the equation.
y + (1/2) = -log₃√(9-x)
[tex]3^-^(^y^ +^ 1^/^2^) = 9-x[/tex]
[tex]x = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]
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Gordon runs for 28 minutes on Monday and 43 minutes on Wednesday. Write and solve an equation to find how many more minutes Gordon ran on Wednesday
Compared to Monday, Gordon ran for an additional 15 minutes on Wednesday.
Let x be the number of additional minutes Gordon ran on Wednesday compared to Monday. Then, we can write an equation based on the given information:
43 minutes (Wednesday) = 28 minutes (Monday) + x minutes (additional time on Wednesday)
To solve for x, we can isolate it on one side of the equation:
43 minutes - 28 minutes = x minutes
15 minutes = x
Therefore, Gordon ran 15 more minutes on Wednesday compared to Monday.
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A sleep study was given to 20 randomly selected people between the ages of 1 and 16. The graph shows the relationship between the age of the person and the number of hours they slept.
Which of the following describes the pattern of association between the variables, based on the graph?
There is a positive linear association.
There is a positive nonlinear association.
There is a negative linear association.
There is a negative nonlinear association.
(HURRY) Based on the data in the graph, to the nearest degree, how much greater is the mean temperature of the orange juice than the mean temperature of the water?
The mean temperature of orange juice is 5 degrees greater than the mean temperature of water.
The mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in the dataset and then dividing by the total number of values.
According to the graph, the different temperatures of water and orange juice on different time can be taken into consideration.
Sum of Temperature of Water at different time
= 55 + 62 + 69 + 71 + 79 + 75
= 441 degrees
Mean Temperature of Water
= 441/6
= 68.5 degrees
Sum of Temperature of Orange juice at different time
= 59 + 65 + 72 + 79 + 85 + 81
= 441 degrees
Mean Temperature of Orang juice
= 441/6
= 73.5 degrees
Difference = 73.5 - 68.5 = 5 degrees
Hence, the mean temperature of orange juice is 5 degrees greater than the mean temperature of water.
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What are the polar coordinates of the point A shown below?
A point plotted on a polar coordinate plane.
Select the correct answer below:
(−2,3π4)
(1,−π4)
(1,−7π4)
(2,−π4)
(−2,π4)
(1,3π4)
Answer:(1,−7π/4)
Step-by-step explanation:
Note that the point is on the circle whose radius is labeled 1, so r=1 or −1. Of the choices available, only an angle of −7π4, drawn from the positive x axis plots at the point A. So θ=−7π4, and r must be positive, as the angle is measured from the positive x axis. Thus, the polar coordinates are (1,−7π4).