Answer:
Step-by-step explanation:
The equation for the cost of parking in Garage A for t hours is:
A = 3t + 7
The equation for the cost of parking in Garage B for t hours is:
B = 4t + 3
To find the number of hours parked, t, that would make the cost of each garage the same, we can set the two equations equal to each other and solve for t:
3t + 7 = 4t + 3
Subtracting 3t from both sides, we get:
7 = t + 3
Subtracting 3 from both sides, we get:
4 = t
Therefore, if Bella parks for 4 hours, the cost of parking in Garage A and Garage B will be the same.
To verify, we can substitute t = 4 into the two equations:
A = 3(4) + 7 = 19
B = 4(4) + 3 = 19
So, if Bella parks for 4 hours, the cost of parking in Garage A and Garage B will be $19.
Answer:
Bella is deciding between two parking garages. Garage A charges an initial fee of $7 to
park plus $3 per hour. Garage B charges an initial fee of $3 to park plus $4 per hour.
Let A represent the amount Garage A would charge if Bella parks for t hours, and let
B represent the amount Garage B would charge if Bella parks for t hours. Write an
equation for each situation, in terms of t, and determine the hours parked, t, that
would make the cost of each garage the same.
A = $7 + $3
B = $3 + $4
Danny is opening a savings account with an initial deposit of 45$. He saves $3 per day
The equation of the line is slope intercept form is y = 3x + 45.
What is a graph?
The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, Danny is opening a savings account with an initial deposit of $45 and he saves $3 per day.
Let y be the total amount he saves and x is the no. of days.
As he starts with $45 deposit it'll be added as a constant.
∴ The equation of the required line is y = 3x + 45.
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a number of teenagers are playing with their calculators. one of them multiplies their ages (in whole numbers) together and finds that the product is eighteen million seven hundred and twenty seven thousand two hundred. how many teenagers are in the group
Answer:
Step-by-step explanation:
We need to find the number of teenagers in the group, given that the product of their ages is 18,727,200.
To solve this problem, we need to factorize the given number into its prime factors and then determine how many distinct factors there are.
18,727,200 can be factorized as:
18,727,200 = 2^6 × 3^2 × 5^2 × 13^2
To find the number of distinct factors, we add 1 to each exponent and then multiply them together:
(6+1) × (2+1) × (2+1) × (2+1) = 7 × 3 × 3 × 3 = 189
Therefore, there are 189 factors of 18,727,200, which means that there are 189 ways to multiply whole numbers together to get this number.
Since we want to find the number of teenagers in the group, we need to look for combinations of factors that result in whole numbers for the ages. We can start by dividing the total number of factors by 2 (since we are looking for pairs of factors) and then slowly increase the divisor until we find the smallest number that results in a whole number.
189 ÷ 2 = 94.5 (not a whole number)
189 ÷ 3 = 63 (not a whole number)
189 ÷ 4 = 47.25 (not a whole number)
189 ÷ 5 = 37.8 (not a whole number)
189 ÷ 6 = 31.5 (not a whole number)
189 ÷ 7 = 27 (a whole number)
Therefore, there are 27 pairs of factors that result in whole numbers for the ages. Each pair corresponds to a group of teenagers, and since each group has the same number of teenagers, there are 27 teenagers in the group.
How many feet does Ava walk in one second
Ava walks 2.5 feet in one second.
How do we calculate?Ava walks 5 feet in 2 seconds, which means that the ratio of feet to seconds is 5 to 2.
We will use proportionality concept , to find out how many feet Ava walks in one second,
Let x be the number of feet Ava walks in one second. Then we can set up the proportion:
5 feet / 2 seconds = x feet / 1 second
solving for x, we can cross-multiply:
5 feet * 1 second = 2 seconds * x feet
Simplifying, we get:
5 feet = 2x feet
Dividing both sides by 2, we get:
x = 2.5 feet
In conclusion, Ava walks 2.5 feet in one second.
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Complete question:
. Ava is walking at a constant speed where for every 5 feet it takes 2 seconds. So, the ratio of feet to seconds is 5 to 2.
(c) How many feet does Ava walk in one second?
3 Cassie wants to determine the length of the shadow that a 60-foot tall telephone pole casts without measuring it. If Cassie's mailbox, which is 42 inches in height, casts a shadow that is 31.5 inches in length, how long is the shadow that the telephone pole casts? A. 43 feet B. 45 feet C. 52 feet D. 55 feet
The answer is (B) 45 feet
Step-by-step explanation:
We can use proportions to solve this problem.
Let x be the length of the shadow cast by the telephone pole. Then we have:
(42 / 31.5) = (60 / x)
We can cross-multiply to get:
42x = 31.5 * 60
Simplifying this equation, we get:
x = (31.5 * 60) / 42
x = 45 feet
Therefore, the length of the shadow that the telephone pole casts is 45 feet.
16 cm
14 cm
28 cm
What is the area of the trapazoid
What will be the result of substituting 2 for x in both expressions below?
Substituting for x in an expression means replacing the variable x with a specific value or expression. This is often done to evaluate the expression for that particular value or to simplify the expression.
What is the substituting for x in expressions?Substituting 2 for x in the first expression, we get:
[tex]1/2(2) + 4(2) + 6 - 1/2(2) - 2 = 1 + 8 + 6 - 1 - 2 = 12[/tex]
Substituting 2 for x in the second expression, we get:
[tex]2(2) + 2 - 1 = 5[/tex]
One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
Therefore, the first expression evaluated with x = 2 is 12, and the second expression evaluated with x = 2 is 5. Since they do not have the same value, the correct option is:
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The given question is incomplete. The complete question is given below:
What will be the result of substituting 2 for x in both expressions below? One-half x + 4 x + 6 minus one-half x minus 2 Both expressions equal 5 when substituting 2 for x because the expressions are equivalent. Both expressions equal 6 when substituting 2 for x because the expressions are equivalent. One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent. One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
Find the sum. -
3/4 + 1/2 =
Answer:
Is the problem -3/4 + 1/2 or 3/4 + 1/2?
I'll just do both then.
-3/4 + 1/2 = -1/4
3/4 + 1/2 = 5/4 or 1 1/4
Step-by-step explanation:
You're welcome.
Answer:
[tex] \frac{3}{4 } + \frac{1}{2} [/tex]
take lcm of denominators i.e. 4and 2
so, the lcm of 4 and 2 is 4.
[tex] \frac{3}{4} + \frac{2}{4} [/tex]
[tex] \frac{3 + 2}{4} [/tex]
[tex] \frac{5}{4} [/tex]
Step-by-step explanation:
hope this will be helpful:)
Find the value of each variable.
The values of the variables in the semicircle shown are:
x = 63 degrees; y = 90 degrees.
What is the Angle Inscribed in a Semicircle Theorem?A semi-circle is exactly half of a full circle and has a measurement of 180 degrees; the two endpoints of the diameter form the endpoints of the semi-circle. If an angle is enclosed inside a semi-circle, the angle formed measures 90 degrees.
Therefore, it means the value of the variable, y = 90 degrees.
Thus, using the triangle sum theorem, we have:
x = 180 - 90 - 27
x = 63 degrees.
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At Christmas, Ben, Sam and Tom received cards in the ration 2 : 3 : 12.
If Tom received 60 cards.
(a) What fraction of the cards did Ben receive?
(b) What fraction did Ben and Sam receive between them?
(c) How many cards did Sam receive?
(d) How many cards did they receive altogether?
The accompanying table shows the results from a test for a certain disease. Find the probability of selecting a subject with a negative test result, given that the subject has the disease. What would be an unfavorable consequence of this error?
The individual actually had the disease
Yes
No
Positive
320
9
Negative
12
1160
Question content area bottom
Part 1
The probability is enter your response here.
(Round to three decimal places as needed.)
The probability to three decimal places is 0.036 and the unfavorable consequence of this result will be that the patients who tested negative will not be treated and as such will spread the disease.
How to solve the probabilityTo find the probability of an event, we often use divide the total number of possible results by the total results. In this case, we are told to find the total number of persons who tested negative for the disease by the total number of positive cases. 320 + 12 persons tested positive for the disease. The sum is 332.
The total number of negative cases recorded from this sum is 12. Thus, the probability will be 12/332 = 0.036. An unfavorable consequence of this error will be that the subjects who tested negative will not be treated and can thus spread the disease.
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What is the area of a rectangle with a length of 3 1/3 feet and a width of 1 2/3
0 2 7/9 ft
0 3 2/9 ft²
0 5 5/9 ft²
0 8 1/3 ft²
Answer:
[tex]5 \frac{5}{9} \: {ft}^{2} [/tex]
Step-by-step explanation:
[tex]a \: (length) = 3 \frac{1}{3} \: ft[/tex]
[tex]b \: (width) = 1 \frac{2}{3} \: ft[/tex]
[tex]a \: (rectangle) = a \times b[/tex]
[tex]a = 3 \frac{1}{3} \times 1 \frac{2}{3} = \frac{10}{3} \times \frac{5}{3} = \frac{50}{9} = 5 \frac{5}{9} {ft}^{2} [/tex]
Please help need to get a good score
This graph shows the solutions to the inequalities y > 3x + 14 and y < 3x + 2.
Does the system of inequalities have solutions? If so, which region contains
the solutions?
A
C
This graph in the figure shows the no solutions to the inequalities
Define inequalitiesinequalities can be defined as if two real numbers or the algebraic expressions can be related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called inequalities.
For example, x>3 (x should be greater than 3)
given:system of inequalities y>3x+14 and y<3x+2
the system of inequalities have solutions only when the shaded part satisfies the given inequalities
We are given with the graph of inequalities . The given inequalities have 'and' in between.
so we look at the graph where both inequalities intersects
From the graph we can see that there is no intersection part of both shaded portions
So , we conclude that there is no solution.
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The complete question is:
This graph shows the solutions to the inequalities. does the system of inequalities y>3x+14 and y<3x+2. Does the system of inequalities have solutions? If so, which region contains the solutions?
h (x) = (3x - 4) (x + 2)^2 (x - 5)
• (2, 0)
• (-3/4, 0)
• (4/3, 0)
• (5, 0)
The zeros of the function H(x) = (3x - 4)(x + 2)^2(x - 5) are (4/3, 0), (-2, 0), and (5, 0).
Calculating the zeros of the polynomial functionTo find the zeros of the function H(x), we need to find the values of x that make the function equal to zero.
H(x) = (3x - 4)(x + 2)^2(x - 5)
Setting H(x) equal to zero, we have:
(3x - 4)(x + 2)^2(x - 5) = 0
Using the zero product property, we can see that H(x) will be equal to zero when any of the factors are equal to zero.
So, the zeros of the function H(x) are:
3x - 4 = 0, which gives x = 4/3
x + 2 = 0, which gives x = -2
x - 5 = 0, which gives x = 5
Therefore, the zeros of the function H(x) are (4/3, 0), (-2, 0), and (5, 0).
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Bob drove 845 miles in 13 hours.
At the same rate, how many miles would he drive in 9 hours ?
Answer:
585 miles
Step-by-step explanation:
845 miles ÷ 13 hours = 65 mph
645 mph * 9 hours = 585 miles
Please help quick!! Given m || n, find the value of x.
In the given angles the required value of x is 17° respectively.
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
Angles created by two rays are in the plane where the rays are located.
The meeting of two planes also creates angles. We refer to these as dihedral angles.
Based on the measurement, there are many kinds of angles in geometry.
The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.
So, we know that:
2x+5 + 8x+5 = Straight angle
2x+5 + 8x+5 = 180
Now, solve for x as follows:
2x+5 + 8x+5 = 180
10x+10 = 180
10x = 170
x = 17
Therefore, in the given angles the required value of x is 17° respectively.
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solve this please! i've been trying for a while but i cant get it
The three-dimensional object in the figure has a surface area of 52 square yards.
What does surface area dimension mean?Surface area is the two-dimensional measure or area of a three-dimensional space's boundary, just as perimeter is the one-dimensional measure or length of a two-dimensional area's boundary.
The object's rectangular base has a length of 4 yards and a width of 3 yards, as seen in the figure. As a result, the base's area is:
Area of base = length x width = 4 x 3 = 12 square yards
Area of a triangular face = (1/2) x base x height = (1/2) x 4 x 5 = 10 square yards
Since the object has four triangular faces, the total area of the four triangular faces is:
Total area of triangular faces = 4 x 10 = 40 square yards
We add the base's area to the sum of the four triangle sides to determine the object's surface area:
Surface area = Area of base + Total area of triangular faces
Surface area = 12 + 40 = 52 square yards
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Bug S Bug S and Bug F is fast. Both bugs start at 0 on a number line and move in the positive direction. The bugs leave 0 at the same time and move at constant speeds. Four seconds later, F is at 12 and S is at 8. When will F and S be 100 units apart?
Answer:
Let's call the speed of Bug F v_F and the speed of Bug S v_S. Since both bugs started at 0, we can express their positions at any time t as:
Position of Bug F = 12 + v_F * t
Position of Bug S = 8 + v_S * t
To find out when F and S will be 100 units apart, we need to find the time t at which their positions differ by 100 units. In other words, we need to solve the following equation:
|12 + v_F * t - (8 + v_S * t)| = 100
We can simplify this equation by expanding the absolute value and rearranging the terms:
|4 + (v_F - v_S) * t| = 100
Now we can split this equation into two cases:
Case 1: 4 + (v_F - v_S) * t = 100
In this case, we have:
v_F - v_S > 0 (since Bug F is faster)
t = (100 - 4) / (v_F - v_S)
Case 2: 4 + (v_F - v_S) * t = -100
In this case, we have:
v_F - v_S < 0 (since Bug S is faster)
t = (-100 - 4) / (v_F - v_S)
Since we're only interested in positive values of t, we can discard the second case. Therefore, the time at which F and S will be 100 units apart is:
t = (100 - 4) / (v_F - v_S)
t = 96 / (v_F - v_S)
We don't know the values of v_F and v_S, but we can use the fact that Bug F is at 12 and Bug S is at 8, four seconds after they started. This gives us two equations:
12 = 4v_F + 0v_S
8 = 4v_S + 0v_F
Solving these equations for v_F and v_S, we get:
v_F = 3
v_S = 2
Substituting these values into the equation for t, we get:
t = 96 / (3 - 2)
t = 96
Therefore, F and S will be 100 units apart 96 seconds after they start.
Which function represents the exponential graph given that (0, 1) and (4, 81/16 ) are points that lie on the graph?
f(x)=(2/3)^x
f(x)=(4)^x
f(x)=(1)^x
f(x)=(3/2)^x
The f(x) = (3/2)ˣ is the correct function that represents the given exponential graph.
What is exponential graph?An exponential graph is a type of graph that represents an exponential function. An exponential function is a mathematical function in which a constant base is raised to a variable exponent. The general form of an exponential function is: y = a * bˣ.
What is graph?A graph is a visual representation of data or information that allows us to quickly and easily understand patterns, trends, and relationships. Graphs are used to present information in a way that is easy to interpret and understand.
In the given question,
The function that represents the exponential graph given that (0, 1) and (4, 81/16 ) are points that lie on the graph is:
f(x) = (3/2)ˣ
To verify that this is the correct function, we can substitute x=0 and x=4 into the function to see if the corresponding y-values match the given points on the graph.
When x=0, f(0) = (3/2)⁰ = 1, which matches the point (0, 1).
When x=4, f(4) = (3/2)⁴ = 81/16, which matches the point (4, 81/16).
Therefore, f(x) = (3/2)ˣ is the correct function that represents the given exponential graph.
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a bakery has 17 pounds of flour they want to put into 6 containers. They put the same amount of flour in each container. If they want to use up all the flour, how much flour should they put in each container?
Answer:
2.83333 pounds of flour in each container
A container contains 145.2 ounces of lemonade. If the lemonade is poured equally into 15 cups, how many ounces will be poured into each cup?
A. 8.78
B. 9.12
C. 9.64
D. 9.68
Show answer.
Answer: D. 9.68
Step-by-step explanation:
145.2 oz/ 15 cups = 9.68 oz per cup
Question 29 Which expression represents the distance between points J and K on the number line?
On the number line, there are five spaces between the points J and K.
What does a number line exactly mean?A number line is a horizontal line with consistently spaced numerical increments. How you respond to the number on the line will depend on the numbers on the line. Depending on the question that goes with it, a number can be used in a variety of ways, such as when graphing a point.
The absolute value of the difference in the coordinates between points J and K on the number line can be used to calculate the distance between them.
Points J and K in this instance have coordinates of -4 and 1, respectively. As a result, the following formula may be used to indicate the distance between locations J and K:
|1 - (-4)|
If we condense this expression, we get:
|1 + 4|
= |5|
= 5
Hence, the distance on the number line between points J and K is 5.
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PLEASE HELP Area of Cross Sections
Answer:
396 in²
Step-by-step explanation:
To answer this question we need to use pythagorean theorem (a² + b² = c²)
In our case, a would be 14 and b would be 17
14² + 17² = ?²196 + 289 = 485[tex]\sqrt{485}[/tex] = 22.02Now we have to multiply this by 18
22.02 x 18 = 396.36Which rounded would be 396
Hope this helps, have a lovely day! :)
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 28, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B
Which animal shelter has the dog that weighs the least?
shelter A
Step-by-step explanation:
The minimum weight for shelter A is not provided in the given information, but we can compare the minimum weight of shelter B with shelter A's box plot.
As per the given information, the whisker of shelter A ranges from 8 to 30, which means the minimum weight in shelter A is 8 pounds. On the other hand, the whisker of shelter B ranges from 10 to 28, which means the minimum weight in shelter B is 10 pounds. Therefore, shelter A has the dog that weighs the least.
Answer:
Your answer is correct, it's shelter A.
Step-by-step explanation:
PLS COMPLETE ALL OF IT!! 50 POINTS!
A. The length of the cord needed to reach corner C is 17.6 m
B. The distance between the electrical outlet and corner N is 14.3 m
A. How do i determine the length of cord needed?The length of the cord needed can be obtained as follow:
Length BC = Opposite = 8 mAngle (θ) = 27°Length of cord =?Sine θ = opposite / hypotenuse
Sine 27 = 8 / Length of cord
Cross multiply
Length of cord × sine 27 = 8
Divide both sides by sine 27
Length of cord = 8 / sine 27
Length of cord = 17.6 m
B. How do i determine the distance between electrical outlet and corner NFirst, we shall determine the length OB. Details below:
Angle (θ) = 27°Length BC = Opposite = 8 mLength OB =?Tan θ = Opposite / Adjacent
Tan 27 = 8 / Length OB
Cross multiply
Length OB × tan 27 = 8
Divide both sides by tan 27
Length OB = 8 / tan 27
Length OB = 15.7 m
Finally, we shall determine the distance between the electrical outlet and corner N. Details below:
Length OB = 15.7 mLength BN = 30 mLength ON = Distance =?Length BN = Length OB + Length ON
30 = 15.7 + Distance
Collect like terms
Distance = 30 - 15.7
Distance = 14.3 m
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Which of the following sets of numbers could represent the three sides of a
triangle?
{7, 15, 20}
{7, 16, 23}
O {11, 22, 35}
O {5, 17, 22}
The following sets of numbers could represent the three sides of a
triangle is {7, 15, 20}.
How to determine the set that represent the three sides of a triangleThe set of numbers {7, 15, 20} could represent the three sides of a triangle, but the other sets of numbers do not satisfy the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side. Checking the sets of numbers:
For {7, 15, 20}, 7 + 15 > 20, 7 + 20 > 15, and 15 + 20 > 7, so they satisfy the triangle inequality theorem and could represent the sides of a triangle.
For {7, 16, 23}, 7 + 16 < 23, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.
For {11, 22, 35}, 11 + 22 < 35, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.
For {5, 17, 22}, 5 + 17 < 22, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.
Therefore, the answer is {7, 15, 20}.
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please help answer this!!
Given m∥n, find the value of x.
(6x+9)° (4x-19)°
Answer:
Since alternative angles are equal then
Janelys has a points card for a movie theater.
She receives 20 rewards points just for signing up.
• She earns 12.5 points for each visit to the movie theater.
She needs at least 165 points for a free movie ticket.
Write and solve an inequality which can be used to determine x, the number of visits
Janelys can make to earn her first free movie ticket.
Answer: 12 times
Step-by-step explanation:
165-20=145
12.5x11=137.5
12.5x12=150
Answer: 12.5x+20≥165
x≥11.6
Step-by-step explanation:
How to get the unadjusted cost of sales in cost and management accounting
Answer:
Step-by-step explanation:
To calculate unadjusted cost of goods sold, sum the beginning inventory value and the cost of goods manufactured, then subtract the ending inventory value.
2. Zara stores in the United States stocks a particular type of designer denim jeans in the United States. It stores 500 pairs of jeans each month from its two suppliers. The Hong Kong supplier charges Zara $11 per pair of jeans, and the Colombian supplier charges $16 per pair (and then Zara marks them up almost 1,000%). Although the jeans from Hong Kong are less expensive, they also have more defects than those from Colombia. Based on past data, Zara estimates that 7% of the Hong Kong jeans will be defective compared to only 2% from Colombia and Zara does not want to import any more than 5% defective items. However, Zara does not want to rely on a single supplier, so it wants to order at least 20% from each supplier every month. a. Formulate a linear programming model for this problem. b. Solve the linear programming model graphically. Use either iso-line or corner point method. How many of each should Zara buy? c. How much will Zara pay for them? d. If the Hong Kong supplier were able to reduce its percentage of defective pairs of jeans from 7% to %5, what would be the effect on the solution. Solve c in a separate sheet. First copy the sheet you solved a, b and c. Then change the necessary line and re-solve.
Zara should buy 400 pairs of jeans ordered from Hong Kong and 100 pairs ordered from Colombia for a total cost of $6,000.
See below for other solutions
Formulation of the linear programming model:Let x be the number of pairs of jeans ordered from Hong Kong and y be the number of pairs ordered from Colombia.
Objective function:
Maximize profit, C(x, y) = 11x + 16y
Subject to the following constraints:
The total number of jeans ordered cannot exceed 500: x + y ≤ 500Zara wants to order at least 20% from each supplier: x ≥ 0.2(x+y) and y ≥ 0.2(x+y)Zara does not want to import more than 5% defective items: 0.07x + 0.02y ≤ 0.05(x+y)Non-negativity constraint: x, y > 0Graphical solution using the corner point method:See attachment for the graph, where we have the following corner points
(x, y) = (100, 400), (300, 200), (400, 100)
By substitution, we have
C(100, 400) = 11(100) + 16(400) = 7500
C(300, 200) = 11(300) + 16(200) = 6500
C(400, 100) = 11(400) + 16(100) = 6000
The minimum cost above is $6000
So, Zara should buy 400 pairs of jeans ordered from Hong Kong and 100 pairs ordered from Colombia.
The amount paid for themThe amount paid for them is $6,000
Reducing the percentage of defective pairsIf the Hong Kong supplier were able to reduce its percentage of defective pairs of jeans from 7% to 5%, we would need to update the constraint accordingly:
0.05x + 0.02y ≤ 0.05(x+y)
The new optimal solution would be to order 425 pairs of jeans from the Hong Kong supplier and 75 pairs of jeans from the Colombian supplier, for a total cost of $5875
i.e. C(425, 75) = 11(425) + 16(75) = 5875
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