The system of equations is solved and the number of toy cars of each machine of Company A should produce to have equal number of toy cars is t = 375 toys
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of toy cars produced by Company A be A
Let the number of toy cars produced by Company B be B
The number of machines for A = 18 machines
The number of machines for B = 15 machines
The number of toy cars produced by A = t cars
The number of toy cars produced by B = 75 + t
And ,
The total number of toy cars of A = 18 x t
The total number of toy cars of B = 15 ( 75 + t )
So , in order for both the company's to have the same toys is
18t = 15 ( 75 + t )
On simplifying the equation , we get
18t = 1125 + 15t
Subtracting 15t on both sides of the equation , we get
3t = 1125
Divide by 3 on both sides of the equation , we get
t = 375 toys
Hence , the equations is A = 18t and B = 15 ( 75 + t )
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suppose you own a swimming pool with dimensions 4.93 m x 9.69 m x 1.75 m. what is the volume of your pool in gallons?
22084.78 gallons is the volume of your pool.
Any rectangular solid's volume, V, is equal to the sum of its dimensions, height, width, and depth. In terms of the area of the base, we might alternatively express the formula for a rectangular solid's volume. The base's surface area, B, is equal to its length x width.
Dimensions of the pool = 4.93 m x 9.69 m x 1.75 m
Volume = 4.93 x 9.69 x 1.75
= 83.6 cubic meter
1 cubic meter = 264.172 gallons
83.6 cubic meter = 83.6 x 264.172
= 22084.78 gallons
Hence, 22084.78 gallons is the volume of your pool.
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Tell whether the lines are "parallel", "perpendicular", or "neither. " 3x – 2y = –15 2x + 3y = –15
Equation of the two lines 3x – 2y = –15 , 2x + 3y = –15 are perpendicular to each other.
Equation of the two different lines are :
3x – 2y = –15
2x + 3y = –15
Convert both the equation into slope intercept form :
y = mx + c
Where 'm' represents the slope of the line and 'c' represents the y- intercept.
Equation of first line
3x – 2y = –15
⇒ 2y = 3x + 15
⇒ y = 3/2x + 15/2
Here slope 'm₁ ' is equal to 3/2.
2x + 3y = –15
⇒ 3y = -2x -15
⇒ y = -2/3x - 5
here slope 'm₂ ' is equal to -2/3
For parallel lines slope should be equal.
here m₁ ≠ m₂
Not parallel lines.
For perpendicular lines :
m₁ × m₂ = -1
Here , (3/2 ) × ( -2/3 ) = -1
Lines are perpendicular to each other.
Therefore, the product of the slope is equal to -1 lines are perpendicular to each other.
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Find the equation of line that passes through the points (2,0) and (5,12). Write the equation in slope-intercept form.
Answer:
y=4x+2
Step-by-step explanation:
slope (12-0)/(5-2)=4
y=4x+b
plug in (2,0)
b=2
y=4x+2
15. An airplane is traveling at a fixed altitude with a negligible wind factor. The airplane is headed N 30° W at a speed of 500 miles per hour. As the airplane reaches a certain point, It encounters a wind with a velocity of 70 mph in the direction of N 45' E.
What are the resultant speed and direction of the airplane?
The resultant speed is 52.48 and the direction of the airplane is west to north.
The resultant velocity of an object is defined as the sum of its individual vector velocities, and the sum of the vector forces on an object is equal to the scalar product of the object's mass and its acceleration vector.
Given
The plane is initially flying with a velocity of magnitude v=500mph.
at an angle of 30° North toward the west
The velocity of the plane airplane can be written as:
[tex]v_a=-500(sin 30i+cos30j)[/tex]
Now the wind is encountered with the speed of v=70mph at an angle of N 45°E
[tex]v_w=70(cos45i+sin45j)\\[/tex]
resultant velocity:
[tex]v_R=v_a=v_w\\\\[/tex]
[tex]v_R=-500(sin 30i+cos30j)+70(cos45i+sin45j)\\\\v_R=i(-250+49.49)+j(433.01+49.49)\\\\v_R=i(-200.51)+j(482.5)\\\\tan\alpha =\frac{482.5}{-200.51} \\\\tan\alpha =2.406\\\\\alpha =tan^-^1(2.406)[/tex]
α=52.48° west of North.
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27×9^3x can be written as 3^k
[tex]27\cdot 9^{3x}\implies 3^3\cdot (3^2)^{3x}\implies 3^3\cdot 3^{6x}\implies {\Large \begin{array}{llll} 3^{3+6x} \end{array}}[/tex]
Which triangles are similar to ΔDEF?
Answer:
A) ΔDFG
and
C) ΔFEG
Answer: FEG
Step-by-step explanation:
It can't be the others, so process of elimination.
LMNO is a parallelogram. If NM = x + 12 and OL = 2x + 8, find the value of x and then find NM and OL.
The value of the sides, NM and OL are 16 and 8 respectively
How to determine the value
To determine the value of x, we have the note the properties of a parallelogram.
The properties of a parallelogram includes;
Opposite sides of a parallelogram are parallelOpposite sides of a parallelogram are congruentOpposite angles of a parallelogram are congruentInterior angles are supplementaryEach diagonal of a parallelogram divides it into two congruent trianglesThe diagonals of a parallelogram bisect each other at right angleThen, we have;
NM = OL
substitute the values
x + 12 = 2x + 8
Now, collect like terms
x = 4
NM = 4 + 12 = 16
OL = 16
Hence, the value are 4 and 16
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What is the perimeter of the given composite figure? I believe it’s 140 but would like a check from someone smarter than I lol.
The perimeter of the given composite figure is given as follows:
105 ft.
How to obtain the perimeter of a polygon?The perimeter of a polygon is obtained as the sum of all the outer side lengths of the polygon.
The side lengths for the polygon in this problem are given as follows:
45 ft.40 ft.15 ft.5 ft.Hence the perimeter for the polygon is calculated as follows:
45 + 40 + 15 + 5 = 105 ft.
(sum of all the outer side lengths).
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Elle wants to spend at most Php80 on dairy products. Each liter of goat milk costs
Php130 and each liter of cow's milk costs Php65. Find the possible number of each dairy product
Elle can buy maximum 0.6 liters of goat milk and 1.2 liters of cow's milk.
What System of linear inequalities?
A system of linear inequalities is similar to a system of linear equations, except that it is made up of inequalities rather than equations. To represent scenarios with various restrictions, systems of linear inequalities are utilized.
Let x be the number of liters of goat milk and y be the number of liters of cow's milk that Elle wants to buy. We know that:
x + y ≤ 80 (because Elle wants to spend at most Php80)
130x + 65y ≤ 80 (because each liter of goat milk costs Php130 and each liter of cow's milk costs Php65)
This is a system of linear inequalities, and the solution set is the set of all possible combinations of x and y that satisfy both inequalities.
The inequality 130x + 65y ≤ 80 represents a line in the plane, and the inequality x + y ≤ 80 represents a region that is "bounded" by this line.
The solution set for the inequalities are x <= 0.6 and y <= 1.2.
So, Elle can buy maximum 0.6 liters of goat milk and 1.2 liters of cow's milk.
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a certain museum has five visitors in two minutes on average. let a poisson random variable denote the number of visitors per minute to this museum. find the probability that this museum gets at least three visitors in a minute (round off to second decimal place).
The exact probability that this museum gets at least 3 visitors in a minute is approximately 0.224
A Poisson distribution is a probability distribution that models the number of times an event occurs within a given time or space, if these events are rare and independently of the time since the last event. The Poisson distribution is characterized by the mean number of occurrences λ in a given interval.
In this case, the mean number of visitors per minute is λ = 5 visitors / 2 minutes = 2.5 visitors per minute.
We can use the Poisson probability mass function to find the probability that this museum gets at least 3 visitors in a minute.
To find the probability that this museum gets at least 3 visitors in a minute by using:
1 - P(X < 3)
Where X is the number of visitors in a minute and 3 is the lower limit of the number of visitors we want to include in the sample.
Thus, P(X>=3) = 1 - P(X < 3) = 1 - 0.776 = 0.224
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Drag each set of column entries to the correct location in the augmented matrix. Not all sets of entries will be used.
Mac traveled to three cities on one highway. The total distance one way was 320 miles. The distance from his original location to the first city was 20 miles more than half
the distance from the first city to the second city. The distance from the second city to the third city was 75 miles less than the distance from the first city to the second
city. Let xrepresent the distance from the original location to the first city, y represent the distance from the first city to the second city, and z represent the distance from
the second city to the third city. Place the correct sets of column entries in the augmented matrix that models Mac's situation,
Vital phrases there are more than and lesser than, so if he went, say, 75 miles from his residence to the first city the first one they would claim that he actually traveled 10 miles less between the first and second cities.
The total distance is 320 miles because, according to the very last sentence, the initial distance between the first and second cities was approximately 75 miles, and if the distance between the second and third cities was the same, the equation would be (160*2)+75. In order to solve this equation correctly, you must use P.E.M.D.A.S., which stands for parenthesis, exponents, multiplying, dividing, and adding subtracting.
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I need help with this!
Use your formula 1/2(a+b)h, to determine the height of a trapezoid with an area of 24 cubic centimeters and base lengths of 9 cm and 7 cm.
Answer:
H (Height) = 3
Step-by-step explanation:
We have the formula A = 1/2(a+b)h
Let's identify all variables
A = 24
a = 9
b = 7
h = ?
Lets plug all that in:
24 = 1/2(9+7)h
9+7 = 16
24 = 1/2(16)h
Half of 16 is 8 so to simplify the rest...
24 = 8h
To get h alone we will divide both sides of the equation by 8
24/8 = h
24/8 = 3
Making H = 3
Mike drew a four sided figure with four right angles. It is 4 cm long and 3 cm wide. What type of figure did Mike draw?
The figure drawn by Mike is rectangle according to the angles and dimensions.
As the statement mentioned, the sides are at 90° degree or perpendicular to each other. It is seen in only two figures, which are square and rectangle. The square has all the sides equal whole rectangle has opposite sides equal.
As the length and width is different in the figure, the opposite sides signifying length and width will be equal. Therefore, opposite sides will be equal in the figure and hence it will be rectangle.
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May I have help on this please?
Answer:
yeah you can
Step-by-step explanation:
what do you need help with lol
4.
What is the constant of proportionality? What does it represent?
Answer:
In Explanation
Step-by-step explanation:
The constant of proportionality is a value that relates two variables that have a proportionate relationship. It is often represented by the letter "k".
For example, if two variables x and y are directly proportional, their relationship can be represented by an equation of the form y = kx, where k is the constant of proportionality. In this equation, the value of k represents the ratio of y to x and it is constant, meaning that it does not change as the values of x or y change.
In physics, the constant of proportionality also appears in many mathematical models of natural phenomena, such as Hooke's law (F = km) which relates the force applied on an object (F) to its displacement (x) with a spring constant (k), and Ohm's law (V = IR) which relates the voltage (V) across a resistor to the current (I) flowing through it with a resistance constant (R).
The constant of proportionality can have different units of measure depending on the context and is used to make quantitative predictions about the relationship between the variables. In some cases, it can be used to determine the behaviour of a system or physical process.
(Please give brainlist)
Alan Louden deposits $615.00 in a savings account. The account pays an annual interest rate of 5%. He makes no other deposits and withdrawals. After 3 months, the interest is calculated. How much simple interest did his money earn?
Answer:
The interest earned on the account would be $30.75. (6150.053/12=30.75)
Step-by-step explanation:
using only quarters, nickels, and pennies, what is the minimum number of coins needed to make $0.88?
The local Farmers Market sells peppers at five for $2. 25.
Complete the rate table.
Number of Peppers
0
1
2
3
4
5
10
15
20
Cost ($)
0
0. 45
0. 90
1. 35
1. 8
$2. 25
4. 5
6. 75
9 What is the constant rate of change (CROC)? How do you know?
Is this a proportional relationship? How do you know?
The proportionality is 0.45, then the equation is C = 0.45 n. The number of peppers you buy for $20 will be 44.44. Then the table is completed below.
What are proportion and ratio?
A collection of consecutively ordered numbers a and b expressed as a/b, where b is never equal to zero, is referred to as a ratio. A statement is considered proportionate when there is equality between two items.
Let n be the number of peppers and C be the price. The proportionality is then provided as,
C ∝ kn
With n = 5 and a cost of C = 2.25, we obtain
2.25 = k (5) (5)
k = 2.25 / 5
k = 0.45
The equation is then presented as,
C = 0.45 n
You will be told how many peppers you get for your $20 purchase as,
20 = 0.45 n
n = 44.44
Then the table is completed below.
Number of peppers Cost
1 $0.45
2 $0.90
3 $1.35
4 $1.80
5 $2.25
10 $4.50
15 $6.75
20 $9
100 $45
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-2(x + 5)² = 20
solve by square root!
Louise sold 168 soft pretzels. If she sold them in groups of 12 soft pretzels, how many groups did she sell?
3) Make the following number 100 times
greater.
6.4
Answer: 640
Step-by-step explanation:
6.4 * 100 = 640
g the speed limit on certain interstate highways is 75 miles per hour. (a) what is this in feet per second? ft/s (b) how many kilometers per hour is this? km/h
(a) The speed in feet per second is 110 feet per second.
(b) The speed in kilometers per hour is 120.75 kilometers per hour
The speed limit on certain interstate highways, s = 75 miles per hour
a) We have to find the speed in feet per second.
1 mile = 5280 feet
75 miles = 75 x 5280
75 miles = 396,000 feet
s = 396,000 feet/hour
s = 39600/3600 feet/second
s = 110 feet per second
b) We have to find the speed in kilometers per hour.
1 mile = 1.61 km
75 miles = 75 x 1.61
75 miles = 120.75 km
s = 120.75 kilometers per hour
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15 foot ladder leaning agaisnt a building touches the wall 12 feet above the ground how far from the building is the bottom of the ladder
The bottom of the ladder is 9 feet from the wall.
Using the Pythagorean Theorem, we can calculate the distance from the wall. The Pythagorean Theorem states that for a right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. In this case, the hypotenuse is 15 feet and the side adjacent to the wall is 12 feet.
The formula for the Pythagorean Theorem is a^2 + b^2 = c^2.
We can solve for the distance from the wall (a). a^2 = c^2 - b^2, so a^2 = 15^2 - 12^2, which equals a^2 = 225 - 144, so a^2 = 81. Taking the square root of both sides, a = 9 feet.
Therefore, the bottom of the ladder is 9 feet from the wall.
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Determine whether the pairs of triangles are congruent.
~Circle yes, no, or not enough information. Explain your choice.
Answer:
No
Step-by-step explanation:
I got the postulates mixed up. These triangles have the same angle measurements but the lengths of the sides are different so the answer is no. These triangles do not follow the AAS, SSS, SAS, or ASA postulates.
Answer:
Step-by-step explanation:
Yes, it is congruent because SSA.
Ken’s seventh grade class plans to collect empty aluminum pop cans as a fund raiser to buy two new books for the school library. The books will cost a total of $50.
a. If $0. 25 per pound is the current price for aluminum at the recycling center, how many pounds of empty cans will the class have to collect? (3 points) Work: Answer __________________
b. Six empty cans weigh about 3. 5 ounces. How many empty cans will the class have to collect to meet their quota of pounds? Round your answer to the nearest whole number. (3 points) Work: Answer __________________
a.) The number of pounds of empty cans needed by the class is 200 pounds.
b.) The number of empty cans needed by the class to collect are 5486 cans.
The books will cost a total amount of $ 50.
If $ 0.25 per pound is the current price for aluminium at the recycling centre, the number of pounds the class will have to collect is found by dividing the total amount needed by cost per pound is,
⇒ 50/0.25 = 200
b.) Six empty cans weigh 3.5 ounces.
1 pound = 16 ounces
200 pounds = 200 × 16 = 3200 number of ounces
3200/3.5 = 914.29
914.29 × 6 = 5485.7 cans ≈ 5486 cans
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The outside tempature dropped 20°F from the time arianna ate breakfast until the time she ate dinner. When she ate dinner the tempature was 35°F. Write and solve an equation to find the outside tempature t when arianna ate breakfast
The outside temperature t when Arianna ate breakfast was 55°F.
An equation is a mathematical statement showing that two expressions are equal. It is written with an equal sign (=) between two expressions, with one expression on the left side of the equal sign, and the other expression on the right side.
According to the given statements-
Let the outside temperature at the time of breakfast be t°F.
The temperature dropped by 20°F by the time of dinner.
So the temperature at the time of breakfast = t - 20
Also, when she ate dinner the temperature was 35°F
So the equation for outside temperature t when Arianna ate breakfast will be -
t - 20 = 35
Simplifying we get,
t = 35 + 20
t = 55°F
Hence, the outside temperature t when Arianna ate breakfast was 55°F.
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4 If you have 5 pounds of trail mix, how many bags can you make so that each bag
contains 1 pounds?
Answer:
5 bags
Step-by-step explanation:
if there are 5 pounds of trail mix and each bag needs to contain 1 pound, that can be equally divided into 5 bags where each bag contains 1 pound each
for a random sample of 100 people, what is the probability that the sample mean will be within 5 points of the population mean
The probability that the sample mean will be within 5 points of the population mean is 0.95 or 95%
Central Limit TheoremThe Central Limit Theorem (CLT), a foundational idea in statistics, holds that, regardless of the underlying population distribution, the distribution of the sample means will be about normal given a big enough sample size. The CLT is crucial because it enables us to draw conclusions about a population based on a sample, even when the population is not normal.
According to the CLT, as the sample size grows, sample means will approach population means and their standard deviations will fall. The standard error, also known as the standard deviation of the sample means, is calculated by dividing the standard deviation of the population by the square root of the sample size.
According to the Question
The sample mean for a random sample of 100 individuals is most likely to be within 5 points of the population mean. The distribution and standard deviation of the population, however, would determine the precise likelihood. The standard error may be used to determine a confidence interval for the population mean if the population standard deviation is known. A 95% confidence interval is frequently used, which is equivalent to 1.96 standard deviations from the mean. In this instance, especially with a large sample size, there is a good likelihood that the sample mean will be within 5 points of the population mean.
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The resistances of then randomly selected 100-ohm resistors have been recorded: 79. 9, 85. 9, 87. 0, 96. 7, 107. 4, 100. 8, 115. 4, 117. 9, 98, and 102. 6 ohms. The individual resistances are known to follow a normal distribution with a mean of 100 ohms and a standard deviation of 10 ohms. (a) Calculate the sample mean resistance associated with the ten resistors. (b) For a sample size of ten, find the probability of obtaining a sample mean as large as or larger than the one calculated in part (a). (c) For a sample size of ten, find the probability of obtaining a sample mean with a resistance between 95 and 105 ohms
If the individual resistances are known to follow a normal distribution with a mean of 100 ohms and a standard deviation of 10 ohms , then the sample mean resistance associated with the ten resistors is 99.16 ohms .
The resistors of randomly selected 100 ohms resistors are recorded as :
⇒ 79.9, 85.9, 87.0, 96.7, 107.4, 100.8, 115.4, 117.9, 98, and 102.6 ;
we have to fins the sample mean resistance associated with the 10 resistors .
the number of resistors(n) = 10 ;
the sum of 10 resistors is ⇒ 79.9 + 85.9 + 87.0 + 96.7 + 107.4 + 100.8 + 115.4 + 117.9 + 98 + 102.6
⇒ 991.6/10 = 99.16 .
Therefore , the sample mean resistance is 99.16 ohms .
The given question is incomplete , the complete question is
The resistances of then randomly selected 100-ohm resistors have been recorded: 79.9, 85.9, 87.0, 96.7, 107.4, 100.8, 115.4, 117.9, 98, and 102.6 ohms. The individual resistances are known to follow a normal distribution with a mean of 100 ohms and a standard deviation of 10 ohms.
Calculate the sample mean resistance associated with the ten resistors .
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The value your tikto channel is depreciating at a rate of 13% per year. In 2002, it was worth $288. Find the value of your declining channel in 2016.
Round your answer to the cent place
The value of your declining channel in 2016, given the depreciation rate, would be $ 40. 99
How to find the value of the channel ?The value of the channel can be found by the formula :
= Original value of the channel x ( 1 - rate of depreciation ) ^ number of years
Rate of depreciation = 13 %
Number of years :
= 2016 - 2002
= 14 years
The value of the channel is therefore:
= 288 x ( 1 - 13 %) ¹⁴
= $ 40. 99
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