Answers
The system of equations that can be used to find the length of each workout and the duration of each workout are as follows;
(a) 5·x + 3·y = 10
2·x + 6·y = 10
(b) Length of each Plan A workout: 1.25 hours
Length of each Plan B workout: 1.25 hours
What are linear system of equations?A linear system of equation consists of two or more linear equations that share common variables.
(a) The number of Plan A workouts Mary trained on Wednesday = 5
Number of Plan B workouts she trained on Wednesday = 3
The total time (in hours) Mary trained both workouts on Wednesday = 10
Where x represents the length (in hours) of each of the Plan A workout, and B represents the time in hours of each of the Plan B workout, we get;
5·x + 3·y = 10
Similarly, the number of Plan A workouts trained on Thursday = 2
Number of Plan B workout trained on Thursday = 6
The duration of training of all workouts on Thursday = 10 hours
Therefore, we get;
2·x + 6·y = 10
The system of equations that could be used to find the length (in hours) of each type of workout can be presented as follows;
5·x + 3·y = 102·x + 6·y = 10(b) The first equation from the system of equations indicates that we get;
5·x + 3·y = 10
3·y = 10 - 5·x
y = (10 - 5·x)/3Plugging the value of y above into the second equation from the system of equations, we get;
2·x + 6·y = 10
2·x + 6 × ((10 - 5·x)/3) = 10
2·x + 2·(10 - 5·x) = 10
2·x + 20 - 10·x = 10
20 - 8·x = 10
8·x = 20 - 10 = 10
x = 10/8 = 1.25
The length of each Plan A workout, x = 1.25 hoursy = (10 - 5·x)/3,
x = 1.25, therefore;
y = (10 - 5 × 1.25)/3 = 1.25
y = 1.25
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Related Questions
riya wants to buy a mirror which one of these shapes has only one line of symmetry
Answers
Answer:
Of the shapes you mentioned (circle, square, triangle, rectangle), the only one that has only one line of symmetry is the triangle. All other shapes have multiple lines of symmetry.
Step-by-step explanation:
Place the following set of scores in a frequency distribution table.
7, 5, 6, 4, 4, 3, 8, 9, 4, 7, 5, 5, 6
9, 4, 7, 5, 10, 6, 8, 5, 6, 3, 4, 8, 5
Are the scores clustered together, or are they spread out across the scale? a. Most of the scores are clustered within 1 or 2 points of X = 6. b. The scores are spread out fairly evenly across the scale. c. Most of the scores are clustered within 1 or 2 points of X = 8. d. The scores are clustered in two peaks near X = 3 and near X = 9.
Answers
GIven the set of scores, it is seen that a. Most of the scores are clustered within 1 or 2 points of X = 6.
What is a Frequency Table?
A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample.
Here is a frequency distribution table for the given set of scores:
Score Frequency
3 2
4 5
5 5
6 5
7 2
8 3
9 2
10 1
You can see that the scores are clustered around X = 6, with the highest frequency (5) at score 6 and the next highest frequency (5) at score 5.
The scores are not evenly spread out across the scale.
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The ratio of first- class, second- class and third-class passengers who survived the ship wreak is
101:59:89. How many passengers were saved if the total number of first-class passengers were 202?
Answers
Answer: If the ratio of first-class, second-class, and third-class passengers who survived the shipwreck is 101:59:89, then for every 101 first-class passengers who survived, there were 59 second-class and 89 third-class passengers who survived.
If the total number of first-class passengers was 202, then there were 202 * 59/101 = 118 second-class passengers who survived, and 202 * 89/101 = 180 third-class passengers who survived.
Therefore, the total number of passengers who survived the shipwreck is 202 + 118 + 180 = 500 passengers.
Step-by-step explanation:
Supervisor: "Your average time to process a sale is 14 minutes. You have to decrease
that by 25% this month in order to meet your goals."
Employee: "Thank you for the feedback. I will work on lowering my processing time to
minutes by the end of the month."
3.5
7
10.5
12
17.5
Answers
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 14}}{\left( \cfrac{25}{100} \right)14}\implies \text{\LARGE 3.5}[/tex]
Can someone please help me with this equation
Answers
The measure of the angles m∠BOX = 77.5° and m∠AOX = 77.5°.
What is the angle bisector of an angle?
The angle bisector of an angle is a line or line segment that divides the angle into two equal parts, creating two smaller angles that are congruent (i.e., have the same measure). The angle bisector starts from the vertex of the angle and extends to the opposite side or ray of the angle, dividing the angle into two smaller angles that have the same number of degrees.
By the definition of the angle bisector of an angle, the angle bisector divides the angle in two equal measures.
As m∠AOB = 155°
m∠BOX = 1/2 * m∠AOB
m∠BOX = 1/2 * 155
m∠BOX = 77.5°
also m∠AOX = 77.5°
Hence, the measure of the angles m∠BOX = 77.5° and m∠AOX = 77.5°.
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 21 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized? (Round your answer to 2 decimal places.)
Answers
A student would have to score approximately 0.84 standard deviations above the mean to be publicly recognized.
Is a high standard deviation desirable?The dispersion of asset prices from their average price, or market volatility, can be calculated with the use of standard deviation. A large standard deviation indicates a dangerous investment when prices move erratically. Low standard deviation indicates stable prices, which lowers the risk associated with investments.
The remaining 79 percent of pupils are not recognised if just the top 21% of students receive public recognition. Since a normal distribution is assumed, the conventional normal distribution and its corresponding z-scores can be used to provide the solution.
The percentage of scores that are higher than a certain z-score is shown by the area under the standard normal distribution to its right. Finding the z-score that represents the top 21% of scores is equivalent to locating the z-score that represents the bottom 79% of scores. By using a calculator or a table of the ordinary normal distribution, we can determine that the z-score for the bottom 79 percent of scores is roughly 0.84.
In order to be officially acknowledged, a student would need to get a score that is roughly 0.84 standard deviations above the mean.
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Jonathan is a single taxpayer. His taxable income before deductions was $63,110. He was able to reduce his taxable income by $10,312 when he filled out Schedule A and Schedule 1.
a. How much did he save in tax by using Schedule A?
Answers
In a linear equation. , $12,215 did he save in tax by using Schedule A .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Given,
Taxable income with out deductions = $63,110
total deductions = $10,312
the tax is given in the row 63.100 63,150 and in the column 'single' of the tax table is
tax = $12,215
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How can the statement be rewritten as a conditional statement in if-then form? the sum of the digits of a two-digit number is less than the value of the original two-digit number.
Answers
The statement "the sum of a two-digit number is less than the value of the original two-digit number" can be rewritten as conditional statement. If the sum of two digits of a two-digit number is less than the value of the original two-digit number, the number is valid.
A conditional statement, "if p, then q," with p representing the hypothesis and q representing the conclusion. We can identify the hypothesis and conclusion by rewriting the statement "the sum of the digits of a two-digit number is less than the value of the original two-digit number" as an if-then conditional statement.
The hypothesis is the condition that must be satisfied in order to valid the conclusion. In this case, the hypothesis is "the sum of the digits of a two-digit number is less than the value of the original two-digit number".
By combining these, we can rewrite the statement as follows:
If the sum of a two-digit number's digits is less than the value of the original two-digit number, the number is valid.
The hypothesis (the sum of the digits of a two-digit number is less than the value of the original two-digit number) is a sufficient condition for the conclusion, according to this conditional statement (the number is valid). In other words, if the hypothesis is correct, we can be certain that the conclusion is correct as well.
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Which of the following is an example of a continuous random variable?a. A Bernoulli trial
b. Binomial random variable
c. Normal random variable
d. Discrete uniform random variable
Answers
An example of a continuous random variable is a Normal random variable.
What is a normal random variable?
A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable can be either discrete (having definite values) or continuous (any value in a continuous range).
Here, we have
We have to determine the example of a continuous random variable.
We concluded that the example of a continuous random variable is a normal random variable.
Hence, an example of a continuous random variable is a Normal random variable.
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Circles and please answers please just need help Thank you so much
Answers
The area of the shaded region is given as follows:
As = 324(2π - 1) in².
What is the area of the shaded region?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr².
For this problem, the circle has a radius of [tex]18\sqrt{2}[/tex], as the radius is the diagonal of the square, hence the area is given as follows:
A = π x [tex](18\sqrt{2})²[/tex]
A = 648π in².
The area of a square of side length s is given by the square of the side length, hence the area of the square is given as follows:
A = 18²
A = 324 in².
Hence the area of the shaded region is given as follows:
As = 648π - 324
As = 324(2π - 1) in².
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rj and is 2 brother are given php2000 weekly allowance they have allocoted 60% for food 8% for fare 15% for school needs and the remaining 17% for savings how much is allocoted for the following
Answers
Answer:
RJ and his 2 brothers are given a weekly allowance of PHP 2,000. They have allocated 60% for food, 8% for fare, 15% for school needs, and 17% for savings.
For food, the allocation would be: PHP 2,000 x 60% = PHP 1,200.
For fare, the allocation would be: PHP 2,000 x 8% = PHP 160.
For school needs, the allocation would be: PHP 2,000 x 15% = PHP 300.
For savings, the allocation would be: PHP 2,000 x 17% = PHP 340.
So, for food, the allocation is PHP 1,200, for fare, it's PHP 160, for school needs, it's PHP 300, and for savings, it's PHP 340
Choose all of the values that are solutions to inequality x < -2
Answers
Answer:
The solution to the inequality x < -2 is all real numbers that are less than -2. This means that any number that is less than -2 will satisfy the inequality, but any number that is greater than or equal to -2 will not.
So, the solution set for x < -2 is all real numbers that are less than -2. This solution set can be expressed as (-∞, -2).
Therefore, the values that are solutions to the inequality x < -2 are:
• all real numbers less than -2, such as -3, -4, -5, etc.
Note that -2 itself is not part of the solution set, since it is not less than -2.
Find an equation for the perpendicular bisector of the line segment whose endpoints are (−2 ,− 9) and (−6,7). PLSLLSLS
Answers
The equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The midpoint of the line segment joining (-2, -9) and (-6, 7) can be found using the midpoint formula:
Midpoint = ( (x₁+x₁)/2 , (y₁+y₁)/2 )
Midpoint = ( (-2-6)/2 , (-9+7)/2 )
Midpoint = (-4,-1)
Next, we need to find the slope of the line joining the two points (-2, -9) and (-6, 7). We can do this using the slope formula:
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (7 - (-9)) / (-6 - (-2))
Slope = 4
The slope of the line perpendicular to the line segment is the negative reciprocal of the slope of the line joining the two points. So the slope of the perpendicular line is -1/4.
Using the point-slope form of a line, the equation of the perpendicular bisector can be written as:
y - y₁ = m(x - x₁), where (x₁, y₁) is the midpoint and m is the slope of the line.
Plugging in the values we found, we get:
y - (-1) = (-1/4)(x - (-4))
y + 1 = (-1/4)(x + 4)
y + 1 = (-1/4)x - 1
y = (-1/4)x - 2
Therefore, the equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2.
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Graph the line with slope -1 passing through the point (1,-5)
Answers
Answer:
please review the attachment
Use calculator to find 61.6 to the nearest hundredth
Answers
Answer : 61.60
Step-by-step explanation:
Answer:61.60
Step-by-step explanation:
i just typed it in
Solve the equations for x
Answers
Answer:
Step-by-step explanation:
5=cx-ax=x(c-a)
x(c-a)/5=1
(c-a)/5=1/x
x=5/(c-a)
The lunch special at Rachel's Restaurant is a sandwich, a drink and a dessert. There are 2 sandwiches, 3 drinks, and 2 desserts to choose from. How many lunch specials are possible?
Answers
Answer:
3 lunch specials are possible.
Her little sister's birthday is next week, so Brittany is planning a bubble-themed birthday party! She buys a big bottle of bubble solution and divides it equally among 6 small bottles. Each small bottle holds 1/8 of a gallon of bubble solution.
Use an equation to find the amount of bubble solution in the big bottle.
Answers
There is 3/4 of a gallon of bubble solution in the big bottle.
What is an equation?
In mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equal sign (=). An equation contains one or more variables, which are symbols that represent unknown values, and may also contain constants, coefficients, and arithmetic operations such as addition, subtraction, multiplication, and division.
Let's use "x" to represent the amount of bubble solution in the big bottle, in gallons.
According to the problem, the big bottle was divided equally among 6 small bottles, and each small bottle holds 1/8 of a gallon of bubble solution. Therefore, the total amount of bubble solution in the big bottle is equal to the sum of the amounts in the 6 small bottles:
x = 6 * (1/8)
Simplifying the right-hand side of the equation, we get:
x = 3/4
Therefore, there is 3/4 of a gallon of bubble solution in the big bottle.
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The value of a machine, V , at the end of t years
Answers
The value of machine after 2 years is $346.4.3
What is Rate of Depreciation?Subtract the asset's cost from its salvage value (what you anticipate it to be worth at the end of its useful life) to determine depreciation using the straight-line technique. The amount that can be depreciated, or the depreciable basis, is the outcome. Subtract this sum from the asset's useful life, which is measured in years.
Given:
C = $707 (the original cost),
r = 0.3 (the rate of depreciation),
and t = 2 (years that have gone by)
Using the Formula
V = C [tex](1-r)^t[/tex]
V = (707)(1 - 0.3)²
V = (707)(0.7)²
V = (707)(0.49)
V = 346.43
Thus, the value of machine is $346.43
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i need help with this question ASAP
Answers
In the image of the trapezoid the value of angle C is 82 degrees
What is a trapezoid?A trapezoid is a quadrilateral with one pair of parallel sides.
Opposite angles of a trapezoid are angles that are located across from each other, with a side of the trapezoid between them.
In a trapezoid, opposite angles are always congruent, meaning they have the same measure. This is a result of the fact that a trapezoid is a parallelogram, which means that its opposite sides are parallel and equal in length.
When opposite sides of a parallelogram are parallel, it follows that opposite angles are congruent.
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if an object is projected horizontally from a height of 5m with an initial velocity of 7 m/s what is the value of V0y?
Answers
The value of the final velocity before striking the ground will be 9.899 meters per second.
What is a vector?The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.
If an object is projected horizontally from a height of 5m with an initial velocity of 7 m/s.
We know that if the object is projected horizontally, so initially the object has a vertical speed is zero. Then it increases due to acceleration due to gravity.
The speed of the object before striking the ground is given as,
v² - u²= 2gh
v² - 0² = 2 × (9.8) × (5)
v² = 98
v = 9.899 meters per second
The value of the final velocity before striking the ground will be 9.899 meters per second.
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A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called
Answers
Answer:
sampling distribution
Step-by-step explanation:
:)
(c) 10:35 f the foll ing ratio
Answers
The ratio 10:35 can be simplified to 2:7.
What is a Ratio?
A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
The ratio 10:35 can be simplified to 2:7.
To simplify a ratio, you can divide both values by the greatest common factor. In this case, the greatest common factor of 10 and 35 is 5, so 10 divided by 5 is 2, and 35 divided by 5 is 7.
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Simply the following ratio 10:35
Jan, Freda and Pieter share some money.
Freda gets 3 times as much as Jan.
Pieter gets half as much as Freda.
(a) Write down the ratio of the amounts of money that they each get.
Give your answer in its simplest form.
Answers
The ratio of the amounts of money that they each get:
1 : 3 : 3/2
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Let's represent the amount of money that Jan gets as x.
Then, the amount of money that Freda gets is 3x,
and the amount of money that Pieter gets is:
= (1/2) x 3x
= 3/2 x (x)
The ratio of the amounts of money that they each get can be written as:
⇒ x : 3x : 3/2 x (x)
⇒ 1 : 3 : 3/2
So, Jan gets 1 unit of money, Freda gets 3 units of money, and Pieter gets 3/2 units of money.
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What is the image of (1, 0) after a dilation by a scale factor of 4 centered at the
origin?
Answers
Answer:
(4, 0)
Step-by-step explanation:
You want the image point coordinates of (1, 0) dilated by a factor of 4 centered at the origin.
DilationWhen the dilation is centered at the origin, all coordinate values are multiplied by the scale factor.
(1, 0) ⇒ 4(1, 0) = (4, 0)
The image of the point is (4, 0).
A young channel catfish weighs about 0. 1 pound. During the next 8 weeks, its weight increases by about 23% each week.
Answers
Weight is 0.229 pounds after 4 weeks.
As a young channel catfish only weights 0.1 pounds,
It gains weight over the following 8 weeks at a rate of roughly 23% every week.
In this case, the exponential growth function is as follows:
Exponential formulas are provided by.
[tex]y=a(1+r)^{x}[/tex]
where an is the starting amount, r is the growth rate, x is the duration, and y is the weight at the end of "x" weeks.
Our values are a = 0.1, r = 0.23 (or 23%), and t = 4.
As a result,
[tex]y=0.1(1+0.23)^{4} \\[/tex]
y = 0.1(2.289)
y = 0.229
Consequently, the weight at 4 weeks is 0.229 pound.
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Complete question:
A young channel catfish weighs about 0.1 pound. During the next 8 weeks, its weight increases by about 23% each week. About how much will the catfish weigh after 4 weeks? Round your answer to the nearest thousandth of a pound.
The width of a table is 4 2/5
feet. The length of the table is 2 1/5
times as long as its width.
Which equation shows the length of the table?
Please answer ASAP
Answers
The equation that shows the length of the table is length = 11/5 × 22/5
What is a fraction?A fraction can be defined as the part of a whole number, variable or element.
The different types of fractions are;
Proper fractionsImproper fractionsMixed fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
Length = 2 1/5 × Width
Width = 4 2/5 feet
Turn into improper fractions
Width = 22/5 feet
Then, length = 11/5 × 22/5
Hence, the equation is 11/5 × 22/5
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Find the value of x that makes each sentence true.
If (5 1/5)^5=25x then x =
If (8 1/3)^2= 4x, then x =
Answers
The first equation is:
(5 1/5)^5 = 25x
To solve for x, we need to simplify the left side of the equation first.
(5 1/5)^5 = (5 + 1/5)^5 = 6^5 = 7776
So,
7776 = 25x
Therefore,
x = 7776/25 = 311.04
For the second equation:
If (8 1/3)^2 = 4x, then x =
We need to simplify the left side of the equation first.
(8 1/3)^2 = (8 + 1/3)^2 = 9^2 = 81
So,
81 = 4x
Therefore,
x = 81/4 = 20.25
So the values of x that make each sentence true are 311.04 and 20.25, respectively.
Suppose you invest $500 into an account earning simple interest. The APR is 2% and you invest it for 5 years. Choose two answers: How much would your investment be worth at the end? What equation should you use to calculate this?
1a. $2500.10
2a. $550
3a. $1000
4a. $2550
5a. $5500
1b. A = 500 ( 1 + 2(5))
2b. A = 500 (1 + 0.2(5))
3b. A = 500 (1 + 0.02(5))
Answers
Answer:
a=1000.10
Step-by-step explanation:
what is the least common denominator for 5/18, 11/12, and 6/13
Answers
Answer:
LCD → 468
Step-by-step explanation:
[tex]\frac{5}{18} = \frac{5}{18} * \frac{26}{26} = \frac{130}{468}[/tex]
[tex]\frac{11}{12} = \frac{11}{12} * \frac{39}{39} = \frac{429}{468}[/tex]
[tex]\frac{6}{13} = \frac{6}{13} * \frac{36}{36} = \frac{219}{468}[/tex]
Hence, the least common denominator for these three fractions would be 468.
