Answer:
x=2, y=8
Step-by-step explanation:
This is a system of equations, so we need to substitute one equation for another one but they are both equal to y.
4x=5x-2
-x=-2
x=2
y=4x
y=4(2)
y=8
A group of 25 students is asked to attend a meeting. 20 of the 25 students were able to attend. What percentage of the students were able to attend?
Answer:
80%
Step-by-step explanation:
We Know
A group of 25 students is asked to attend a meeting.
20 of the 25 students were able to attend.
What percentage of the students were able to attend?
We Take
(20 ÷ 25) x 100 = 80%
So, 80% of the students were able to attend.
Cora bought 60 feet of cable for $13.20. She needs 20 more feet. If the unit price is the same, how much will she pay for the extra 20 feet of cable? She will pay an extra $].
Answer:
$4.40
Step-by-step explanation:
The price per foot is $13.20/60 = 0.22 per foot. To find the cost of the extra 20 feet of cable, we can multiply the price per foot by the number of feet needed:
0.22 x 20 = $4.40
Therefore, Cora will pay $4.40 for the extra 20 feet of cable.
help asappp will give brainliest !!!!!!!!!!!!
The surface area of the figure when d = 2cm is 3.14 cm².
How to find the surface area
To find the surface area of a circle with a diameter of 2 cm, we can first begin by using the formula: A = πr².
Next, we note that the diameter radius is the diameter divided by 2. So, 2 cm divided by 2 equals 1 cm. Plugging this into the equation, we will have the following:
A = 3.14 * 1²
So, surface area = 3.14 cm² when rounded to the nearest hundredth centimeter.
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the statistic that half of all marriages end in divorce is an accurate depiction of the situation. question 12 options: true false
The actual divorce rate in the United States is around 39%, and it is important to consider the specific factors that contribute to divorce rates rather than relying on a generalization about marriage.
The statistic that half of all marriages end in divorce is not an accurate depiction of the situation.
The statement is false.The statement that half of all marriages end in divorce is a widely held belief that has been perpetuated by popular media, but it is not an accurate depiction of the situation.
The actual divorce rate in the United States has been declining since the 1980s and is currently around 39%.The misconception about the high divorce rate is due in part to the fact that many people get divorced more than once, inflating the overall divorce rate.
Additionally, certain demographics are more likely to get divorced than others, such as those who marry at a young age or those with lower levels of education. Therefore, it is important to consider the specific factors that contribute to divorce rates rather than relying on a generalization about marriage.In conclusion, the statement that half of all marriages end in divorce is false.
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URGENT PLEASE HELP! IM GIVING OUT POINTS LIKE ITS CANDY! please explain. who wants brainliest?
Use triangle ABH for problems 8-9.
8. Use triangle ABH to prove the the identity: (sin A)² + (cos A)² = 1.
9. Use triangle ABH to explain why sin A=cos(90°-A)
Answer:
Step-by-step explanation:
where angle A is opposite to side BH, angle B is opposite to side AH, and angle H is opposite to side AB.
Problem 8:
Using the Pythagorean theorem, we have:
AB² = AH² + BH²
Dividing both sides by BH², we get:
AB²/BH² = AH²/BH² + 1
(sin A)² + (cos A)² = 1, since sin A = AH/BH and cos A = BH/AB.
Therefore, (sin A)² + (cos A)² = 1, which is the identity we wanted to prove.
Problem 9:
Using the definition of cosine, we have:
cos(90°-A) = BH/AB
Using the Pythagorean theorem, we have:
AB² = AH² + BH²
Dividing both sides by AB², we get:
AB²/AB² = AH²/AB² + BH²/AB²
1 = (sin A)² + (cos A)², since sin A = AH/AB and cos A = BH/AB.
Therefore, sin A = √(1 - (cos A)²).
Substituting cos A = BH/AB, we get:
sin A = √(1 - (BH/AB)²)
Multiplying the numerator and denominator by AB², we get:
sin A = √(AB²/AB² - BH²/AB²)
sin A = √(1 - (BH/AB)²), which is the desired result.
Therefore, sin A = cos(90°-A).
6. Given the fact that a credit card balance can change every day, which of the following
best describes how interest is calculated?
Interest is calculated yearly using the total amount spent that year.
Interest is calculated monthly but only on the carry-over balances.
Interest is calculated monthly using the total amount spent that month.
Interest is calculated using average daily balances.
a.
b.
C.
d.
Answer: b
Step-by-step explanation:
khan
Find the value of x (xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx)
Answer:
x = - 2
Step-by-step explanation:
using the rules of exponents
[tex]a^{m}[/tex] ×[tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
given
[tex]\frac{9^{3}(9^{1}) }{9^{6} }[/tex]
= [tex]\frac{9^{(3+1)} }{9^{6} }[/tex]
= [tex]\frac{9^{4} }{9^6} }[/tex]
= [tex]9^{(4-6)}[/tex]
= [tex]9^{-2}[/tex] = [tex]9^{x}[/tex]
then equating exponents
x = - 2
!!HELP!!
12x^5+24x^4+27x^3 Name the polynomial by number of terms.
A. Binomial
B. 6 Term Polynomial
C. Trinomial
D. Monomial
Answer
the answer is a 6 Term polynomial
roughly, what do you expect the ratio of the time taken to compute lu factorization vs. back/forward substitution to be?
The ratio of the time taken to compute LU factorization vs. back/forward substitution depends on several factors such as the size and sparsity of the matrix, the specific implementation of the algorithms, and the hardware used to perform the computations.
However, in general, LU factorization takes more time than back/forward substitution. This is because LU factorization involves decomposing the original matrix into two matrices, L and U, which requires more computations than simply solving the system of equations using back/forward substitution once the L and U matrices are available.
As a rough estimate, the time taken for LU factorization can be several times larger than the time taken for back/forward substitution, especially for large and dense matrices.
However, the exact ratio can vary widely depending on the specific factors mentioned above.
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solve the inequality 4x - 7 is more than or equal to 13
Answer:
np
Step-by-step explanation:
To solve the inequality 4x - 7 >= 13, we can follow these steps:Add 7 to both sides of the inequality:
4x - 7 + 7 >= 13 + 7Simplify the left side and right side:
4x >= 20Divide both sides by 4 (since we want to solve for x, not 4x):
4x/4 >= 20/4Simplify:
x >= 5Therefore, the solution to the inequality 4x - 7 >= 13 is x >= 5.
Kwasi and Lola wrote equations to help them solve the previous angle puzzle. Kwasi's equation: b+132=180 Lola's equation: 132+f=180 Who wrote a true equation?
Angle B and angle C must have a total measure of 180 - 48 = 132 degrees.
What is Linear Equation ?
A linear equation is an equation that represents a straight line on a graph. It is an algebraic equation in which each term is either a constant or the product of a constant and a single variable.
Both Kwasi and Lola wrote true equations.
Kwasi's equation, b+132=180, is true because in a triangle, the sum of the interior angles is always 180 degrees. The angle measures opposite to sides b and c are a and f, respectively, so b+a+f=180. Since a+f=48+132=180- b, we can substitute and get b+132=180, which is true.
Similarly, Lola's equation, 132+f=180, is also true because the sum of the angles in a triangle is always 180 degrees, and angle A has a measure of 48 degrees,
Therefore, angle B and angle C must have a total measure of 180 - 48 = 132 degrees.
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5 pound box of detergent will wash 20 loads. A 5 pound box cost $3.50. A 15 pound box cost $10.00. About how much will you save per load if you buy the 15 pound box?
Hence, if you purchase the 15-pound box rather than the 5-pound box, you will save roughly $0.0083 every load.
what is unitary method ?A problem-solving technique known as the unitary method is determining the value of only one unit and utilising that value to determine the value of another quantity which is either a multiple or indeed a fraction of the unit. It is frequently employed in maths, particularly in numeracy and algebra. In the unitary technique, a ratio or percentage is used to solve a problem where two quantities are related to one another by a constant number, that is, the value of one unit. This approach can be used to solve issues involving rates, costs, ratios, and other comparable quantities.
given
Let's start by calculating the price per load of the 5-pound package.
Cost per load is calculated as Box Cost / Number of Loads ($3.50 / 20 = $0.175).
Let's now calculate the price per load for the 15-pound box:
Cost each load is box price / the number of loads, which is $10.00 / (3 x 20) = $10.00 / 60 = $0.1667 per load.
to calculate the amount you will save per load if you purchase the 15-pound package.
Expense per load of a 5-pound box minus savings per load - The price per 15-pound box load.
Savings per load are equal to $0.175 - $0.1667, or $0.0083. (rounded to the nearest cent)
Hence, if you purchase the 15-pound box rather than the 5-pound box, you will save roughly $0.0083 every load.
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∠a is an acute angle in a right triangle. given that cosa=1517, what is the ratio for sina? enter your answer in the boxes as a fraction in simplest form $$
The ratio for sin(a) is 8/17.
To find the ratio for sin(a),
we can use the Pythagorean identity for trigonometric functions in a right triangle:
sin²(a) + cos²(a) = 1. Given that cos(a) = 15/17, we can proceed with the following steps:
1. Square the given cosine ratio:
(15/17)² = 225/289.
2. Subtract the squared cosine ratio from 1:
1 - 225/289 = 64/289.
3. Take the square root of the result to find sin(a):
√(64/289) = 8/17.
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Triangle ABC is similar to triangle ADE.
AB= 8CM
BC= 6CM
BD= 4CM
Work out the length of DE.
In the above mentioned similar triangles the length of DE is 5.25 cm.
What is triangle?A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.
Since triangles ABC and ADE are similar, their corresponding sides are proportional. We can use this fact to set up a proportion:
AB / AD = BC / DE
Substituting the given values, we get:
8 / AD = 6 / DE
Multiplying both sides by DE, we get:
8DE / AD = 6
Dividing both sides by 8/AD, we get:
DE = (6/8)AD
We need to find AD to solve for DE. To do this, we can use the fact that BD is an altitude of triangle ABC and triangle ADE is similar to triangle ABC. Therefore, triangle ABD is also similar to triangle ABC, and we can set up another proportion:
BD / AB = AD / AC
Substituting the given values, we get:
4 / 8 = AD / (8 + 6)
Simplifying, we get:
1/2 = AD / 14
Multiplying both sides by 14, we get:
AD = 7
Substituting this value back into the first equation, we get:
DE = (6/8)AD = (6/8)7 = 21/4 = 5.25
Therefore, the length of DE is 5.25 cm.
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write an equivalent equation to ab=ac using a−1 such that, when it is simplified, the resulting equation will simplify to b=c.
The equivalent equation to ab=ac is b = c.
How we get the equivalent equation?An equivalent equation to ab=ac using a−1 that simplifies to b=c is:
Simplifying the expression by canceling out a⁻¹a, we get:
b = c
Therefore, the correct option is b = c.
We can start with the equation ab = ac and multiply both sides by a−1, which is the inverse of a. This gives us:
a⁻¹(ab) = a⁻¹(ac)
Simplifying the left-hand side of the equation by using the associative property of multiplication, we get:
(a⁻¹a)b = (a⁻¹a)c
Since a⁻¹a is equal to 1, we can simplify the expression to:
1b = 1c
Which simplifies to b = c, as required.
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Ms. Wells bought some bananas for $0.40 per pound and some oranges for $0.80 per pound. Her fruit purchase cost $8.00 and weighed 11.75 pounds. How many pounds of bananas did she buy?
A-2.375 pounds
B- 3.50 pounds
C- 8.25 pounds
D- 9.375 pounds
Answer: Let's assume Ms. Wells bought x pounds of bananas and (11.75 - x) pounds of oranges.
The cost of bananas is $0.40 per pound, so the cost of x pounds of bananas is 0.4x.
The cost of oranges is $0.80 per pound, so the cost of (11.75 - x) pounds of oranges is 0.8(11.75 - x).
The total cost of the fruit purchase is $8.00, so we can write:
0.4x + 0.8(11.75 - x) = 8
Simplifying this equation:
0.4x + 9.4 - 0.8x = 8
-0.4x = -1.4
x = 3.5
Therefore, Ms. Wells bought 3.5 pounds of bananas.
So the answer is (B) 3.50 pounds.
Step-by-step explanation:
How much money did she get back?
Answer:
Step-by-step explanation:
The change Melody receives:
=
$
41.58
Explanation:
Cost of skateboard
=
$
79.81
Cost of helmet
=
$
26.41
Total
=
$
106.22
She uses a
45
%
off coupon, this means she pays
55
%
(
100
−
45
)
of the total cost:
She needs to pay only:
55
100
×
106.22
=
$
58.421
Since she uses a
$
100
bill the change she receives is:
100
−
58.42
=
$
41.58
Answer: She got back $42.67
Step-by-step explanation:
$79.81 + $24.41 = $104.22
%45 off of $104.22 = $57.32
$100 - $57.32 = $42.67
you organize a chess tournament and 15 people sign up. you would like each person to play against 5 others to decide who makes the elimination round. is this possible? explain why or why not
It is not possible to have each of the 15 participants play against exactly 5 others in your chess tournament.
Here's why:
1. In a tournament where each person plays against 5 others, the total number of matches played can be calculated using the combination formula: C(n, k) = n! / (k!(n-k)!),
where n is the number of participants and k is the number of opponents each player faces.
In this case, n = 15 and k = 5.
2. Applying the formula, we get C(15, 5) = 15! / (5!(15-5)!) = 15! / (5!10!) = 3,003 matches in total.
However, since each match involves two players, the actual number of matches played is 3,003 / 2 = 1,501.5.
This is not a whole number, so it is impossible to have exactly 5 matches per player in this scenario.
3. To further confirm this, we can also analyze the problem using graph theory.
Each participant can be represented as a node in a graph, and a match between two participants can be represented as an edge connecting the corresponding nodes.
4. In this case, we want each node to have a degree of 5 (i.e., 5 edges connecting to it).
The Handshaking Lemma states that the sum of the degrees of all nodes in a graph is equal to twice the number of edges in the graph.
Thus, in our scenario, the sum of all degrees would be 15 * 5 = 75.
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one group of 3 adults and 5 childern paid a total of $32.50 for admisson.another group of 4 adults and 4 children paid $34.00 for admisson. what is the cost of admisson for one child
The cost of admission for one child is $5.60.
To find the cost of cost of admisson for one child, we can set up a system of linear equations using the given information.
Let A represent the cost of admission for one adult and C represent the cost of admission for one child.
We can write two equations based on the information given:
3A + 5C = $32.50 (for the first group)---------(1)
4A + 4C = $34.00 (for the second group)---------(2)
We can solve these equations step-by-step to find the value of C:
Multiply equation (2) by -1 so that we can eliminate A when adding both equations:
-4A - 4C = -$34.00
Add equations (1) and the modified equation (2) to eliminate A:
(3A + 5C) + (-4A - 4C) = $32.50 + (-$34.00)
-A + C = -$1.50
Multiply the whole equation by -1 to get rid of the negative sign:
A - C = $1.50 ---------(3)
Add equation (2) to the equation we got in step 3 to eliminate C:
(4A + 4C) + (A - C) = $34.00 + $1.50
5A + 3C = $35.50
Divide the equation by 5 to find the value of A:
A = $7.10
Substitute the value of A back into the equation 3:
$7.10 - C = $1.50
Solve for C:
C = $7.10 - $1.50
C = $5.60
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f(x) = 2x
g(x) = -4x + 5
Answer:
for fog(x)
fog=f(g(x))
= 2(-4x +5)
=-8x+10
Need help ASAP! I appreciate it!
Answer:
the answer is c and it's right I think
how to check 12x + 9 = 15
i already know the answer i just need help checking !!
andy's lawn has twice as much area as beth's lawn and three times as much area as carlos' lawn. carlos' lawn mower cuts half as fast as beth's mower and one third as fast as andy's mower. if they all start to mow their lawns at the same time, who will finish first?
In the given word problem, they all start to mow their lawns at the same time, Beth will finish first.
Let's assume that Beth's lawn has an area of x, so Andy's lawn has an area of 2x, and Carlos' lawn has an area of (1/3) × 2x = (2/3)x. Let's also assume that Beth's lawn mower can mow at a rate of 1 unit of area per hour, so Carlos' mower can mow at a rate of 1/2 = 0.5 units of area per hour, and Andy's mower can mow at a rate of 1/3 units of area per hour. We can calculate the time it will take each person to mow their lawn by using the formula:
Time = Area / Rate.
Beth's time = x / 1
= x hours
Carlos' time = (2/3)x / 0.5
= (4/3)x hours
Andy's time = 2x / (1/3)
= 6x hours
According to these facts, it is quite clear that Beth would finish first followed by Carlos and Andy would finish last.
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Find the value of x in the triangle shown below.
X°
125°
21°
Answer:
34 degrees
Step-by-step explanation:
add the two known degrees then subtract from 180
Armando kicks a football into the air. The function f(x) = -6x to the power of 2 + 36x +.23 models the height of the football from the ground, in feet, with respect to the time x in seconds. Use a graph or table to estimate the time for the ball to return to the ground after being kicked.
Thus, the total time to reach the ball at ground after being kicked is 6 seconds.
Define about the quadratic function:The maximum value or minimum value of a quadratic function are located at its vertex, which is shaped like a U. The quadratic function's axis of symmetry crosses the function (a parabola) at its vertex.
This graph's opening side plus vertex determine the quadratic function's range. To ascertain the quadratic function's range, locate the lowest and highest f(x) values on the function graph.
Standard form for quadratic function:
f(x) = ax² + bx + c,
In which, a, b, and c - real numbers and a ≠ 0.
Given function for the which explain the height of ball with time:
f(x) = -6x² + 36x + 0.23
f(x) is the height of ball taken from ground.
x is the time in seconds.
Draw the graph of the function using the graphing tool.
The diagram is attached.
The vertex of the graph lies at (3, 54.23).
x - 3 seconds
f(x) = 54.23 ft
So, time taken by ball to reach at height of 54.23 ft is 3 seconds.
Total time to reach the ball at ground = 2*3 = 6 seconds
Thus, the total time to reach the ball at ground after being kicked is 6 seconds.
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a computer is printing out subsets of a 6 element set (possibly including the empty set). (a) at least how many sets must be printed to be sure of having at least 2 identical subsets on the list?
To find the minimum number of subsets that must be printed to ensure at least two identical subsets on the list, we can use the concept of Pigeonhole Principle. At least 65 sets must be printed to be sure of having at least 2 identical subsets on the list.
1. First, we need to find the total number of possible subsets in a 6-element set. We use the formula 2^n, where n is the number of elements. In this case, n = 6.
2. Calculate the total number of subsets: 2^6 = 64.
3. According to the Pigeonhole Principle, if there are N pigeonholes (subsets) and more than N pigeons (printed subsets), at least one pigeonhole will have more than one pigeon.
4. To ensure that we have at least 2 identical subsets, we need to print one more subset than the total number of possible subsets: 64 + 1 = 65.
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lottery: every day, jorge buys a lottery ticket. each ticket has a probability of 0.2 of winning a prize. after seven days, what is the probability that jorge has won at least one prize? round your answer to four decimal places.
The probability after seven days of buying a lottery that Jorge would have at least one prize is 0.9364, rounded to four decimal places.
The question suggests that the probability of winning a prize on a single lottery is 0.2. This means that the probability of not winning a prize on that ticket is 0.8. This is because the probability is a total sum of 1. Hence, probability of not winning the prize:
1 - 0.2 = 0.8.
If Jorge has bought the tickets consistently, the probability would be multiplied the specific times. Therefore, the probability of not winning a prize on that ticket after seven days is equal to (0.8)⁷. Now the probability of winning a prize after seven days would be:
1 - (0.8)⁷ = 0.9364.
Therefore, the probability that Jorge has won at least one prize after seven days of buying lottery tickets is 0.9364 rounded to four decimal places.
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Pls help fast, I need the answer soon
Write 3a^2b^3c^5/8x^4y^3z using no denominator. (fraction line is necessary. Use x for multiplication between numbers.)
(The x 2 is required, and also I crossed out the spaces that aren't needed
Answer:
3a^2b^3c^5
—————— x 2^(-3) x^(-4)y^(-3)z^(-1)
8
As elevation increases, the atmospheric air pressure decreases. The air pressure P in pascals given the altitude a in meters is a = 15,500 (5 - log₁0 P). What is the air pressure at the peak of Mount Marcy, which has an elevation of 1629 meters? Round your answer to the nearest whole pascal.
The air pressure at the peak of Mount Marcy is approximately 164.17 pascals.
What is air pressure?Air pressure, also known as atmospheric pressure, is the force exerted by the weight of the Earth's atmosphere on any given surface. It is the weight of the column of air that extends from the Earth's surface up to the top of the atmosphere.
What is Pascal?The Pascal (symbol: Pa) is the SI (International System of Units) unit of pressure, named after the French mathematician and physicist Blaise Pascal. One pascal is defined as the pressure exerted by the force of one Newton on an area of one square meter. In other words, 1 Pa = 1 N/m².
According to the given informationWe are given the formula that relates the altitude (a) and the atmospheric air pressure (P):
a = 15,500 (5 - log₁0 P)
We are also given that the altitude at the peak of Mount Marcy is 1629 meters. We can use this information to find the atmospheric air pressure at the peak of Mount Marcy by plugging in a = 1629 and solving for P:
1629 = 15,500 (5 - log₁0 P)
Dividing both sides by 15,500, we get:
(5 - log₁0 P) = 1629 / 15,500
Subtracting 5 from both sides, we get:
-log₁0 P = (1629 / 15,500) - 5
Simplifying the right-hand side, we get:
-log₁0 P = -1.5454
Taking the inverse logarithm (base 10) of both sides, we get:
P = 10⁻¹.⁵⁴⁵⁴
Using a calculator, we can evaluate this expression to get:
P ≈ 164.17 pascals
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what when two variables are related such that people with high scores on one tend to have high scores on the other and people with low scores on one ten to have low scores on the other.(s) of variables are appropriate for a correlation?
When two variables are related in such a way that people with high scores on one variable tend to have high scores on the other, and people with low scores on one variable tend to have low scores on the other, it is called a positive correlation. This type of relationship between variables is appropriate for a correlation analysis.
A correlation is a statistical technique used to measure the strength and direction of the association between two variables. The most common correlation coefficient is the Pearson's correlation coefficient, which ranges from -1 to 1. A positive correlation indicates a direct relationship between the variables, while a negative correlation indicates an inverse relationship. A correlation close to 0 suggests no relationship between the variables.
To conduct a correlation analysis, the variables should be continuous or ordinal, which means that they can be measured on a scale with meaningful intervals. Examples of continuous variables include age, height, and weight, while ordinal variables could include rankings, such as class rank or satisfaction levels.
Here's a step-by-step explanation for conducting a correlation analysis:
1. Identify the two variables of interest, ensuring they are continuous or ordinal.
2. Collect the data for each variable from a sample of individuals or observations.
3. Calculate the mean and standard deviation for each variable.
4. Compute the covariance between the two variables, which measures the degree to which they change together.
5. Normalize the covariance by dividing it by the product of the standard deviations of the two variables. This produces the correlation coefficient, which represents the strength and direction of the relationship between the variables.
In summary, a correlation analysis is appropriate when examining the relationship between two continuous or ordinal variables, such as in the case of a positive correlation where high scores on one variable are associated with high scores on the other, and low scores on one variable are associated with low scores on the other.
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