As tickets are selling for a high school play. student tickets cost $4 and general admission tickets cost $6 and sell 31 tickets and collect $170.
Therefore, the system of equation is
8$4 + 23$6 = $32 + $138 = $170 total
A system of equations is a set of one or more equations with many variables. A solution to a system of equations is a variable map such that all component equations are satisfied. That is, the point where all those equations intersect.
Given that :
Ticket cost = $ 4 and $6
and collection = $170.
Now,
4S+6G = 170 ------------------------ (1)
S+G = 31 ----------------------- (2)
Therefore, subtract from 1st equation to eliminate one variable:
4S+ 4G = 124 ----------------------------- (3)
Now,
2G = 46
⇒ G = 23 tickets
putting G = 23 in equation(2)
S = 31-23
= 8 student tickets
The system of equation is:
8$4 + 23$6 = $32 + $138
= $170 total
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What is 1/9 in percent?
In percent, the fraction [tex]\frac{1}{9}\\\\[/tex] can be calculated as 11.11%.
A percentage is a common way to represent statistical data, and it is usually used to indicate one-hundredth, with the symbol "%." To calculate the percentage, it is given by:
Percentage (%) = value ÷ total value multiplied by 100%
What is the formula for converting a fraction to a percentage?% = [tex]\frac{1}{9}\\\\[/tex] × 100%% = 0.111111111 × 100%% = 11.1111111%Rounded value: [tex]\frac{1}{9}\\\\[/tex] = 11.11%In conclusion, the percentage of a fraction [tex]\frac{1}{9}\\\\[/tex] is 11.11%.
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Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number. Enter your probability as a fraction.)
rolling a number greater than 5 or doubles
The probability of rolling a number greater than 5 or doubles will be 0.78.
What is probability? What is a mathematical equation? What do you mean by domain and range of a function?The formula to calculate the probability of occurrence of an event [A] can be written as -P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes.
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have two dices are rolled.
The sample space for sum greater than 5 will be 26. For doubles, we will add 2 pairs (1, 1) and (2, 2) to 26 to get a total sample space of 28. Remaining doubles are already in 26. So, the probability of rolling a number greater than 5 or doubles will be -
P(A) = 28/36 = 0.78
Therefore, the probability of rolling a number greater than 5 or doubles will be 0.78.
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[Question in english -
From a point on the ground located 4m from a pole, its upper part can be seen with an elevation angle of 37°. What is the height of the pole?]
if abc is 1 degree and 25' what is acd? give your answer in degrees and minutes
If abc is 1 degree and 25', the angle ACD is 178° 35'.
What is angle?An angle is a figure in Euclidean geometry formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are termed dihedral angles. An angle is generated when two straight lines or rays meet at a shared terminus. The common point of contact is called the vertex of an angle.
Here,
∠ACB and ∠ACD are supplementary, so they add up to 180°.
First, convert to degrees (there are 60 minutes in a degree).
∠ACB = 1°25' = 1° + (25/60)° = 1.4167°
Now find the supplementary:
∠ACD = 180° − 1.4167°
∠ACD = 178.5833°
∠ACD = 178° 35'
The value of angle ACD is 178° 35' if abc is 1 degree and 25' .
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q. jenny can walk 4 miles in (m 3) minutes. at that pace, how many miles can she walk in 15 minutes?
If she moves at a speed of 1.33 miles per minute while walking 4 miles in 3 minutes, she can cover 20 miles in 15 minutes.
What is division?A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
Here,
In 3 minutes, she walk 4 miles,
speed=distance/time
=4/3 miles/minute
distance=speed*time
=4/3*15
=20 miles
She can walk 20 miles in 15 minutes if she walks 4 miles in 3 minutes with a speed of 1.33 miles/minute.
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what is the principal of a 10-month, 8% note that will earn $800 of interest?
Principal will be $1000
Given values
Simple interest, SI= $800
Interest rate, R=8%
Time, T=10 months
Principle, P= Y
As we know;
[tex]Simple Interest, SI=P×R×T[/tex]
By substituting the values, we get
$800= Y ×8% ×10
$800=0.8Y
$800÷0.8= Y
$1000=Y
Thus the above response is correct.
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For each set of atoms, identify the isotopes Set I: Set 2: '8A YB Yc "D RE # #G #u Select the isotopes_ Select the isotopes:
The isotopes in the set I are [tex]^{14} _{7} B[/tex] and [tex]^{15} _{7} C[/tex] and set II are [tex]^{20} _{10} E, ^{21} _{10}F[/tex] and [tex]^{22} _{10} G[/tex].
Isotopes are variations of chemical elements that have a varied number of neutrons but the same number of protons and electrons. In other words, isotopes are different forms of the same element that have different amounts of nucleons (the sum of protons and neutrons) because of variations in the total number of neutrons in each of their individual nuclei.
Isotopes are elements with the same atomic number but different mass.
In this case, the elements in set I- B and C has the same atomic number 7 but had different mass numbers and the elements in set II- E, F and G had the same atomic number 10 and different mass numbers, therefore they are known as isotopes.
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I need help with this someone please explain it to me
The length of the Antenna will be;
⇒ h = 18 meters
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Tyler is 1.8 meters and his shadow is 6 meters.
And, Tyler is standing 54 meters from the antenna.
Now,
Since, Tyler is 1.8 meters and his shadow is 6 meters.
And, Tyler is standing 54 meters from the antenna.
Let the length of the Antenna = x
Hence, We get by definition of proportional, we get;
⇒ 1.8 / 6 = h / (54 + 6)
⇒ 0.3 = h / 60
⇒ h = 0.3 × 60
⇒ h = 18 meters
Thus, The length of the Antenna will be;
⇒ h = 18 meters
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If m∠ XYZ=68 and m∠ WXZ=71, find m∠ WZX
The measure of angle WZX is given as follows:
m < WZX = 41º.
How to obtain the angle measure?The measure of angle XYZ is of 68º, hence, due to the bisection, we have that:
m < WYZ = 34º.m < ZYX = 34º.The measure of angle WXZ is of 71º, hence the measure of angle WXY is found as follows:
m < 2 x 71 = 142º.
(as the bisection of angle X means that it is divided into two parts of equal measure).
As the figure is a parallelogram, the opposite angles have the same measure, thus the measure of angle WZY is given as follows:
m < WZY = 142º.
Then, applying the bisection, the measure of angle WZX is given as follows:
m < WZX = 0.5 x 142º = 41º.
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what is the purpose of the permutation test? group of answer choices for hypothesis testing of mean, median, and quartiles, it is used to synthesize the population distribution of the statistic of interest for hypothesis testing of mean, median, and quartiles, it is used to synthesize the sampling distribution under the null
Permutation test is used to synthesize the population distribution of the statistic of interest for hypothesis testing of mean, median, and quartiles
An estimation of the population distribution—the distribution from which our observations originated—is the goal of a permutation test. We can then calculate how uncommon our observed values are in comparison to the population.
I find the permutation test to be more natural, and it only relies on the assumption of random assignment of treatment groups.
In a permutation test, you compare the observed test statistic to the distribution of values
you get when the treatment group assignments are shuffled/randomized/permuted.
The null hypothesis that two distinct groups originate from the same distribution is tested using permutation tests, also known as exact tests, randomization tests, or re-randomization tests. A permutation test can be used for hypothesis testing or significance testing (including A/B testing) without requiring any presumptions to be made about the distribution of the samples, such as that the samples must be normally distributed.
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(1 point) from a group of 8 men and 6 women a committee consisting of 4 men and 4 women is to be formed. how many different committees are possible if (a) 2 of the men refuse to serve together? answer: (a) 2 of the women refuse to serve together? answer: (a) 1 man and 1 woman refuse to serve together? answer:
If two men refuse to serve together we can choose in a) 1275 ways. If b) 2 women refuse to serve together we can choose in 110 ways and if c) 1 man and 1 woman refuse to serve together then we can choose in 750 ways.
a)
Here we can get 3 cases.
The first man is elected
The second man is elected
Neither f the 2 is included
In the first 2 cases, we need to choose 4 men from 7 while in the third case we need to choose 4 men from 6.
Therefore we get
⁷C₄ X ⁶C₄ + ⁷C₄X ⁶C₄ + ⁶C₄X ⁶C₄
35 X 15 + 35 X 15 + 15 X 15
= 1275 ways
b)
Just like before we will have 3 cases here.
Here we will have to choose 4 women from 5 for the first 2 cases and 4 from 4 for the third case. Hence we get
⁵C₄ X ⁸C₄ + ⁵C₄ X ⁸C₄ + ⁴C₄ X ⁸C₄
= 50 + 50 + 10
= 110 ways
c)
Here we will have 3 cases again
The man is included
The woman is included
neither is included
Therefore we will get
⁸C₄ x ⁵C₄ + ⁷C₄ X ⁶C₄ + ⁷C₄ X ⁵C₄
= 10 X 5 + 35 X 15 + 35 X 5
= 750 ways
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What is the area of a rectangle 3 meters long and 7 meters high
Answer:
21 sq. meters
Step-by-step explanation:
you just need to multiply the width and the height, so 3x7.
3x7=21
Answer: 21m^2
Step-by-step explanation:
The equation finds the area of a rectangle is
Area= Width times Height
So take 7 times 3 = 21 m^2
Martha loves to wear socks with crazy patterns. She finds a great deal for these kinds of socks at her favorite store, Rock Those Socks. There is a proportional relationship between the number of pairs of socks that Martha buys, x, and the total cost (in dollars), y.
Martha can buy 2 pairs of socks for $6. Write the equation for the relationship between x and y.
The equation which represent the proportional relationship between the number of pairs of socks that Martha buys, x, and the total cost (in dollars), y is y = bx
How to write equation?Number of pairs of socks that Martha buys = xTotal cost (in dollars) = yy = bx
Where,
b = constant
If y = $6 and x = 2 pairs
y = bx
6 = b × 2
6 = 2b
divide both sides by 2
b = 6/2
b = 3
In conclusion, the proportional relationship between number of pairs of socks that Martha buys, x, and the total cost (in dollars), y is y = bx
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how long will it take for 1000 to grow to 1750 if invested at 5.75% compounded quarterly?
10 years it takes for 1000 to grow to 1750 if invested at 5.75% compounded quarterly.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The formula for quarterly compound interest formula:
[tex]A=P(1+\frac{r}{4} )^{4t}[/tex]
P is the principle amount
t is time
r is rate of interest
A is final amount
[tex]1750=1000(1+\frac{0.0575}{4} )^{4t}[/tex]
[tex]1750=1000(1+0.0144)^{4t}[/tex]
[tex]1750=1000(1.0144)^{4t}[/tex]
Divide both sides by 1000
[tex]1.75=1.0144^{4t}[/tex]
Take log on both sides
log1.75=4tlog1.0144
0.243=4t(0.006)
0.243=0.024t
Divide both sides by 0.024
t=10.12
t=10 years
Hence, 10 years it takes for 1000 to grow to 1750 if invested at 5.75% compounded quarterly.
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How do you solve a/15 = 4/5 ?
The value of a=12
Simply use cross multiplication :
The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equals to symbol. Cross multiplication is a method for comparing fractions.
Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.
[tex]\frac{a}{15}=\frac{4}{5}[/tex]
or, 5a=4*15
or, a= 4*15/5
or, a= 12
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If y=tan u, u=v-1/v, and v=lnx, what is the value of dy/dx at x=e?
The partial derivative dy/dx at x = e is given as follows:
[tex]\frac{dy}{dx}(e) = -\frac{2}{e}[/tex]
How to obtain the partial derivative?The function in this problem is defined as follows:
y = tan(u).
The function y is a function of the variable u, which is a function of the variable v, which is a function of variable x, then the function of variable x can be written as follows:
[tex]y = \tan{\left(\ln{x} - \frac{1}{\ln{x}}\right)}[/tex]
Then, applying the chain rule, the derivative is the derivative of the outer tangent function multiplied by the derivative of the inner ln function.
The inner function is of:
[tex]\ln{x} - \frac{1}{\ln{x}}[/tex]
Which has a derivative of:
[tex]\frac{1}{x} + \frac{1}{x\ln^2{x}}[/tex]
The outer tangent function has a derivative of:
-sec²(x).
Then the complete derivative is of:
[tex]\frac{dy}{dx} = -\sec^2{\left(\ln{x} - \frac{1}{\ln{x}}\right)} \times \left(\frac{1}{x} + \frac{1}{x\ln^2{x}}\right)[/tex]
At x = e, the numeric value of the derivative is given as follows:
[tex]\frac{dy}{dx}(e) = -\sec^2{0} \times \frac{2}{e}[/tex]
[tex]\frac{dy}{dx}(e) = -\frac{2}{e}[/tex]
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Just number 4 pleaseee
Answer:
blip
Step-by-step explanation:
blipgg
How do you solve 2x+3=9?
Answer:
x = 3
Step-by-step explanation:
You want to know how to solve 2x +3 = 9.
SolutionA solution is an equation of the form ...
x = constant
ProcessYou can get a clue to the solution process by considering what happens to the variable. Here, ...
the variable is multiplied by 23 is added to the sumThe solution process reverses these operations, starting with the last one first. The properties of arithmetic and equality are used.
Undo additionWe can undo the addition of 3 by adding -3 to both sides of the equation.
2x +3 -3 = 9 -3
2x +0 = 6 . . . . . . . . . . . adding 3 and its additive inverse gives zero
2x = 6 . . . . . . . . . . . . . 0 is the additive identity element, so 2x+0 = 2x
Undo multiplicationWe can undo the multiplication by multiplying by the multiplicative inverse of 2. That is, we can multiply by 1/2.
(1/2)2x = (1/2)6
1x = 3 . . . . . . . multiplying 2 and its multiplicative inverse gives 1
x = 3 . . . . . . 1 is the multiplicative identity element, so 1x = x
Please note that multiplying by 1/2 is the same thing as dividing by 2. That is, multiplication and division are inverse operations.
The solution is x = 3.
CheckIt is wise to check that the solution you found makes the equation be true.
2x +3 = 9
2(3) +3 = 9 . . . . . substitute for x
6 + 3 = 9 . . . . . . . true
__
Additional comment
This solution process works for just about any "solve for ..." situation, if an algebraic solution is possible. In high school math, you are introduced to just about every kind of equation we know how to solve. The list is fairly short.
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please help me slove these problems!! offering 30 points for good answers and explanation on it
here's two, I used mathday but day with a w
Step-by-step explanation:
good website for it and it gives good explanation! Gl
5(2x-3) < 35, the solution set is {x|x <(blank) }
Answer:
x<5
Step-by-step explanation:
5(2x-3) < 35
_____ ___
5 5
2x-3<7
2x<10
_ _
2x 2x
x < 5
Lillian bought snacks for her team's practice. She bought a bag of apples for $2.36 and a 4-pack of juice bottles. The total cost before tax was $6.48. How much was each bottle of juice?
The price of each bottle of juice is $1.03
What is an equation?
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
Let 'x' be the price of each bottle of juice. Then,
According to the question,
2.36 + 4x = 6.48
or, 4x = 6.48 - 2.36
or, 4x = 4.12
or, x = 4.12/4
or, x = 1.03
Hence, the price of each bottle of juice is $1.03
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Doug bought a new car for $25,000. He estimates his car will depreciate, or lose value, at a rate of 20% per year. The value of his car is modeled by the equation V=P(1-r)^t, where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car. According to the model, what will be the approximate value of his car after 4 1/2 years
According to the equation model V=P(1-r)^t, the approximate value of Doug's car after 4¹/₂ years is $9,200.
What is the equation?The equation is a mathematical statement or model that shows that two mathematical expressions are equal.
In this situation, the mathematical expressions equal to each other are V, the car's depreciated value, and P(1-r)^t, which combines variables.
Cost of the new car = $25,000
Depreciation rate per annum = 20%
Value of the car = V
The price paid initially = P = $25,000
The annual rate of depreciation = r
Depreciation period = 4¹/₂ years
Equation model: V=P(1-r)^t
Depreciated value after 4 1/2 years, V = $25,000 (1 - 0.2)^4¹/₂
= $9,158.93
= $9,200
Thus, using the equation model, after 4¹/₂ years, the value of Doug's car has depreciated to $9,200.
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What conditions are necessary to use the chi-square goodness-of-fit test?
The chi-square goodness-of-fit test is a statistical test that is used to determine whether a sample comes from a population with a specific distribution. There are a few conditions that must be met in order to use this test:
1. The data must be collected from a random sample. This ensures that the sample is representative of the population, which is necessary for the test to be valid.
2. The data must be categorical. This means that the observations must fall into distinct categories, rather than being continuous or ordinal.
3. The expected frequencies for each category should be at least 5. This ensures that the chi-square test statistic is approximately normally distributed, which is necessary for the test to be valid.
4. The data must be independent. This means that the outcome of one observation should not influence the outcome of another observation.
If these conditions are not met, the chi-square goodness-of-fit test may not be appropriate. In such cases, it may be necessary to use a different statistical test.
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Help me on this problem!
Answer:
B. Since [tex]\triangle ABC \cong \triangle DEF[/tex] by SSS and [tex]\triangle DEF \cong \triangle GHJ[/tex] by SAS, [tex]\triangle ABC \cong \triangle GHJ[/tex] by the Transitive Property of Congruence.
The congruent statement and the reason why the triangles are congruent is (b) Since AC ≅ GJ and CB ≅ JH, AB must be congruent to GH. So, ABC ≅ GHJ by SSS
How to determine the congruent statement and the reason?From the question, we have the following parameters that can be used in our computation:
Triangles = ABC, DEF and GHJ
There are several theorems that make any two triangles to be congruent
One of these theorems is the SSS congruent theorem
The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent
From the question, we can see that the following corresponding sides on the triangles ABC and GHJ have the same mark
AC and GJ
CB and JH
This implies that these sides are congruent sides
For the triangle to be congruent by SSS, the following angles must also be congruent
AB must be congruent to GH
Hence, the congruent statement on the congruency of the triangles is (d)
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Find the two numbers which on multiplication with √360 gives a rational number. Are these numbers rational or irrational? Please explain in detail it is urgent 50 points.
A trapezoid has an area of 35 mm2. What is the height of the trapezoid?
The height of the trapezoid is 5mm.
What is a trapezoid?
A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. It is referred to as a trapezium in British and other varieties of English.
In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases. If the remaining two sides are parallel, the trapezoid is a parallelogram and has two pairs of bases; if not, they are referred to as the legs (or lateral sides). A scalene trapezoid is a trapezoid without equal-sized sides.
Given: Area of trapezoid = [tex]35mm^{2}[/tex]
We know, area of trapezoid = [tex]\frac{(a+b)}{2} .h[/tex]
⇒ [tex]\frac{(8+6)}{2} .h=35[/tex]
⇒ [tex]7h=35[/tex]
⇒ [tex]h=5mm[/tex]
Hence, the height of the trapezoid is 5mm.
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a contractor is considering a sale that promises a profit of 240000.0 dollars with a probability of 0.76 or a loss (due to bad weather, strikes, and such) of 20000.0 with a probability of 0.24. what is the expected profit?
The expected profit that the contractor will earn from the sale is equal to $177600.
Whenever a contactor does sale of a certain commodities, he expects that whatever he does he earns a profit from the sales. Profit is earned when the selling price of the commodity is more than the price at which the commodity was brought by the contractor.
The expected profit from the sale is calculated as the sum of the profits multiplied by their respective probabilities. In this case, the expected profit is given by:
Expected profit = (240000.0 * 0.76) + (-20000.0 * 0.24) = 182400.0 + (-4800.0) = $177,600
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Determine if the table shows a proportional relationship.
IT'S DUE TOMORROW
x 18.6 54.3 58.8
y 6.2 18.1 19.6
Yes, it is proportional because all y over x ratios are equivalent to one third.
Yes, it is proportional because all y over x ratios are equivalent to one fourth.
No, it is not proportional because 18.6 over 6.2 does not equal 18.1 over 54.3.
No, it is not proportional because 18.1 over 54.3 does not equal 58.8 over 19.6.
It is proportional because all y over x ratios are equivalent to one-third. I.e., the proportionality constant of the given table is k = 1/3.
How to determine the proportionality relationship?The proportionality relationship between two variables is determined by its proportionality constant. The proportionality constant is the ratio of y over x.
I.e., k = y1/x1 = y2/x2 = y3/x3 = ... = yn/xn
Calculation:The given data table is as follows:
x - 18.6, 54.3, 58.8
y - 6.2, 18.1, 19.6
So, the proportionality constant is calculated as
y1/x1 = 6.2/18.6 = 1/3
y2/x2 = 18.1/54.3 = 1/3
y3/x3 = 19.6/58.8 = 1/3
Since all three ratios are the same, then the data in the table are proportional to each other.
Therefore, option A is correct.
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How many solutions can be found for the linear equation 4(2x+3)=2(4x+6)
Answer:
All real numbers are solutions
Step-by-step explanation:
Open the bracket
4(2x+3)=2(4x+6)
8x +12=8x +12
8X-8X=12- 12
=0
The equation is an identity hence, all real numbers are solutions(1,2,3,4 etc)
Microsoft Excel Assessment Which chart type can display two different data series as different series types within the same chart? 60% 50% 4096 30% 20% 11 10% 0% France Austria Spain Germany Portugal Forested area (%) Agricultural land (%) bubble chart
An Excel Combo Chart can display two different data series as different series type. A single Excel chart with two Y-axis that allows users to compare data is known as a combo chart.
How do you arrange data in a combo chart?
Step 1: Arrange the data in the worksheet's columns and rows.
Step 2: Choose the information.
Step 3: Click the Combo chart icon on the Ribbon under the Charts group on the INSERT tab.
Step 4: Click each icon with your mouse.
step 5 Double-click the chart type that suits your data.
What is a combo chart?A combo chart combines two column charts, two line graphs, or a column chart and a line graph into one visual representation.
An Excel Combo Chart can display two different data series as different series type. A single Excel chart with two Y-axis that allows users to compare data is known as a combo chart.
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How do I use DeMoivre's theorem to find (1−i)^10?
−32i is the answer if you use DeMoivre's theorem to find (1−i)^10.
A formula for determining the powers of complex numbers is provided by De Moivre's theorem. It might be easier to comprehend de Moivre's theorem if we first look at what happens when we multiply a complex number by itself. This illustrates how the argument is multiplied by two and the absolute value is squared when squaring a complex number.
One of the most important and useful theorems in the study of complex numbers is DeMoivre's Theorem, which combines trigonometry with complex numbers. It's also helpful to find relationships between trigonometric functions at different angles. The name of the theorem pays homage to the well-known mathematician De Moivre, who made several contributions to mathematics, notably in the areas of probability theory and algebra. Attached below is the answer.
Here is another question with an answer similar to this about De Moivre's theorem: brainly.com/question/28999678
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