The system of equations that models the situation is as follows:
7t + 3w = 438
4t + 9w = 336
How to represent a situation with system of equation?Mai bought seven Christmas trees and three Christmas wreaths for a total of $438. Samantha Bought 4 Christmas trees and nine Christmas wreaths for a total of $336 from the same store.
The system of equations modelling the situation is represented as follows:
let
t = cost of Christmas trees.w = cost of Christmas wreathsTherefore,
Mai total cost:
7t + 3w = 438
Samantha total cost:
4t + 9w = 336
Hence,
7t + 3w = 438
4t + 9w = 336
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different data sets that have a median of 13
Two different data sets that have a median of 13 are
9, 10, 13, 18, 2010, 13, 13, 18How to determine the datasets?From the question, we have the following parameter
Median =13
The median of a dataset is the number at the middle position
So, we can make use of the following dataset
9, 10, 13, 18, 20
This is so because the middle number is 13
Another possible dataset is
10, 13, 13, 18
Similarly, this is because the middle number is 13
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In 1980, about 17.7 million households had cable television. This was about 25.8% of the households that had cable in 2000. How many households had cable in 2000?
In 2000, cable was available in 45683700000 homes.
What is percentage?Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
In 1980, 17700000 = 25.8%\s1% = 4566600000
Then, in 2000, there were 45683700000 households (17 700 000 + 4566 600 000).
Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages. Let's assume that we are interested in the proportion of employed women who are female.
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When would you calculate an expected value? a. When your data points occur on different datesb. When your data points have various probabilities of occurringc. When you need to know the exact outcome of a future, unknown eventd. When you only have one data point
We calculate an expected value when the given data points have various probabilities of occurrence .
The expected value , applies best when we are performing the test or experiment many times. For example, EV applies well to gambling situations to describe expected results for thousands of gamblers per day, repeated day after day after day. However, the EV does not very accurately predict one particular outcome on one specific test.
For example, when drawing a playing card from a standard deck, on one specific draw, the likelihood of drawing a 2 is equal to the likelihood of drawing a 6 or 7 or 8 or any other numbered card.Over many many draws, the theoretical value to expect is 6.538. Obviously, there is no “6.538” card in the deck. But if you were gambling, you would expect to draw a card higher than 6 more often than not.To learn more about expected value
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Find the exact value of sin(u + v) given that sinu = 5/3 and cos v =-4/5. (Both u and v are in Quadrant I.)
The exact value of sin(u + v), obtained using trigonometric identities is for sine and cosine is 16/65
What are trigonometric identities?Trigonometric identities are equations that involve trigonometric functions that are valid for all values of the input variable.
The possible value of sin(u) obtained from a similar question posted online is; sin(u) = 5/13
Both u and v are in quadrant II
The trigonometric identity of the addition formula for the sine of the sum of two angles, indicates;
sin(u + v) = sin(u)·cos(v) + sin(v)·cos(u)
sin(u) = 5/13
cos(v) = -4/5
sin(v) = √(1 - (cos(v))²)
Therefore;
sin(v) = √(1 - (-4/5)²) = 3/5
cos(u) = √(1 - (sin(v))²)
Therefore;
cos(u) = √(1 - (5/13)²) = 12/13
Therefore;
sin(u + v) = (5/13) × (-4/5) + (3/5) × (12/13) = 16/65
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12) Which is a value for h that makes the following true?
Answer:-7
Step-by-step explanation:
-3(-7)+6>=24
21+6>=24
27>=24
Answer:
-7
Step-by-step explanation:
-3h + 6 is greater than or equal to 24.
Solve by simplifying the equation to get h standing alone
1. Subtract the 6 on both sides. -3h [tex]\geq[/tex] 18
2. Divide by -3 on both sides. h [tex]\leq[/tex] -6 (You swap the sign when you divide by a negative.
3. Choose the value less than -6. -7
A wall is being built with 16,351 stones the buliders have placed 8,361 stones and have 7,944 stones left Do they have enough stones how many more stones do they need?
1. What quantities are given in the problem and what do they mean?
2.Show how to find the number of stones the builders have in all then write and solve an equation do they have enough?
3.Show how to find the difference of how many more stones the builders need then write and solve an equation
They do not have enough stones and the quantity that they need is of 46 stones.
How to verify if they have enough stones?The quantities in this problem are given as follows:
16351: total number of stones in the wall.8361: number of stones that already have been placed in the wall.x number of stones that still need to placed into the wall.Then the equation to obtain the solution for x is given as follows:
x + 8361 = 16351.
x = 16351 - 8361
x = 7990 stones remaining.
The amount of stones that they have is given by:
7944.
Which is less than 7990 stones, hence the do not have enough stones and the quantity that they need is given by the subtraction of 7990 and 7944 as follows:
7990 - 7944 = 46 stones.
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Find the sum of (8 + 2 − 4) and (3 − 5).
Answer:
4
Step-by-step explanation:
(8+2-4)+(3-5)
(10-4)+(-2)
6-2
4
Hopes this helps please mark brainliest
per the barron's report the average weeks unemployed is 21.5 (population mean) with a population standard deviation of 5 weeks and a sample of 55. in the next five questions we will be calculating the probability that the sample of 55 will provide a mean within 1 week of the population mean. what is the probability to 4 decimals for (x<22.5)? use the rounded standard error of the mean in calculations.
Probability up to 4 decimal would be 0.0694.
Data: mean = 21.5, standard deviation Σ = 5
n = 55
μ = 21.5
n = 5 √55 = 0.6742
P( X < 20.5)
= P((μ X ) / Σbar X < (20.5 - 21.5) / 0.6742)
= P(z < -1.48)
= 0.0694
Using standard normal table.
Probability = 0.0694
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.
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chapter 17 review questions how does a b-tree differ from a b -tree? why is a b -tree usually preferred as an access structure to a data file?
The difference in b-tree and b +tree, b -tree is a self balancing tree data structure that maintains sorted data and b +tree is a modified version of b -tree.
b -tree is used to sort the data with various pieces facilities such as insertion ,deletion and search etc whereas b +tree is a modified version of b -tree providing all the functions smoothly and quickly .
In b -tree, both internal nodes and leaf nodes are used to store records and keys whereas in b +tree keys are stored in internal nodes whereas records are storing leaf nodes
In b +tree, no duplication is allowed but in b +tree duplication may occur
A b +tree usually preferred as an access structure to a data file as as the height of the tree remains balanced and less as compared to b -tree . We can assess the data stored in b +tree sequentially as well as directly . keys are used for indexing . Faster search queries as the data is stored only on a leaf nodes.
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1. (04.02)
What is the quotient when x³ - 5x² + 2x + 5 is divided by x - 2?
Answer: x²+3x-4 i
Step-by-step explanation: pretty sure its A
Please help again 10 points again to first one
Answer: it would be 18 candies that are left
Step-by-step explanation:
I did the math
Explain what the solutions to the inequality represent. Choose all that apply. (2 points) A. The outside air temperature must be greater than −40° F. B. The outside air temperature must be greater than 120° F. C. The outside air temperature must be less than 120° F. D. The outside air temperature must be less than or equal to 120° F. E. The outside air temperature must be less than −40° F. F. The outside air temperature must be greater than or equal to −40° F.
The linear inequality to represent the temperature is -40 < x < 120
What is Linear InequalityLinear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1. There are several ways to represent various kinds of linear inequalities.
Linear inequalities are usually in form of expressions where any two values are often compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be numerical or algebraic or a combination of both.
But in this case, we wouldn't need that as we are only required to represent the problem with an inequality.
The linear inequality -40 < x < 120 shows that the outside air must be between the range of -40 degrees to 120 degrees.
This can be explained as the least temperature must be above -40°F and the highest temperature must not exceed 120°F
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You have saved $2.82 to buy a magazine that costs $7.39. Estimate how much more money you need to buy the magazine
HELPPPPPP MEEEEEEEE Ps. THIS IS DECIMALS AND STUFF
Zucchini costs $1.50 per pound and broccoli costs $2 per pound how many pounds each of zucchini and broccoli can andre get that ways 10 pounds and costs $17
If Zucchini costs $1.50 per pound and broccoli costs $2 per pound. With the amount Andre has Andre can get
Zucchini = $15broccoli = $34What is unit price?The cost per unit of an item is represented by the unit price.
To determine the unit price of an item, we divide the price of a specific number of units by the number of units.
How to find the quantity Andre can getWith the cost of Zucchini at $1.50 per pound 10 pounds of zucchini is
= $1.50 * 10
= $15
With the cost of broccoli at $2 per pound, 17 pounds of broccoli is
= $2 * 17
= $34
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What i the exact difference from (-4, 2) to (4, 6)
A) qrt 24 unit
B) qrt 86 unit
C) qrt 100 unit
D) qrt 128 unit
Option D √128 unit is the precise distance between the two points (-4, -2) and (4, 6).
Given,
The points;
(x₁, y₁) = (-4, -2)
(x₂, y₂) = (4, 6)
We have to find the exact distance from the points;
Here,
Distance between two points (x₁, y₁) and (x₂, y₂);
D = [tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2} -y_{1})^{2} }[/tex]
Here,
(x₁, y₁) = (-4, -2)
(x₂, y₂) = (4, 6)
Then,
Distance, D = [tex]\sqrt{(4 - -4)^{2} +(6--2)^{2} }[/tex]
Distance, D = [tex]\sqrt{8^{2}+8^{2} }[/tex]
Distance, D = [tex]\sqrt{64+64}[/tex]
Distance, D = √128
That is,
The exact distance between two points (-4, -2) and (4, 6) is option D √128 unit
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Use the distributive property to remove the parentheses.
-(2u-w-2)
Please help.
Solve the inequality show all your work
-4x+5>37
The solution for x in the inequality expression is x < -8
How to determine the solution for x?From the question, we have the following inequality expression that can be used in our computation:
-4x+5>37
Subtract 5 from both sides of the inequality
So, we have
-4x + 5 - 5 >37 - 5
Evaluate the like terms
This gives
-4x > 32
Divide both sides by -4
x < -8
Hence, the solution is x < -8
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A store receives shipments of peaches and wants to categorize them by weight. Drag each shipment to the category that shows the ratio of peaches to pounds in that shipment
the ratio of peaches to pounds in that shipment is Category 2peaches/1lb: Shipment: 1 peach/0.5lb
Shipment: 12 peaches/6lb
Category 1peach/1,5lb:
Shipment: 3peaches/4.5lb
Shipment: 18peaches/27lb
Category 1.5peach/1lb:
Shipment: 15peaches/10lb
To find what category correspond to each shipment, you have to obtain the proportion for each category.
Category 2peaches/1lb proportion of 2.
Category 1peach/1,5lb proportion of 2/3:
Category 1,5peaches/1lb proportion of 3/2:
Now, reduce the shipments to its simplest form.
18/27 simplified by 9 = 2/3 proportion.
1/0.5 multiplied by 2 = 2 proportion.
12/6 simplified by 6 = 2 proportion.
3/4.5 simplified by 1.5 = 2/3 proportion.
15/10 simplified by 5 = 3/2 proportion.
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an open box is to be made from a two-foot by three-foot rectangular piece of metal by cutting equal squares from the corners and turning up the sides. find the volume of the largest box that can be made in this manner. round your final answer to the nearest hundredth.
The volume for the largest box will be 1.056 foot³. This can find out by application of differentiation.
What is AOD?
AOD is nothing but application of differentiation. It implies scopes where we can use differentiation to make our calculations easy.
Here, given
Length and breadth = 2,3 foot
Let us consider length of side of square = x
So, after cutting squares left sides of rectangular sheet = 2-2x , 3-2x
So, volume = (2-2x)*(3-2x)*x
v = 4x³ - 10x² + 6x
To find largest volume , [tex]\frac{dv}{dx}[/tex] = 0
[tex]\frac{dv}{dx}[/tex] = 12x² - 20x + 6
12x² - 20x + 6 = 0
x = 0.4 , 1.3
But, for 1.3 volume will be negative i.e. not possible.
So, volume = 2.2*1.2*0.4
= 1.056 foot³
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The radius of a circular disk is given as 17 cm with a maximum error in measurement of 0.2 cm.
(a) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.)
(b) What is the relative error? (Round your answer to four decimal places.)
(c) What is the percentage error? (Round your answer to two decimal places.)
The a)estimated error in area is 21.352[tex]cm^2[/tex], b)relative error is 0.0235 and c)percentage error is 2.35%.
Given,
radius of disk, r=17cm
maximum error=0.2cm
a)estimation of maximum error in calculated area,
area of disk,
[tex]A=\pi\ r^2[/tex]
differentiating on both sides
[tex]dA=2\pi\ rdr\\[/tex]
here dr = 0.2cm which is error
[tex]dA=2\pi\(17)(0.2)\\\\\\dA=21.352\ cm^2[/tex]
b)To find relative error use formula,
Relative error=[tex]\frac{dA}{A}[/tex]
[tex]=\frac{21.352}{\pi*17^2}\\\\=\frac{21.352}{907.46}\\\\=0.0235[/tex]
c)then percentage error will be
percentage error=0.0235*100=2.35%
Thus, the estimated error in area is 21.352[tex]cm^2[/tex],relative error is 0.0235 and percentage error is 2.35%.
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3. At the school festival, you can win a bicycle by pulling a red bull out of the bag. The first bag has 52 white balls, 27 green balls, and 11 red balls. The second bag has 25 white balls, 25 green balls, 25 yellow balls, and 10 red balls.
a. What are the odds of pulling a red ball from the first bag?
b. What are the odds of pulling a red ball from the second bag?
a) The Odds of pulling a red ball from the first bag is; 12.2%
b) The Odds of pulling a red ball from the second bag = 10/85 = 0.1176 = 11.76%
What is the probability of selection?We are given;
Number of white balls in first bag = 52
Number of green balls in first bag = 27
Number of red balls in first bag = 11
Total number of balls in first bag = 52 + 27 + 11 = 90 balls
Number of white balls in second bag = 25
Number of green balls in second bag = 25
Number of red balls in second bag = 10
Number of yellow balls in second bag = 25
Total number of balls in second bag = 25 + 25 + 10 + 25 = 85 balls
a) Odds(probability) of pulling a red ball from the first bag = 11/90 = 0.122 = 12.2%
b) Odds(probability) of pulling a red ball from the second bag = 10/85 = 0.1176 = 11.76%
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A vehicle uses 1\frac{1}{8} gallons of gasoline to travel 13\frac{1}{2} miles. Create a rate to represent the miles the vehicle can travel per gallon of gasoline.
The vehicle can travel 12 miles per gallon of gasoline.
What is the Mixed fraction ?
A mixed fraction is one that is represented by both its remainder and quotient. Consequently, a mixed fraction is created by combining a whole number and a proper fraction.
What is the Rate ?
A rate is the comparison of two comparable amounts expressed in different units. If the ratio's denominator is written as a single unit of one of these quantities, and if it is assumed that this quantity can be modified systematically (i.e., is an independent variable), then the numerator of the ratio indicates the comparable rate of change in the other (dependent) variable.
The vehicle travels 13\frac{1}{2} by using 1\frac{1}{8} gallons of gasoline.
since the units are in mixed fraction, we can simplify it to simple fraction,
distance travelled= 13\frac{1}{2} = [(13 × 2) + 1] / 2 = 27/2 miles.
gasoline used= 1\frac{1}{8} = [(1×8)+1] /8 = 9/8 gallons.
∴ Miles per gallon of gasoline = distance travelled ÷ gasoline used
= 27/2 miles ÷ 9/8 gallons
= 12 miles per gallon of gasoline.
Hence, The rate of miles per gallon of gasoline is 12 miles/gallon of gasoline.
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An animal rescue group recorded the number of adoptions that occurred each week for three weeks:
There were x adoptions during the first week.
There were 10 more adoptions during the second week than during the first week.
There were twice as many adoptions during the third week as during the first week.
There were a total of at least 50 adoptions from the animal rescue group during the three weeks.
Write an inequality that represents all possible values of x, the number of adoptions from the animal rescue group during the first week.
Answer:
Step-by-step explanation:
An inequality that represents all possible values of x is; x ≤ 10
How to solve Inequality word problems?
We are given that there were x number of adoptions during the first week.
We are told that there were 10 more adoptions during the second week than during the first week. Thus;
number of adoptions in second week = 10 + x adoptions
There were twice as many adoptions during the third week as during the first week. Thus;
Number of adoptions in third week = 2x adoptions
There were a total of 50 adoptions from the animal rescue group during the three weeks. Thus, we can say that;
x + 10 + x + 2x ≤ 50
4x ≤ 50 - 10
4x ≤ 40
x ≤ 10
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one thousand independent rolls of a fair die will be made. compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively.
The probability that the number 6 will appear between 150 and 200 times inclusively is 0.926.
In the given question, one thousand independent rolls of a fair die will be made.
We have to compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively.
Let n=1000 are independent trails.
The probability of success is constant, p=1/6
The probability of success is not constant,
q=1-1/6 = 5/6
let X be the number of times the die shows a 6.
μ = np
μ = 1000*1/6
μ = 166.7
σ=√npq
σ=√1000*1/6*5/6
σ=√5000/36
σ=11.785
Now we used the correlation continuity for finding the probability that number 6 will appear between 150 and 200 times is
P(150≤X≤200)=P(X≤200)-P(X<150)
P(150≤X≤200)=P(Z≤(200+0.5-166.7)/11.785)-P(Z≤(150-0.5-166.7)/11.785)
P(150≤X≤200)=P(Z≤2.87)-P(Z≤-1.46)
P(150≤X≤200)=0.998-0.072
P(150≤X≤200)=0.926
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Wade Boggs played professional baseball for three different teams in 18 years. The table shows his total of number hits for each team Red Sox 2,098 , Yankees 702, Devil Rays 210. Suppose he made the same numbers of hits each of the 18 years. If t= total number of hits and a = number of hits per year, which two equations can be used to determine the number of hits he made each year ?
The no. of hits made by him in each year is 167.
What is an Equation ?
A formula known as an equation when it uses the equals sign to express the equality of two expressions.
Given that,
total no. of hits in 18 years = t
the no. of hits for the teams are 2098 (Red Sox), 702 (Yankees) and 210(Devil Rays).
hence, the sum of hits in three teams should be equal to total no. of hits in 18 years.
∴ we get, t = 2098 + 702 + 210 = 3010 ..........equation 1
Now, we know that no. of hits per year is ' a ' and he made the same numbers of hits each of the 18 years.
So, total no. of hits can also be calculated as :
no. of hits per year × 18 = t
no. of hits per year × 18 = 3010 ( from equation 1 )
a × 18 = 3010
a = 3010/18 = 167 hits each year ( approx)
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The mean of 11 numbers is 7 one of the numbers, 13, is deleted. What is the mean of the remaining 10 numbers?.
If mean of 11 numbers is 7 one of the numbers, 13, is deleted then the mean of remaining 10 numbers is 6.4
The mean of 7 numbers = 11
We know,
Mean = Sum of the terms / Number of terms
Substitute the values in the equation
11 = Sum of the terms / 7
The sum of the terms = 11 × 7
= 77
Number 13 is deleted
Sum of the terms = 77 - 13
= 64
Number of terms = 11 - 1
= 10
The mean = Sum of the terms / Number of terms
Substitute the values in the equation
= 64 / 10
= 6.4
Hence, the mean of the remaining 10 numbers is 6.4
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Mars has an atmosphere composed almost entirely of carbon dioxide, with an average temperature of -63 ?C.What is the rms speed of a molecule in Mars's atmosphere? Assume R = 8.315 J/mol?K.Express your answer to two significant figures and include the appropriate units.
The RMS speed of a molecule in Mars's atmosphere is; 345.11 m/s
How to calculate the RMS Speed?
The root mean square (RMS) speed of a gas molecule is simply defined as the classical average speed that a molecule possesses within a collection. The RMS speed of a gas is calculated using the equation:
υ = √(3RT/M)
Where;
R is the gas constant = 8.315 J/mol
T is the temperature (in Kelvin)
M is the molar mass of the gas
Temperature in degree kelvin = -63 + 273.15 = 210.15 K
Molar mass of carbon dioxide is: 44.01 g/mol = 0.04401 kg/mol
Thus;
υ = √(3 * 8.315 * 210.15/0.04401)
υ = 345.11 m/s
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Tell whether the expression is positive or negative without evaluating it. -3/10 X (-8/15)
The expression -3/10 X (-8/15) is positive
Expression
Expression in mathematics has two or more variables, terms and constants. Also, arithmetic expression contains only numbers and mathematical operators and algebraic expression
The expression has negative sign and from mathematical calculation we already know the following relation:
+ x + = +
positive multiply by positive equals Positive
- x - = +
Negative multiply by Negative equals Positive
+ x - = -
Positive multiply by Negative equal Negative
hence, - [tex]\frac{3}{10}[/tex] x - [tex]\frac{8}{15}[/tex]
The negative sign multiply by -3/10 X (-8/15) sign will give positive.
Therefore, the expression -3/10 X (-8/15) is positive.
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Triangle abc is defined by the points a(2,9), b(8,4), and c(-3,-2). Complete the following equation for a line passing through point c and perpendicular ab. Y = x +.
When triangle ABC is defined by the coordinates a(2,9), b(8,4), and c, the equation for the line is 5y=6x+8 (-3,-2).
What is equation of line?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical phrase with two equal sides and an equal sign is called an equation. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations. Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each side.
Here,
A=(2,9)
B=(8,4)
C=(-3,-2)
The slope of line AB,
m=(y2-y1)/(x2-x1)
=(4-9)/(8-2)
=-5/6
Slope of line perpendicular to AB,
m1=-1/m
=-1/(-5/6)
=6/5
This line pass through (-3,-2).
y=mx+c
-2=6/5*(-3)+c
c=-2+18/5
c=8/5
The equation of line,
y=6/5x+8/5
5y=6x+8
The equation of line is 5y=6x+8 when triangle ABC is defined by the points a(2,9), b(8,4), and c(-3,-2).
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A car corporation produced 940
fewer cars this month than last.
Write a signed number to represent this month's change in production
The signed number to represent ''A car corporation produced 940 fewer cars this month than last'' is - 940.
What is meant by signed number representations ?Negative integers in binary number systems must be encoded in computation using signed number representations.In mathematics, negative integers in any base are denoted by a minus sign ("-") before them. However, numbers are solely represented as bit sequences, without any additional symbols, in RAM or CPU registers. The four most popular ways to express signed integers using the binary numeral system are offset binary, ones' complement, two's complement, and sign-magnitude. Some of the other techniques, such negative binary with the base 2, employ implicit signs rather than explicit ones. For different bases, whether positive, negative, fractional, or other elaborations on such themes, corresponding algorithms can be developed.Learn more about signed number refer to :
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