The total area square feet of bark dust should Jon Marc order is 839.1 square feet.
What is area?
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Here we know that , area of the circle = [tex]\pi r^2[/tex] square unit.
Now radius of one flower bed = 6.5 feet. Then,
Area of the bed = [tex]3.14\times 6.5^2[/tex] = 132.6 square feet,
Now diameter of another bed = 30 feet then,
Radius = 30/2 = 15 feet. Then
Area of the bed = [tex]3.14\times15^2[/tex] = 706.5 square feet.
Then total square feet of bark dust should Jon Marc order is
=> 132.6 + 706.5 = 839.1 square feet.
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A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The IQR of 10 is the most accurate to use, since the data is skewed.
The range of 10 is the most accurate to use, since the data is skewed.
The IQR of 45 is the most accurate to use to show that they need more money.
The range of 45 is the most accurate to use to show that they have plenty of money.
Option B : The range of 45 is the most accurate measure of variability to use to represent the data.
The range is the difference between the highest and lowest values in a dataset. In this case, the highest donation was $55 and the lowest was $10, so the range is:
range = highest value - lowest value = $55 - $10 = $45
Since the range takes into account all the values in the dataset, it is an appropriate measure of variability for this skewed dataset. The IQR (interquartile range) would also be a valid measure of variability, but it is less appropriate for skewed data because it only takes into account the middle 50% of the data and is less affected by extreme values. In this case, the extreme values (the two $55 donations) have a large effect on the distribution of the data, so the range is a more appropriate measure of variability.
Therefore, the charity should use the range of $45 to represent the variability of their donations.
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एउटा मोटरसाइकलको मूल्य वि.सं 2070 मा रु. 250,000 थियो र वि.सं. 2072 मा रु. 160,000 छ भने वार्षिक मिश्रह्रास दर पत्ता लगाउनुहोस् । The price of a motorcycle was Rs 250,000 in 2070 B.S. and in 2072 B.S., it is Rs 1,60,000. Find the annual rate of compound depreciation.
Step-by-step explanation:
Solution,
P=2,50,000
T=2072-2070
=2 years
Pt=1,60,000
Pt=P(1-D/100)^2
1,60,000=2,50,000{(100-D)}^2
100
1,60,000/2,50,000={(100-D)}^2
100
0.64={(100-D}^2
100
(0.8)^2={(100-D)}
100
80=100-D
100
80=100-D
D=100-80
D=20%
Hence, the deprecation rate is 20% over the period of 2 years
Solve the system using the substitution
y = -2x + 20 
6x - 5y =12
The solution is _.
Answer:
x=7, y=6
Step-by-step explanation:
One of the ways we can find a value of a variable in a multiple part equation system is via substitution.
What is substitution?
Substitution works by making one equation equal to a variable with no coefficients (that is, a number without any action being done to the variable), then using this said equation and plugging it into the other equation to find the value of one variable. Then, using this value that was found can be plugged again to one of the two equations to find the other variable.
In our situation, one of the equations ([tex]y=-2x+20[/tex] ) is already equal to y; so we can use this equation to plug it in the second equation.
- Given: [tex]y=-2x+20\\6x-5y=12[/tex]
- Insert the first equation: [tex]6x-5(-2x+20)=12[/tex]
- Distribute the -5: [tex]6x+10x+-100=12[/tex]
- Combine like terms: [tex]16x-100=12[/tex]
- Isolate the variable x: [tex]16x-100=12\\~~~~~~+100+100\\16x=112\\\frac{16x}{16} =\frac{112}{16} \\x=7[/tex]
Now that we have the variable x=7, we can use this number to find the value of the variable y.
- Given: [tex]y=-2x+20[/tex]
- Plug in the known variable value: [tex]y=-2(7)+20\\[/tex]
- Solve: [tex]y=-14+20\\y=6[/tex]
Therefore, x=7, and y=6 is your final answer.
Additionally, we can cross reference this on a graphing calculator. Plug both of those formulas in as so, and the intersection between the two lines will be the answer of what x and y are equal to, (x,y).
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x=7 , y=6
_________________________
Substituting y = -2x + 20 =
6x - 5(-2x + 20) = 12
Simplifying =
6x + 10x - 100 = 12
Combining like terms =
16x - 100 = 12
we add 100 =
16x = 12 + 100
16x = 112
Divide both sides by 16 =
x = 112 / 16
x = 7
y = -2(7) + 20
y = -14 + 20
y = 6
x=7 , y=6
given the equations below what is the frist x value where g(x)>f(X)
f(X)=4X=25
g(X)=2(5)x
Answer:There seems to be a typo in the equation for f(x). I will assume that the correct equation is:f(x) = 4x - 25To find the first x value where g(x) > f(x), we can set the two equations equal to each other and solve for x:g(x) = f(x)
2(5)x = 4x - 25
10x = 4x - 25
6x = -25
x = -25/6
Step-by-step explanation:However, we need to check if this value satisfies the condition g(x) > f(x):g(-25/6) = 2(5)(-25/6) = -25
f(-25/6) = 4(-25/6) - 25 = -75/3 - 25/1 = -100/3Therefore, g(x) > f(x) is not true for x = -25/6. We need to keep looking for a larger value of x where g(x) > f(x).To do this, we can graph the two functions and look for the point where the graph of g(x) is above the graph of f(x). Alternatively, we can simply plug in some larger values of x and compare the values of g(x) and f(x) until we find the first x value where g(x) > f(x).Let's try plugging in x = 0:g(0) = 2(5)(0) = 0
f(0) = 4(0) - 25 = -25Since g(0) = 0 and f(0) = -25, we have g(x) > f(x) for x > 0. Therefore, the first x value where g(x) > f(x) is x = 0.
a job recruitment firm runs assessment days for their clients, where potential employees are given a series of tests. part of this assessment day is a multiple-choice exam on general knowledge. the firm is trying to determine if the time of day that the test is given is a factor in how well candidates perform. a study is done, in which three random samples of people are given the same test, with one sample given the test at 9:00 am, one sample given the test at midday, and the final sample given the test at 3:00 pm. each sample has 60 candidates.
A one-way ANOVA test is performed. The following table shows the relevant figures in the ANOVA test: Sum of squares Degrees of freedom Mean squares F P
Between groups 1,493.76 2 746.88 3.4842 0.0328 Within groups 37,941.72 177 214.36
Total 39,435.48 179 Calculate the coefficient of determination, R^2. Give your answer as a percentage to 2 decimal places. R^2 = _____ %
The coefficient of determination (R^2) is 3.78%.
To calculate the coefficient of determination (R^2), we need to first find the total sum of squares (SST) and the sum of squares error (SSE) from the given ANOVA table. SST is the variation between the observed values and the mean value of all observations. SSE is the variation between the observed values and the group means.
SST = Between groups + Within groups = 1,493.76 + 37,941.72 = 39,435.48
SSE = Within groups = 37,941.72
R^2 = (SST - SSE) / SST
Plugging in the values, we get:
R^2 = (39,435.48 - 37,941.72) / 39,435.48
R^2 = 0.0378
To convert this to a percentage, we multiply by 100 and round to two decimal places:
R^2 = 3.78% (rounded to 2 decimal places)
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Help can someone help me
Answer:
70
Step-by-step explanation:
Emily and Josie were randomly choosing a colored chip from the ones show below. What is the probability that Emily will choose a blue chip, keep it, and then Josie chooses a red chip?
The probability that Emily chooses a blue chip and Josie chooses a red chip is 3/28.
What is mutually exclusive events?Events that are mutually incompatible cannot take place at the same moment. If one thing happens, the other thing can't happen. For instance, if we flip a coin, receiving heads and getting tails are mutually exclusive events. The likelihood of two mutually exclusive occurrences happening simultaneously is zero.
Events that are independent of one another are said to be independent. The likelihood of the other event happening is unaffected if one event happens.
Given, 3 blue chips and 2 red chip from a total of 8 chip we have:
P(Emily chooses blue and Josie chooses red) = P(Emily chooses blue) × P(Josie chooses red after Emily chose blue)
= (3/8) × (2/7)
= 6/56
= 3/28
Hence, the probability that Emily chooses a blue chip and Josie chooses a red chip is 3/28.
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The complete question is:
Emily and Josie were randomly choosing a colored chip from the ones show below. What is the probability that Emily will choose a blue chip, keep it, and then Josie chooses a red chip?
The number of chips there are 8 chips. 3 are blue, 2 are red.
The numbers on the number line end at 8. The arrow shows that numbers beyond 8 are also in the solution set. Given Mrs. Sanchez's problem, do you think the solution set can extend forever, or will there be a limit? Explain.
Solution defines by [tex]x\geq 5[/tex]
Define the term number line?A number line is typically a horizontal line that extends infinitely in both directions. It is used to represent both positive and negative numbers, and each point on the line corresponds to a unique real number.
Numbers to the right of zero are positive and increase as you move further to the right, while numbers to the left of zero are negative and decrease as you move further to the left. Zero is the midpoint of the number line and is neither positive nor negative.
Based on the information you've provided about the number line, it is clear that the solution set can extend beyond 8, as indicated by the arrow. This means that there are numbers greater than 8 that are included in the solution set.
Solution defines by [tex]x\geq 5[/tex]
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For Mrs. Sanchez's problem, the solution set can extend forever. Using the number line x ≥ 5.
Define the term number line?A number line is typically a horizontal line that extends infinitely in both directions. It is used to represent both positive and negative numbers, and each point on the line corresponds to a unique real number.
Numbers to the right of zero are positive and increase as you move further to the right, while numbers to the left of zero are negative and decrease as you move further to the left. Zero is the midpoint of the number line and is neither positive nor negative.
Based on the information you've provided about the number line, it is clear that the solution set can extend beyond 8, as indicated by the arrow. This means that there are numbers greater than 8 that are included in the solution set.
Solution defines by x ≥ 5
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mark -1/2 on a number line?
Answer: Answer is below <3
Step-by-step explanation:
It’s in-between zero and negative one because it’s a half number. (Not fully one yet)
Therefore, -1/2 would be in-between the number 0 and -1.
Answer:
-1/2 is "-0.5" in form of decimal
So,
the answer will come between 0 and -1
Kindly mark the answer brainliest
Which of the following is an example of an inequality?
The equation which is an example of an inequality include the following: C. 4x > -16
What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).In this context, we can reasonably infer and logically deduce that the only equation with an inequality symbol is 4x > -16 and as such, it is an example of an inequality.
By evaluating, we have:
4x > -16
x > -16/4
x > -4
In conclusion, we can logically deduce that x is greater than negative four (-4).
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Complete Question:
Which of the following is an example of an inequality
A. x+5=10
B. 2x-3=7
C. 4x>-16
D. 3x-2
Please help me i need it for today!
The solution to the problems are;
1. Area = 108 square feet
2. Area = 342 square feet
3. x = $1, 890, x = $1764
4. Cost, x = $151. 2, $117. 6
How to determine the valuesThe formula for calculating the area of a rectangle is expressed with the equation;
A = lw
Such that;
l is the length of the rectangle.w is the width of the rectangle.From the diagram shown, we have that;
The deck is gray
The garden is white
1. The area of the garden in design A
Area = 9(12) = 108 square feet
2. The area of the deck in design A is;
Area = 18(25) = 450 square feet
The area of the deck without the garden = 450 - 108
Area = 342 square feet
3. If $4. 20 = 1 square feet in design A
Then, x = 450 square feet
x = $1, 890
Area of deck of design B = 21(20) = 420 square feet
cost = $1764
4. If $1. 40 = 1 square feet of garden A
Then, x = 108 square feet
Cost = $151. 2
For garden of design B
Area = 1/2 × (12)(14) = 84 square feet
Then, cost = $117. 6
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There are four points $T,I,P,$ and $O$ in the plane. Suppose $\triangle TIP$ and $\triangle TOP$ are isosceles triangles. Also suppose that $TI=5,$ $PI=7,$ and $PO=11$.
What are all the possible lengths TP
The sum οf all pοssible lengths fοr TP is 12
What is triangle ?A triangle is a type οf pοlygοn with three sides; the pοint where the twο sides meet is knοwn as the vertex οf the triangle. Between twο sides, an angle is created. One οf geοmetry's key cοmpοnents is this.
Triangle prοperties are necessary fοr sοme fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry. Based οn its angles and sides, a triangle can be classified intο variοus types.
Given that triangle TIP and triangle TOP are isοsceles triangles with sides;
TI = 5, PI = 7, PO = 11
Therefοre, given that triangle TIP is an isοsceles triangle, the length οf segment TP will be equal either the length οf segment TI οr segment PI which give;
TP = TI 5 οr TP = PI = 7
The sum οf all pοssible lengths fοr TP is given by the sum οf the twο unequal sides οf triangle TIP which gives;
The sum οf all pοssible lengths fοr TP = 5 + 7 = 12.
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kevin's father age is 5 years more than three times kevin's age. find kevin's age , if his father is 44 years old
Answer:
Kevin's age = 13
Step-by-step explanation:
Now we have to,
→ Find Kevin's age, if his father's age is 44.
Let us assume that,
→ Kevin's age = k
Forming the equation,
→ 3k + 5 = 44
Then the value of k will be,
→ 3k + 5 = 44
→ 3k = 44 - 5
→ 3k = 39
→ k = 39/3
→ [ k = 13 ]
Hence, the value of k is 13.
The age of Kevin is 13 years.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Given that, Kevin's father age is 5 years more than three times Kevin's age.
Let the age of Kevin be k.
Then, the age of Kevin's father is 3k+5
Kevin's father is 44 years old
Thus, 3k+5=44
3k=39
k=13
Therefore, the age of Kevin is 13 years.
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Rewrite from standard form to vertex form
F(x)=x^2-4x+49
Accοrding tο the given infοrmatiοn, the vertex οf the parabοla is at (2, 45), and the minimum value οf the functiοn is 45, which οccurs at the vertex.
What is the vertex fοrm?The vertex fοrm οf a quadratic functiοn is a way οf writing a quadratic functiοn in the fοrm: f(x) = a(x - h)² + k, where (h, k) is the vertex οf the parabοla, a is a cοefficient that determines the shape and directiοn οf the parabοla, and x is the input variable. This fοrm is called the vertex fοrm because it prοvides direct infοrmatiοn abοut the vertex οf the parabοla, which is the pοint where the parabοla changes directiοn.
Tο rewrite the quadratic functiοn f(x) = x² - 4x + 49 frοm standard fοrm tο vertex fοrm, we need tο cοmplete the square by adding and subtracting a cοnstant term inside the parentheses, such that the functiοn can be expressed in the fοrm a(x - h)² + k.
f(x) = x² - 4x + 49
We can cοmplete the square as fοllοws:
f(x) = (x² - 4x + 4) + 45
= (x - 2)² + 45
Therefοre, the vertex fοrm οf the functiοn f(x) is:
f(x) = (x - 2)² + 45
The vertex οf the parabοla is at (2, 45), and the minimum value οf the functiοn is 45, which οccurs at the vertex.
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Check the equation in slope-intercept form to make sure it represents the graph. If it doesnt, cross out the answer and write the correct equation
PLSSSSS!!!!! help i need the answers FAST
The equation y = 2x + 4 is in slope-intercept form with m = 2 and b = 4. This means that the line has a slope of 2 and intersects the y-axis at the point (0, 4).
Define the term equation?An equation is a statement that asserts the equality of two expressions or values, typically separated by an equal sign (=). The expressions or values on either side of the equal sign are called the "sides" of the equation.
Equations are used to represent mathematical relationships between variables and to solve problems involving those variables.
To check if an equation is in slope-intercept form, we need to ensure that it has the form:
y = mx + b
The equation y = 2x + 1/3 is also in slope-intercept form with m = 2 and b = 1/3. This means that the line has a slope of 2 and intersects the y-axis at the point (0, 1/3).
The equation y = 3x/2 + 1 is in slope-intercept form with m = 3/2 and b = 1. This means that the line has a slope of 3/2 and intersects the y-axis at the point (0, 1).
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An oil company is considering two sites on which to drill, described as follows: Site A: Profit if oil is found: $120 million Site B: Profit if oil is found: $180 million Loss if no oil is found: $20 million Loss if no oil is found: $30 million Probability of finding oil: 0.2 Probability of finding oil: 0.1
Two potential locations for drilling are under consideration by an oil corporation.
a) The estimated profit is higher at Site A.
b) We can state that Site A has a larger expected profit than Site B by $17 million because the expected profit for Site A is higher than the expected loss for Site B.
To find the expected profit for each site, we need to multiply the profit from finding oil by the probability of finding oil and subtract the loss from not finding oil multiplied by the probability of not finding oil.
For Site A:
Expected profit = (Profit if oil is found x Probability of finding oil) - (Loss if no oil is found x Probability of not finding oil)
Expected profit = ($120 million x 0.2) - ($20 million x 0.8)
Expected profit = $24 million - $16 million
Expected profit = $8 million
For Site B:
Expected profit = (Profit if oil is found x Probability of finding oil) - (Loss if no oil is found x Probability of not finding oil)
Expected profit = ($180 million x 0.1) - ($30 million x 0.9)
Expected profit = $18 million - $27 million
Expected profit = -$9 million
Therefore, Site A has the larger expected profit of $8 million, while Site B has an expected loss of $9 million.
Since the expected profit for Site A is greater than the expected loss for Site B, we can say that Site A has a larger expected profit than Site B by $17 million ($8 million - (-$9 million)), which is the difference between their expected profits.
The complete question is:-
An oil company is considering two sites on which to drill, described as follows: Site A: Profit if oil is found: $120 million Site B: Profit if oil is found: $180 million Loss if no oil is found: $20 million Loss if no oil is found: $30 million Probability of finding oil: 0.2 Probability of finding oil: 0.1 a. Which site has the larger expected profit? Site A has the larger expected profit. Your answer is correct. Site B has the larger expected profit. The expected profits for both sites are the same. b. If the expected profit for both sites is not the same, by how much is the expected profit larger? $ nothing million (Round to the nearest tenth as needed.) I need answer B and and explanation. Because I can calculate it as bigger, but my anwser doesn't match B.
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A school has raised $525 of their $750 goal for their fundraiser.What percent of the money do they have left to raise?
Answer:
30%
Step-by-step explanation:
750-525/750*100%
225/750*100%
0.3*100%
30%
A greengrocer normally sells 20 carrots for £2.80. In a sale, the cost of the carrots is reduced by 30%. Work out how much 180 carrots cost in the sale. Give your answer in pounds
Answer:
Step-by-step explanation:
180 ÷ 20 = 9
Original Price = 9 x £2.80 = £25.2
Discounted price = £25.2 - (£25.2 x 0.30) = £17.55
In a sale, 180 carrots would cost £17.55.
The locker keys are numbered 27, 84, 15, and 52. Max, Henry, Lisa, and Julio each have a key. Use the clues to determine who has key 84.
Answer:Henry
Step-by-step explanation:
Max doesn’t have the greatest number, crossed out
Julio’s numbers add up to six, 15, crossed out
Lisa’s number is in between Max’s and Julio’s, which means max has 52, and Henry is left.
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Which expression is equivalent to (7^3)5 ⋅ 7^4?
Answer: [tex]7^3\cdot7^{-5}=7^{-2}=\dfrac{1}{7^2}[/tex]
Step-by-step explanation:
If 2 pretzel makers can make 444 pretzels in 6 hours, how long does it take 5 pretzel makers to make 88 pretzels?
As a result, it would take 5 pretzel makers 22.6 minutes, or around 0.376 hours, to manufacture 88 pretzels.
what is unitary method ?To answer mathematical issues involving proportional relationships between various quantities, one can utilize the unitary method. Finding the value of one unit of a quantity and using that value to determine the value of another number of units is what it entails. In business and finance, the unitary technique is frequently used to address issues with cost, price, and quantity. The link between several units of measurement is also computed in physics and other fields.
given
To begin, we can apply the formula:
(Workers' Count) x (Efficiency) x (Time) = (amount of work)
To achieve this, multiply the total quantity of pretzels produced by the two pretzel makers by the sum of the labor hours worked by the number of workers:
One pretzel maker's productivity is calculated as follows: (444 pretzels / 2 workers x 6 hours) = 37 pretzels per worker-hour.
The time it would take for five pretzel producers to produce 88 pretzels may therefore be calculated using this efficiency:
37 pretzels were consumed each worker hour multiplied by five workers yields 88 pretzels.
By solving for time, we obtain:
Time is calculated as follows: 88 pretzels / (5 workers x 37 pretzels per worker-hour) = 0.376 hours.
As a result, it would take 5 pretzel makers 22.6 minutes, or around 0.376 hours, to manufacture 88 pretzels.
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The length of a side of a square is represented by 2x+2, and the length of a side of an equilateral triangle by 4. If the square and the equilateral triangle have equal perimeters, find x.
F) 1
G) 1/2
H).1/3
J) 2/3
K) 1/4
Answer: Therefore, the answer is (G) 1/2.
Step-by-step explanation: Let's first express the perimeter of the square and the equilateral triangle in terms of x:
Perimeter of the square: 4(2x+2) = 8x + 8
Perimeter of the equilateral triangle: 3(4) = 12
Since the two shapes have equal perimeters, we can set the two expressions equal to each other and solve for x:
8x + 8 = 12
8x = 4
x = 1/2
Box A has a length of 12 cm, width of 3 cm, and height of 5 cm. Box B is placed on top of Box A with length of 3 cm, width of 3 cm, and height of 3 cm. Box C is to the side of the other two boxes with length of 3 cm, width of 3 cm, and height of 3 cm.
Part A.
Tisha is putting boxes together to make an art project. She has already put two boxes together. What is the volume of the two boxes, A and B, that Tisha put together?
A.
189 cm3
B.
207 cm3
C.
288 cm3
D.
519 cm3
V = 207 cm^3
Step-by-step explanation:
volume of box A = 12 × 3 × 5 = 180 cm^3
volume of box B = 3 × 3 × 3 = 27 cm^3
total volume of box A and B = 180 + 27 = 207 cm^3
Which statements explain that the table does not
represent a probability distribution?
Select each correct answer.
The probabilities have different
denominators.
The results are all less than 0.
O The sum of the probabilities is 31
12'
The probability is greater than 1.
12
Result
-2
-4
-6
-8
C
Probability
A
23
1
12
53
L
Next
Answer: The correct statements that explain that the table does not represent a probability distribution are:
The results are all less than 0.
The probability is greater than 1.
The sum of the probabilities is 31/12.
A probability distribution must have probabilities between 0 and 1 (inclusive) and the sum of all probabilities must equal 1.
Step-by-step explanation:
whats
6-789=v=c-78930+57y
Answer:
v = c - 78930 + 57y - 6
Step-by-step explanation:
Miranda orange $12 per hour at her job if she say 60% of her earnings for the computer, she’ll be able to buy the computer after working x hours at her job.
What is x?
Miranda needs to work 50 hours at her job in order to purchase the computer.
What is amount?Amount is a term generally used to refer to a numerical value which represents a quantity of something. It can be used to describe the size, magnitude, or total of an object, event, or concept. Amount is often used to refer to money, but it can also be used to refer to other elements such as time, energy, weight, and volume. Amount can also be used to refer to a certain degree or level, such as a certain amount of effort or a certain amount of progress.
To find the amount of hours Miranda needs to work in order to purchase the computer, the following equation can be used:
12 x = Computer Price x 0.6
Where 12 is the hourly wage Miranda earns, x is the amount of hours Miranda needs to work, and 0.6 is the percentage (60%) of Miranda’s earnings that will be used to purchase the computer.
The computer price is not given, so let’s assume it to be $1000. Plugging in the values, the equation becomes:
12 x = 1000 x 0.6
Simplifying the equation, we have:
12 x = 600
Dividing both sides by 12, we get:
x = 600/12
x = 50
Therefore, Miranda needs to work 50 hours at her job in order to purchase the computer.
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In a class of 24 students, 7 students have 2 brothers or sisters. 4 students have 1 brother or sister. 3 students do not have any brothers or sisters. 6 students have 3 brothers or sisters. The remaining students have 4 brothers or sisters.
Samedy says that the total number of brothers and sisters that the class has is 24, because there will be 24 dots above the number line on the line plot. Use the drop-down menus to complete the statement below.
Answer:
Samedy's statement is false. in total the class has 56 brothers and sisters
Step-by-step explanation:
Answer:
A. Samedy's statement is incorrect.
B. In total, the class has 71 brothers and sisters.
To arrive at this answer, we can use the information given in the problem to calculate the total number of brothers and sisters:
7 students have 2 siblings each, so there are 14 siblings in total.
4 students have 1 sibling each, so there are 4 siblings in total.
6 students have 3 siblings each, so there are 18 siblings in total.
The remaining students have 4 siblings each, so there are 4 x (24 - 7 - 4 - 3 - 6) = 4 x 4 = 16 siblings in total.
Adding all of these up, we get a total of 14 + 4 + 18 + 16 = 52 siblings. Therefore, Samedy's statement is incorrect, as the class has 52 siblings and not 24.
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Use the Midpoint Rule with n = 5 to estimate the volume V obtained by rotating about the y-axis the region under the curve y = [tex]\sqrt{1+6x^3[/tex] , 0 ≤ x ≤ 1
The estimated volume of the region obtained by rotating y = √(1 + 6x³) about the y-axis using the Midpoint Rule with n = 5 is 0.702 cubic units.
What is the volume using midpoint rule?To use the Midpoint Rule to estimate the volume V, we first need to divide the interval [0, 1] into n subintervals of equal width. In this case, n = 5, so we have:
Δx = (1 - 0)/5 = 0.2
Next, we need to find the midpoint of each subinterval. The midpoints are:
x₁ = 0.1
x₂ = 0.3
x₃ = 0.5
x₄ = 0.7
x₅ = 0.9
Now we can evaluate the function y = √(1 + 6x³) at each midpoint to get the heights of the cylinders that will make up the approximate volume V:
y₁ = √(1 + 6(0.1)³) ≈ 1.027
y₂ = √(1 + 6(0.3)³) ≈ 1.247
y₃ = √(1 + 6(0.5)³) ≈ 1.466
y₄ = √(1 + 6(0.7)³) ≈ 1.687
y₅ = √(1 + 6(0.9)³) ≈ 1.908
Finally, we can use these heights to calculate the volumes of the cylinders and add them up to get an estimate of V:
V ≈ π(Δx/2)²(y₁ + y₂ + y₃ + y₄ + y₅)
≈ π(0.1)²(1.027 + 1.247 + 1.466 + 1.687 + 1.908)
≈ 0.702
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A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.
Find the probability that the mean actual weight for the 100 weights is greater than 24.9. (Round your answer to four decimal places.)
Thus, the chance according to the equation that the average actual weight for the [tex]100 weights[/tex] is higher than [tex]24.9 pounds[/tex] is roughly [tex]0.9582[/tex]
What is equation?An equation in mathematics is a declaration of the equivalence of two expressions. Two parts of an equation are divided by the algebraic symbol ([tex]=[/tex]). As an example, the assertion "[tex]2x+3=9[/tex]" is supported by the argument that it is true.
Finding the value or values of the variable(s) needed to make the equation correct is the aim of equation solving. It is possible to create regular or nonlinear, straightforward or complex equations that include one or more variables.
For instance, the variable[tex]x[/tex] is raised to the second degree in the equation "[tex]x^{2} +2x-3[/tex]". In many areas of mathematics, such as algebra, calculus, or geometry, lines are used.
The weights are distributed evenly, with a minimum value of [tex]24[/tex] and a highest value of [tex]26[/tex]. The average of the lowest and maximum values, which is the mean weight of a single weight, is
[tex](mean weight)= (24+26)/2 = 25 pounds[/tex]
The standard deviation of a single weight is the difference between the maximum and minimum values divided by[tex]\sqrt{12}[/tex] (since there are [tex]12[/tex]possible values between [tex]24[/tex] and [tex]26[/tex]), which is
[tex]Standard deviation = (24+26)/\sqrt{12}[/tex]
[tex]We know (standard deviation of mean weight ) = 0.57735/\sqrt{100} =0.057735[/tex]
We must standardise this value by taking the mean weight, subtracting it, and dividing the result by the mean weight's standard deviation in order to determine the likelihood that the mean actual weight for the[tex]100[/tex]weights is higher than [tex]24.9 pounds[/tex]:
[tex]( Z- score )= (24.9-25)/0.057735 = -1.7321[/tex]
Probability is [tex]less than[/tex] [tex]-1.7321 in Z- score approx 0.0418[/tex]
However [tex]mean actual weight > 24.9[/tex] which is the complement of the probability i.e, [tex]\leq 24.9[/tex]
After subtracting the probability we found [tex]1[/tex] [tex](mean weight > 24.9)[/tex]
∴[tex]1 -0.0418 = 0.9582[/tex]
Therefore the the average actual weight for the [tex]100 weights[/tex] is higher than [tex]24.9 pounds[/tex] is roughly [tex]0.9582[/tex]
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The histogram shows information about the ages of 150 workers in a London office. A worker is selected at random. Estimate the probability that they are over 45 years old?
A 0.166 probability that they are over 45 years old is discovered using its notion from histogram.
A histogram is a form of graph that is used to show how a dataset is distributed. The horizontal axis shows the range of values in the dataset, while the vertical axis represents the frequency with which those values occur. It is a graphical depiction of a frequency table. Each bar's height corresponds to the number of observations that occur within a given bin, which is created by dividing the data into equal intervals known as bins.
In statistics and data analysis, histograms are frequently used to examine a distribution's form, particularly its central tendency, variability, and skewness. They are especially helpful for locating patterns and trends in the data as well as for spotting outliers, gaps, and clusters. Moreover, histograms can be used to contrast several datasets or look at how a dataset has changed over time.
The number of desired outcomes divided by the total number of outcomes yields a probability.
In this issue:
There are 150 workers overall, according to the histogram.
25 of them are older than 45 years old.
p = 25/150 = 0.166
This idea reveals a 0.166 probability that they are beyond 45 years old.
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