Jack and Jill each improved their yards by planting hostas and shrubs. They bought their supplies from the same store. Jack spent $52 on 11 hostas and 5 shrubs. Jill spent $70 on 5 hostas and 10 shrubs. What is the cost of one hostas and one shrub
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Find all points (a, b, c) in space for which the system has at least one solution. x + 2y + 3z = a 4x + 5y + 62 = b 7x + 8y + 9z = C Find a matrix A that takes vector i=
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The system has at least one solution for all points (a, b, c) in space. The matrix A that takes vector i is [1 2 3; 4 5 6; 7 8 9].
Given the system of linear equations: x + 2y + 3z = a
4x + 5y + 6z = b
7x + 8y + 9z = c
The above system of linear equations can be written in the matrix form as follows:
Ax = b
Where A is the coefficient matrix, x is the variable matrix, and b is the constant matrix.
A = [1 2 3; 4 5 6; 7 8 9]
x = [x; y; z]
b = [a; b; c]
To find the values of a, b, and c for which the system has at least one solution, we can calculate the determinant of the matrix A.
If det(A) ≠ 0, then the system has a unique solution.
If det(A) = 0, then the system has infinite solutions or no solutions.
So, det(A) = 1(5×9 − 6×8) − 2(4×9 − 6×7) + 3(4×8 − 5×7)
= 45 − 36 − 84
= −75
Since det(A) ≠ 0, the given system of linear equations has a unique solution for all values of a, b, and c.
Conclusion: Thus, the system has at least one solution for all points (a, b, c) in space. The matrix A that takes vector i is [1 2 3; 4 5 6; 7 8 9].
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consider the first two terms of this sequence 1/16, -3/16 Determine the 63rd term if this is an arithmetic sequence. Write your answer as a reduced improper fraction. Determine the 63rd term if this is a geometric sequence. Write your answer in scientific notation.
Answers
The 63rd term is \(-\frac{247}{16}\) if it is an arithmetic sequence.
The 63rd term is \(2.385\times 10^{28}\) if it is an geometric sequence.
An arithmetic sequence has the characteristic that the difference between two consecutive elements is the same, that is to say:
\(a_{i+1}-a_{i} = r\) (1)
The expression that represents the elements of the arithmetic sequence is presented below:
\(a(n) = a_{1} + r\cdot (n-1)\) (2)
Where:
\(n\) - Index of the element of the sequence.\(r\) - Increase rate.\(a_{1}\) - First element of the arithmetic sequence.If we know that \(a_{1} = \frac{1}{16}\), \(a_{2} = -\frac{3}{16}\) and \(n = 63\), then the 63rd term of the arithmetic sequence:
\(r = -\frac{3}{16}-\frac{1}{16}\)
\(r = -\frac{1}{4}\)
\(a(63) = \frac{1}{16}-\frac{1}{4}\cdot (63-1)\)
\(a(63) = -\frac{247}{16}\)
The 63rd term is \(-\frac{247}{16}\) if it is an arithmetic sequence.
An geometric sequence has the characteristic that the ratio between two consecutive elements is the same, that is to say:
\(\frac{a_{i+1}}{a_{i}} = r\) (3)
The expression that represents the elements of the geometric sequence is presented below:
\(a(n) = a_{1}\cdot r^{n-1}\) (4)
Where:
\(n\) - Index of the element of the sequence.\(r\) - Increase rate.\(a_{1}\) - First element of the arithmetic sequence.If we know that \(a_{1} = \frac{1}{16}\), \(a_{2} = -\frac{3}{16}\) and \(n = 63\), then the 63rd term of the arithmetic sequence:
\(r = \frac{-\frac{3}{16} }{\frac{1}{16} }\)
\(r = -3\)
\(a (63) = \left(\frac{1}{16} \right)\cdot (-3)^{63-1}\)
\(a(63) = 2.385\times 10^{28}\)
The 63rd term is \(2.385\times 10^{28}\) if it is an geometric sequence.
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Use the Venn diagram to calculate probabilities.
Circles A, B, and C overlap. Circle A contains 12, circle B contains 11, and circle C contains 4. The overlap of A and B contains 5, the overlap of B and C contains 3, and the overlap of C and A contains 6. The overlap of the 3 circles contains 8.
Which probabilities are correct? Select two options.
Answers
In probability theory, a Venn diagram is a diagrammatic representation of sets that shows all possible logical relations between them. Venn diagrams are widely used in probability and statistics to visualize the relationship between different sets of data.
The given Venn diagram shows the relationship between three sets, A, B, and C. In order to calculate probabilities using a Venn diagram, we need to know the number of elements or members in each set, as well as any overlapping regions.
We can then use these numbers to calculate the probability of different outcomes.Let's consider two possible probabilities from the given Venn diagram:1.
The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22. The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3The first probability can be calculated by dividing the number of elements in the overlapping region of sets A and B (which is 0.1) by the total number of elements in set B (which is 0.5).
This gives us a probability of 0.22 or 22%.The second probability can be calculated by dividing the number of elements in the union of sets B and C (which is 0.2) by the total number of elements in either set B or set C (which is 0.6). This gives us a probability of 1/3 or approximately 33%.
Therefore, the correct probabilities are:1.
The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22.
The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3
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Tell whether the two quantities vary directly. Explain your reasoning.
the number of correct answers on a test and the score on the test
Choose the correct answer below.
OA. No, they do not vary directly. When one quantity increases, the other quantity does not increase.
OB. No, they do not vary directly. When one quantity increases, the other quantity also increases.
C. Yes, they vary directly. When one quantity increases, the other quantity also increases.
OD. Yes, they vary directly. When one quantity increases, the other quantity does not increase.
Answers
The correct statement regarding the variation of the two measures is given as follows:
C. Yes, they vary directly. When one quantity increases, the other quantity also increases.
What are positive and negative association?Two variables have a positive association when the values of one variable increase as the values of the other variable increase, that is, the quantities vary directly.Two variables have a negative association when the values of one variable decrease as the values of the other variable increase, that is, the quantities vary inversely.For this problem, we have that when the number of correct answers on the test increases, the score also does, hence the two quantities vary directly, and option c is the correct option for this problem.
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George eats 22 cookies per week, 7 of them are on
weekends. If George eats an equal amount of cookies
each weekday, how many does he eat each weekday?
Answers
Answer: 15 cookies a weekday
Step-by-step explanation:
22 - 7 = 15
this is because we exclude the cookies he eats on weekends because that is not a week day so we are left with 15
George eats 15 cookies on weekdays and 7 cookies on weekends. 15 cookies+7 cookies=22 cookies in total every week
The mean entry-level salary of an employee at a company is $58,000. you believe it is higher for it professionals in the company. state the null and alternative hypotheses.
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Null hypothesis: the mean entry-level salary of an employee and is not significantly less than that of professionals in the company.
Alternative hypothesis: the mean entry-level salary of an employee is significantly less than that of professionals in the company.
What is a hypothesis in a study?A hypothesis in a study is a statement that is made to explain a given observation without prior testing to prove or disprove the statement.
The two types of hypothesis are:
null hypothesisalternative hypothesisThe null hypothesis states that there is no significant difference between two variables while the alternative hypothesis states that there is a significant difference between the variables.
For the given observation:
Null hypothesis: the mean entry-level salary of an employee and is not significantly less than that of professionals in the company.
Alternative hypothesis: the mean entry-level salary of an employee is significantly less than that of professionals in the company.
In conclusion, the null hypothesis is the hypothesis of no significant difference.
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Can anyone help me? Pleaseeeeeeeeeeeeeeeweeeeeeeeeeeeeee
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Given :
height of the model : 4cmvolume of the model : 12cm³volume of the statue : 40,500 cm³ATQ,
the volume of the model is thrice the height of the model
12cm³ = 4cm x 4cm x 4cmso,
the volume of the statue would be thrice it's height
40,500cm³ = 3 x heightheight = 40,500/3height = 13,500 cmhence,the height of the statue would be 13,500 cm
Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
Answers
Based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.
What are z-scores?How closely a value relates to the mean of a set of values is expressed by a Z-score.
The Z-score is created using standard deviations from the mean.
A data point's total value is equal to the mean value when the Z-score of the data point is equal to 0.
So, in order to determine how far the raw score deviates from the mean, the Z score is used.
The following steps are used to determine the Z score:
z = (x - μ)/σ
We know that: x > 550 and μ = 500, σ = 40
z = 550 - 500 / 40
z = 1.25
The graph of the normal distribution indicates:
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Therefore, based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.
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Use the region in the first quadrant bounded by √x, y=2 and the y-axis to determine the volume when the region is revolved around the y-axis. Evaluate the integral.
A. 8.378
B. 20.106
C. 5.924
D. 17.886
E. 2.667
F. 14.227
G. 9.744
H. 3.157
Answers
`V = ∫[a,b] π[f(y)]^2 dy`
Where `a` and `b` are the limits of integration and `f(y)` is the function that represents the region when it is revolved around the y-axis.
In this case, we have `f(y) = √y`, `a = 0` (since the region is bounded by the y-axis) and `b = 2`. So the integral becomes:
`V = ∫[0,2] π[√y]^2 dy`
`V = ∫[0,2] πy dy`
`V = π [y^2/2]_0^2`
`V = π[(2)^2/2 - (0)^2/2]`
`V = π(2)`
`V = 6.283`
Round to three decimal places, the answer is H. 3.157.
What is the amount of simple interest after 3 years if $250 was deposited at a 4% interest rate?
Answers
Answer:
$290
Step-by-step explanation:
250 * 4% (Or 0.04) = $10
$10 is interest per year
$10 * 4 years = $40
$250 + $40 = $290
3. The number of visitors to a website in the first week is 50. The number of visitors each week is double the number of visitors the previous week. What is the total number of visitors to the website in the first 8 week
Answers
The total number of visitors to the website in the first 8 weeks is 12,750.
To determine the total number of visitors to the website in the first 8 weeks, we can analyze the pattern of doubling the number of visitors each week.
Week 1: 50 visitors
Week 2: 2 * Week 1 = 2 * 50 = 100 visitors
Week 3: 2 * Week 2 = 2 * 100 = 200 visitors
Week 4: 2 * Week 3 = 2 * 200 = 400 visitors
Week 5: 2 * Week 4 = 2 * 400 = 800 visitors
Week 6: 2 * Week 5 = 2 * 800 = 1600 visitors
Week 7: 2 * Week 6 = 2 * 1600 = 3200 visitors
Week 8: 2 * Week 7 = 2 * 3200 = 6400 visitors
By following the pattern, we can see that each week the number of visitors doubles from the previous week.
To find the total number of visitors in the first 8 weeks, we sum up the number of visitors from each week:
Total number of visitors = Week 1 + Week 2 + Week 3 + Week 4 + Week 5 + Week 6 + Week 7 + Week 8
Total number of visitors = 50 + 100 + 200 + 400 + 800 + 1600 + 3200 + 6400
Total number of visitors = 12750
Therefore, the total number of visitors to the website in the first 8 weeks is 12,750.
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find m<d
help me please
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therefore, let the measurement of angle D be x
x+88=180
x=180-88
x=92
Please open the document to see the picture of the triangle. Find the area of the triangle. Remember: 1/2bh (1/2 x b x h). Also, remember to label your answer.
Answers
Answer:
So the answer is 12cm square
Step-by-step explanation:
Base is 6cm and hight is 4 so 6×4 is 24÷2 is 12
Please answer this . This is my lash question
Answers
Answer:
Step-by-step explanation:
(m-7)(m-7)=0
m=7
A city is planning an outdoor concert for an Independence Day celebration. To hold speakers and lights, a crew of technicians sets up a scaffold with two platforms by the stage. The first platform is 8 feet 2 inches off the ground. The second platform is 7 feet 6 inches above the first platform. The shadow of the first platform stretches 6 feet 5 inches across the ground. A technician is 5 feet 8 inches tall. The technician is standing on top of the second platform. Find the lengths of the shadow that is cast by the scaffold and the technician to the nearest inch.
Answers
The length of the shadow that is cast by the scaffold and the technician to the nearest inch is approximately 196 inches.
Solutions involving shapes with proportional relationships
Recall that where two triangles are said to be proportional, it means that their perimeters are similar.
Therefore, to solve this, first, we convert all figures into inches.
AC = 8ft 2in. = 98in
CE = 7ft 6in = 90in
AB = 6ft 3in = 75in
Second,
Recall that the height of the technician = 5ft 8in. In inches that will be 68inches.
The height of the scaffold is arrived at by saying 188 + 68 = 256Inc
Recall that the triangles are proportional. Therefore, we say
\(\frac{256}{98}\) = \(\frac{s}{75}\)
if we cross multiply we can then say
s = 75(\(\frac{256}{98}\))
s = 75 * 2.6122449
s = 195.918 or approximately 196 inches. Answer in Feet is 16ft 4in.
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Select all the fractions that are greater than 1/2.
3/5
7/13
7/15
10/7
100/200
1000/2001
Answers
Answer:
3/5
7/13
10/7
Step-by-step explanation:
all of these are greater than 1/2
select the correct statement. a.) the critical z-score for a right-tailed test at a 9% significance level is 1.34. b.) the critical z-score for a two-sided test at a 4% significance level is 1.75. c.) the critical z-score for a two-sided test at a 20% significance level is 0.85. d.) the critical z-score for a left-tailed test at a 12% significance level is -0.45.
Answers
d.) the critical z-score for a left-tailed test at a 12% significance level is -0.45.
The critical z-score is the value on the standard normal distribution that separates the rejection region from the non-rejection region for a given level of significance (alpha). The critical z-score depends on the level of significance and the type of hypothesis test (one-tailed or two-tailed).
For a left-tailed test at a 12% significance level, the critical z-score can be found by looking up the z-score that corresponds to a cumulative probability of 0.12 in the standard normal distribution table. The closest value to 0.12 is 0.1190, which corresponds to a z-score of -1.18. Since this is a left-tailed test, we take the negative of the z-score to get the critical z-score, which is approximately -0.45. Therefore, option d is the correct statement.
Calculate the diameter or a circle with a radius of 12cm. show all your work.
PLZ HELPP
Answers
Answer:
24cm
Step-by-step explanation:
a radius is half the diameter
12x2=24
Answer:
Step-by-step explanation:
Diameter of a circle = 2 x radius
= 2 x 12 = 24cm
Solve the triangle. Round each angle to the nearest degree and round each side to the nearest hundredth. Do not use rounded answers In Your calculations to find missing measures
Answers
Rounded answers In Your calculations to find missing measures is given below.
Given: a = 8.72, b = 11.1, c = 11.7
Using the Law of Cosines, we can calculate angle A:
A = arccos((b2 + c2 - a2)/2bc)
A = arccos((11.12 + 11.72 - 8.722)/(2*11.1*11.7))
A = arccos(2.61/265.57)
A = arccos(0.00984)
A = 89.8°
Using the Law of Sines, we can calculate angle B:
Using the Law of Cosines, we can calculate side c:
c2 = a2 + b2 - 2abcos(C)
c2 = 8.722 + 11.12
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can someone plsss help me with this for 85 points and i can send 50 more points if u help
What characteristics of a trail do you think determines the "trail rating?" Explain your thinking below.
Answers
Answer:
Trees, moguls, slope, length, condition
Step-by-step explanation:
If a run doesn't have that many trees to dodge or avoid, it would be a very easy run. If the run has moguls, or little bumps in the snow, it might have a higher trail rating. If the trail is very steep, it might also have a higher trail rating, as you need more experience to ski on steeper slopes.
Step-by-step explanation:
Trees,moguls,slope,length,condition
find the value of X in X-X³=17
Answers
Answer:
Step-by-step explanation:
Step1: find the interval of roots. Consider -3 and -2
\(f(-3) = -7 <0\)
\(f(-2) = 18 >0\)
Hence, the root must be on [-3,-2]
Step2: consider the middle point -2.5
\(f(-2.5) = 3.875 >0\)
Then, the root must be on [-3, -2.5]
Step 3: Repeat step 2 by finding the value of f at the middle point -2.75
\(f(-2.75) = -1.0468 <0\)
Step 3: Repeat step 2 by finding the value of f at the middle point of the interval [-2.75,-2.5] which is -2.625
\(f(-2.625) = 1.537 >0\)
Step4: Repeat step 2 on [-2.75, -2.625]
Repeat step 2 until you got the root which is -2.701
1/5 de los animales en el zoológico son monos 5/7 de los monos son machos
¿Qué fracción de los animales en el zoológico son monos machos?
Answers
1/7 of the animals in the zoo are male monkeys.
What fraction of the animals in the zoo are male monkeys? Explain with workings.
To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.
Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:
= 1/5
= 5/25.
And 5/7 of the monkeys are male which is written as 5/7.
To get fraction of male monkeys, we will multiply these two fractions:
= (5/25) * (5/7)
= 25/175
= 1/7.
Full question:
1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?
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on a number line, suppose point e has a coordinate of , and eg. what are the possible coordinates of point g? question content area bottom part 1 the possible coordinates for g are
Answers
The possible coordinates of point G on this number line are either -10 or 14.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
Given the following data:
E = 2.
EG = 12.
On this number line, the coordinate of EG is given by this mathematical expression:
EG = |E - G|
Substituting the given parameters into the expression, we have;
12 = |2 - G|
2 - G = ±12
G = 2 ± 12
Simplifying and evaluating the above expression, we have:
G = 2 + 12
G = 14.
OR
G = 2 - 12
G = -10
Therefore, the possible coordinates of point G on this number line are either -10 or 14.
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Complete Question:
On a number line, suppose point E has a coordinate of 2, and EG= 12. what are the possible coordinates of point G?
Find the slope of the line from the pair of points. (-2,0) (-4, -3)
A. 3/2
B. 2/3
C. -3/2
D. 2
Answers
A: 3/2
Slope formula is y2-y1/x2-x1 it is used to find slope from two points
-3-0/-4-(-2)= -3/-2 = 3/2
What is the median of 2 5 7 9?
Answers
The median for the next batch of observations is 5.
What is median?The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.
Here,
given set of observation,
=2,5,7,9
n=4
median=(4)/2
=2nd term
=5
The median for following set of observation is 5.
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The ratio of the angle measures in a triangle is 3 : 5 : 7. What are the measures of the angles of the triangle?
Answers
Answer:
36, 60, 84
Step-by-step explanation:
3+5+7=15
180/15=12
12*3=36
12*5=60
12*7=84
Find the coordinates of point P on \overrightarrow{A B} that partitions the segment into the given ratio A P to P B .
A(0,0), B(3,4), 2 to 3
Answers
The coordinates of point P are \(\dfrac{6}{5} \dfrac{8}{5}\)
Let's assume that point P divides the segment AB into segments AP and PB, where AP is 2 units long and PB is 3 units long. We need to find the coordinates of point P.
The section formula states that if point P divides the segment AB in the ratio m:n, then the coordinates of P can be calculated as follows:
\(\dfrac{ (n \times x_1 + m \times x_2)}{ (m + n) , } \dfrac{ (n * y1 + m * y2) }{ (m + n) ),}\)
Where A\((x_1, y_1)\) And B\((x_2, y_2)\)Are the coordinates of points A and B, respectively, and m and n are the given ratios.
Given:
\(A(0,0), B(3,4),\) ratio\(2:3\)
Using the formula, we can calculate the coordinates of point P:
P(x, y) = \(\frac ((3 \times 0 + 2 \times3){ (2 + 3)} \dfrac{3 \times 0 + 2\times 4) }{(2 + 3)}\)
=\(\dfrac{ 0 + 6} { 5} , \dfrac{0 + 8} { 5 }=\dfrac{6}{5} \times\dfrac{8}{5}\)
Therefore, point P on the vector AB that divides the segment into a ratio of 2:3 has coordinates P\(\dfrac{6}{5} \dfrac{8}{5}\)
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which equation shows the value of -2/5 - -9/15
Answers
Answer:
-⅖ + ⁹/¹⁵ = 3/15
Step-by-step explanation:
-⅖ + ⁹/¹⁵ = 3/15
The correct answer for the given equation is \(\frac{3}{15}\).
What is PEMDAS?PEMDAS is the right standardized way of solving math problems if multiple operations are being used. The acronym stands for parentheses, then exponents, then multiplication and division, then addition and subtraction.
Given the equation, \(-\frac{2}{5} -(\frac{-9}{15} )\) if we follow the PEMDAS then we have to remove the bracket first, and after that negative sign before 9/15 will get positive as follow:
⇒ \(-\frac{2}{5} +(\frac{9}{15} )\)
⇒ \(-\frac{6}{15} +(\frac{9}{15} )\)
\(\frac{3}{15}\) .
Hence, The equation which shows the value of the given Problem is D.
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Can someone answer this for me?
Answers
Answer: as per question statement
we need to set up an equation first
p(t)=1200e(0.052*t)
they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present
we need to find population at t=6
we need to plug t=6 in p(t).
P(6)=1200e(0.052*6)=1639.38
1638.38 bacteria were present at that time t=6
Step-by-step explanation: I hope this helps.
someone please answer please!
Svetlana Masterkova of Russia set a record when she ran 1 mile in 4 minutes, 12.56 seconds. What was her time in miles per hour?
Answers
Answer:
14.04 miles/hours
Step-by-step explanation:
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