Answer:
The system has one solution.
Step-by-step explanation:
We have two equations:
y = -2x - 4
y = 3x + 3
Equalling them:
y = y
-2x - 4 = 3x + 3
5x = -7
[tex]x = -\frac{7}{5}[/tex]
And
[tex]y = 3x + 3 = 3(-\frac{7}{5}) + 3 = \frac{-21}{5} + 3 = \frac{-21}{5} + \frac{15}{5} = -\frac{6}{5}[/tex]
Replacing in the other equation we should get the same result.
[tex]y = -2x - 4 = -2(-\frac{7}{5}) - 4 = \frac{14}[5} - 4 = \frac{14}{4} - \frac{20}{5} = -\frac{6}{5}[/tex]
So the system has one solution.
An icicle it's in the shape of an inverted cone with a diameter of 12 m m and a height of 100 mm. How much Frozen water is in the icicle? Round to the nearest hundredth.
Answer:
3768 mm ^ 3
Step-by-step explanation:
We have that the volume of a cone is given by:
V = 1/3 * Ac * h
Where Ac is the area of the circle, we know that the radius is half the diameter then:
r = d / 2
r = 12/2
r = 6
And Ac is equal to:
Ac = pi * r ^ 2
replacing:
Ac = 3.14 * 6 ^ 2
Ac = 113.04
113.04 mm ^ 2 is the area of the circle, replacing the volume form knowing that h = 100
V = 1/3 * 113.04 * 100
V = 3768
Therefore they fit a total of 3768 mm ^ 3
When converting measurements in the metric system, you can move the decimal point to the left or to the right. Why? Select all that apply. A. When converting from smaller to larger units, you are dividing by a power of 10. B. Moving a decimal point is the same as adding or subtracting. C. The metric system is based on powers of 10. D. When converting from larger to smaller units, you are multiplying by a power of 10.
Answer:
This has multiple answers, A, C, And D
Step-by-step explanation:
Answer:
It is definitely A, C, and D.
Step-by-step explanation:
I just answered this question and got it right. I hope this helps and please mark brainliest!
A professor gives her 100 students an exam; scores are normally distributed. The section has an average exam score of 80 with a standard deviation of 6.5. What percentage of the class has an exam score of A- or higher (defined as at least 90)? Type your calculations along with your answer for full credit; round your final percentage to two decimal places.
Answer:
6.18% of the class has an exam score of A- or higher.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 80, \sigma = 6.5[/tex]
What percentage of the class has an exam score of A- or higher (defined as at least 90)?
This is 1 subtracted by the pvalue of Z when X = 90. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90 - 80}{6.5}[/tex]
[tex]Z = 1.54[/tex]
[tex]Z = 1.54[/tex] has a pvalue of 0.9382
1 - 0.9382 = 0.0618
6.18% of the class has an exam score of A- or higher.
Which sequences are geometric? Check all that apply.
O 1,5, 25, 125, ...
3, 6, 9, 12,...
3, 6, 12, 24, ...
3, 9, 81, 6, 561, ...
10, 20, 40, 60, ...
Answer:
1, 5, 25, 125, ...
3, 6, 12, 24, ...
Step-by-step explanation:
a geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio1, 5, 25, 125, ...
yes, the common ratio is 53, 6, 9, 12,...
no3, 6, 12, 24, ...
yes, the common ratio is 23, 9, 81, 6, 561, ...
no10, 20, 40, 60, ...
noPlaybill magazine reported that the mean annual household income of its readers is $119,155 (Playbill, January 2006). Assume this estimate of the mean annual household in- come is based on a sample of 80 households, and based on past studies, the population standard deviation is known to be a = $30,000. a. Develop a 90% confidence interval estimate of the population mean. b. Develop a 95% confidence interval estimate of the population mean. c. Develop a 99% confidence interval estimate of the population mean. d. Discuss what happens to the width of the confidence interval as the confidence level is increased. Does this result seem reasonable? Explain.
Answer:
a) CI = (113,637.5 , 124,672.5)
b) CI = (112,581 , 125,729)
c) CI = (110,501.4 , 127,808.6)
Step-by-step explanation:
You have the following information:
[tex]\overline{x}[/tex]: mean annual household income = 119,155
σ: standard deviation = 30,000
n: sample = 80
The interval of confidence is given by the following expression:
[tex]\overline{x}\pm Z_{\alpha/s}(\frac{\sigma}{\sqrt{n}})[/tex]
Z_α/2: distribution density factor
where α and Z_α/2 are given by the range of the confidence interval.
a) For a 90% confidence interval you have:
α = 1 - 0.9 = 0.1
Z_0.1/2 = Z_0.05 = 1.645 (found in a table of normal distribution)
You replace in the equation (1) to obtain the confidence interval:
[tex]119,155\pm (1.645)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm5,517.5[/tex]
Then, the confidence interval is (119,155 + 5,517.5 , 119,155 - 5,517.5 )
= (113,637.5 , 124,672.5)
b) For a 95% confidence interval you have:
α = 1 - 0.95 = 0.05
Z_0.05/2 = Z_0.025 = 1.96
[tex]119,155\pm (1.96)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 6,574.0[/tex]
The confidence interval is (112,581 , 125,729)
c) For a 99% confidence interval:
α = 1 - 0.99 = 0.01
Z_0.01/2 = Z_0.005 = 2.58
[tex]119,155\pm (2.58)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 8,653.6[/tex]
The confidence interval is (110,501.4 , 127,808.6)
d) When the confidence level increases the width of the confidence increases too. This can be noticed in the normal distribution, when the confidence level is higher, the area of the tails is reduced, and so, the confidence interval is higher.
Find the equation for the plane through the points Upper P 0 (5 comma 4 comma 5 ), Upper Q 0 (negative 5 comma negative 1 comma negative 4 ), and Upper R 0 (negative 2 comma 1 comma negative 2 ). The equation of the plane is nothing.
Answer:
The equation of the plane is
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 7y - 5z + 13 = 0
Step-by-step explanation:
Given 3 points, P(x₁, y₁, z₁), Q(x₂, y₂, z₂), and R(x₃, y₃, z₃).
We can calculate the equation of the plane through those points as
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0, where (x₀, y₀, z₀) are the coordinates of any one of the points P, Q, or R, and <a,b,c> is a vector perpendicular to the plane.
The vector perpendicular to the plane is obtained by writing vector PQ and PR and taking the cross or vector product.
For this question,
P = (5, 4, 5)
Q = (-5, -1, -4)
R = (-2, 1, -2)
PQ = (-5, -1, -4) - (5, 4, 5) = (-10, -5, -9)
= (-10î - 5ĵ - 9ķ)
PR = (-2, 1, -2) - (5, 4, 5) = (-7, -3, -7)
= (-7î - 3ĵ - 7ķ)
PQ × PR is then
| î ĵ ķ |
|-10 -5 -9|
|-7 -3 -7|
= î [(-5×-7) - (-9×-3)] - ĵ [(-10×-7) - (-9×-7)] + ķ [(-10×-3) - (-7×-5)]
= î (35 - 27) - ĵ (70 - 63) + ķ (30 - 35)
= 8î - 7ĵ - 5ķ
Hence, (a, b, c) = (8, -7, -5)
And using point P as (x₀, y₀, z₀) = (5, 4, 5)
The equation of the plane is
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 40 - 7y + 28 - 5z + 25 = 0
8x - 7y - 5z = 40 - 28 - 25 = -13
8x - 7y - 5z + 13 = 0
Hope this Helps!!!
The price of a visit to the dentist is $50. If the dentist fills any cavities, an additional charge of $100 per cavity
gets added to the bill.
Answer:
Cost of visit = 50 + 100n
Step-by-step explanation:
$50 is the set price of the visit.
$100 is the cost per cavity.
N is the number of cavities.
Since we don't know the number of cavities, 'n' will fill that spot.
100 x n will be the total cavity cost.
Cavity cost + set price of visit will equal the total cost of the visit.
Find the equation of a line perpendicular to 2x-4y=1 that contains the point (-4, -2).
Answer:
y = -2x - 10
Step-by-step explanation:
1. rearrange to find the gradient.
the gradient of the original equation is 1/2 hence why a line PERPENDICULAR to that equation would have a gradient of -2.
2. substitute into y - y1 = m (x - x1)
y - (-2) = -2 (x - (-4))
y = -2x - 10
Match each linear equation with the name of its form.
y=-x+8
slope-intercept form
2x - 5y = 9
standard form
y + 6 = -3(x - 1)
point-slope form
Answer:
y + 6 = -3(x - 1) - Point Slope
y=-x+8 - Slope Intercept
2x - 5y = 9 - Standard
Step-by-step explanation:
Point Slope Form is: [tex]y-y_1=m(x-x_1)[/tex]
y + 6 = -3(x - 1) would be in point slope form, where the point is (1,-6) and the slope is '-3'.
Slope-intercept form is: [tex]y=mx+b[/tex]
y=-x+8 is in slope intercept form, where '-1' is the slope and '8' is the y-intercept.
This only leaves 2x - 5y = 9, which is in standard form.
All the correct linear equation with the name of its form are,
1) y = -x + 8 = Slope-intercept form
2) 2x - 5y = 9 = Standard form
3) y + 6 = -3(x - 1) = Point-slope form
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
All the expressions are,
1) y = -x + 8
2) 2x - 5y = 9
3) y + 6 = -3(x - 1)
Now, All the correct linear equation with the name of its form are,
1) y = -x + 8 = Slope-intercept form
2) 2x - 5y = 9 = Standard form
3) y + 6 = -3(x - 1) = Point-slope form
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What is the value of -(3/4) to the power of -4
The answer would be -3 13/81 (simplified)
The math department faculty at a large university wanted to know what portion of the student body believes students should be able to enroll in any math class without meeting a prerequisite. The statistics department offered to cooperate in conducting a survey, and a simple random sample of 500 students was selected from all the students enrolled in statistics classes. A survey form was sent by email to these 500 students and 236 responded. What is the population of interest for this study?
Answer:
The population of interest for this student is the students whom are enrolled in statistics classes.
Step-by-step explanation:
Sampling
This is a common statistics practice, when we want to study something from a population, we find a sample of this population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.
The population of interest are all residents of New York State.
A simple random sample of 500 students was selected from all the students enrolled in statistics classes.
This means that the population of interest for this student is the students whom are enrolled in statistics classes.
At the beginning of the week, Josh had 32 computer games, 133% as many computer games than Peter had. By the end of the week, Josh gave Peter 25% of his computer games. How many computer games did Josh and Peter each have bythe end of the week?
a. Josh had 8 games; Peter had 24 games.
b. Josh had 24 games; Peter had 8 games.
c. Josh had 24 games; Peter had 32 games.
d. Josh had 32 games; Peter had 24 games.
Answer:
The correct answer is letter c. Josh had 24 games and Peter had 32 by the end of the week.
Step-by-step explanation:
We know that Josh has a total of 32 games, while that value is 133% as many as Peter's, therefore the number of games Peter had at the beginning of the week is:
[tex]josh = \frac{133}{100}*peter\\peter = \frac{josh}{1.33}\\peter = \frac{32}{1.33}\\peter = 24.06[/tex]
At the beginning of the week Peter had 24 games. At the end of the week Josh gave Peter 25% of his games, therefore Peter's total is:
[tex]peter = 24 + 0.25*josh\\peter = 24 + 0.25*32\\peter = 24 + 8 = 32[/tex]
While Josh had:
[tex]josh = 32 - 8 = 24[/tex]
The correct answer is letter c.
At a football game, a vender sold a combined total of 152 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Answer:
38 hot dogs114 sodasStep-by-step explanation:
Sometimes problems of this nature are easily worked by considering groups of items. Here, it is convenient to consider a group as 1 hot dog and 3 sodas, so the number of sodas in the group is 3 times the number of hotdogs in the group.
Each group is 4 items, so 152/4 = 38 groups were sold.
In the 38 groups, there were 38 hot dogs and 3×38 = 114 sodas.
114 sodas and 38 hot dogs were sold.
Triangle ABC has been dilated about point A by a scale factor of One-third.
Triangle A B C. Side A C has a length of 39, side A B is 30, side C B is 48. Triangle A prime B prime C prime.
What are the lengths, in units, of the three sides of Triangle A prime B prime C prime?
Answer:
10,16,13
Step-by-step explanation:
got that right
The lengths of the sides of the triangle after the dilation is 13 , 10 and 16 respectively
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the triangle be represented as ABC
Now , the dilated triangle is represented as A'B'C'
The dilation scale factor is d = 1/3
The measure of side AC = 39
The measure of side AB = 30
The measure of side BC = 48
Now , after the dilation of 1/3 , we get
The measure of side A'C' = 39 ( 1/3 ) = 13
The measure of side A'B' = 30 ( 1/3 ) = 10
The measure of side B'C' = 48 ( 1/3 ) = 16
Hence , the dilation triangle is having lengths 13 , 10 and 16
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Which steps can be used to solve for the value of y?
(2013
(y +57) = 178
Answer: [tex]y = 121[/tex]
[tex](y+57) = 178[/tex]
[tex]y+57= 178[/tex]
[tex]y = 178 -57[/tex]
[tex]y = 121[/tex]
A school needs 1,860 pencils for its students. The pencils are sold in boxes of 12. How many boxes does the school need to order?
Answer:
Step-by-step explanation:
155
The number of boxes required by the school to order is 155.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have been given that the school needs 1,860 pencils for its students. Also, the pencils are sold in boxes of 12.
We need to find the school needs to requires boxes to order.
Total number of pencil = 1,860
Number of boxes = 12
Therefore, boxes needed = 1,860 / 12
= 155
Hence, the number of boxes required by the school to order is 155.
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What would be the approximate 95% confidence interval for the mean number of ounces of catchup bottle in the sample
Answer:
The 95% confidence interval for the mean number of ounces of ketchup bottle is (23.8, 24.2).
Step-by-step explanation:
The complete question is:
Suppose that a restaurant chain claims that its bottles of ketchup contain 24 ounces of ketchup on average, with a standard deviation of 0.8 ounces. If you took a sample of 49 bottles of ketchup, what would be the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample?
Solution:
The (1 - α)% confidence interval for the population mean is:
[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\bar x=24\\\sigma=0.8\\n=49\\\text{Confidence Level}=95\%[/tex]
The critical value of z for 95% confidence level is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
*Use a z-table.
Compute the 95% confidence interval for the mean number of ounces of ketchup per bottle as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
[tex]=24\pm1.96\cdot \frac{0.80}{\sqrt{49}}\\\\=24\pm 0.224\\\\=(23.776, 24.224)\\\\\approx (23.8, 24.2)[/tex]
Thus, the 95% confidence interval for the mean number of ounces of ketchup bottle is (23.8, 24.2).
Solve 2x - 11 = k for x.
PLEASE HELP MEEEEEE!!!!!
Answer:
Read below
Step-by-step explanation:
To graph the inequality, place an open circle on -2.5 because there is no line under the > sign. Draw the arrow pointing to the right because the inequality reads "x is greater than -2.5.
As for the check box questions, only B and C should be checked. The arrow points right, and the circle is open.
verify clairaut's theorem for u=e^xysiny
The illustration below is an example of a semi regular tessellation
true or false?
The correct answer is False
Explanation:
A tessellation refers to a regular pattern created by using regular polygons; additionally, in a tessellation, there are no gaps or spaces between the polygons. Besides this, a tesselation is categorized as regular if there is only one type of polygon in all the pattern or as semi-regular if there are two or more polygons but these still form a regular pattern. According to this, the illustration below is not a semi-regular tessellation because this only includes one polygon (hexagons), and therefore this would be classified as a regular tessellation.
Answer:
B
Step-by-step explanation:
what is 0.84÷3 matggggg
[tex]0.84 \div 3 = 84 \div 300 = 0.28[/tex]
Find the area of a circle with radius, r = 6.89m.
Give your answer rounded to 2 DP (2 decimal points)
The photo is attached below
Answer:
149.14 [tex]m^{2}[/tex]
Step-by-step explanation:
Area of a circle = π[tex]r^{2}[/tex]
so A = π * 6.89^2 = 149.14 (to 2d.p.)
Write an equation in slope-intercept form for the line that passes through (0,1) and (1,3)
Answer:
y= 2x+1
Step-by-step explanation:
Points:
(0,1) and (1,3)Form of the line:
y=mx+b, m- the slope, b- y-interceptFinding the slope:
m= (y2-y1)/(x2-x1)m=(3-1)/(1-0)= 2/1= 2Line is now:
y= 2x+bUsing one of the given points to find out the value of b:
1=2*0+bb=1So the equation for the line is:
y= 2x+1evaluate the formula of A=lw, for l=10.8 cm and w=2.5 cm
Answer:
A = 27 cm²
Step-by-step explanation:
[tex]A = lw\\Where, l=10.8 cm , w = 2.5 cm\\[/tex]
Putting in the above formula
A = (10.8)(2.5)
A = 27 cm²
In a survey of students, 60% were in high school and 40% were in middle school. Of the high school students, 30% had visited a foreign country. If a surveyed student is selected at random, what is the probability that the student is in high school and has visited a foreign country?
Answer:
The probability that the student is in high school and has visited a foreign country is 0.18.
Step-by-step explanation:
We are given that in a survey of students, 60% were in high school and 40% were in middle school.
Of the high school students, 30% had visited a foreign country.
Let the Probability that students were in high school = P(H) = 60%
Probability that students were in middle school = P(M) = 40%
Also, let F = event that students had had visited a foreign country
So, Probability that high school students had visited a foreign country = P(F/H) = 30%
Now, probability that the student is in high school and has visited a foreign country is given by = Probability that students were in high school [tex]\times[/tex] Probability that high school students had visited a foreign country
= P(H) [tex]\times[/tex] P(F/H)
= 0.60 [tex]\times[/tex] 0.30
= 0.18 or 18%
Use the table of values to find the line of regression and if justified at the 0.05 significance level, use it to find the predicted quality score of a TV set with a price of $1900. If the data does not suggest linear correlation, then use the average quality score as a prediction.
Price: 2,300, 1,800, 2,500, 2,700, 2,000, 1,700, 1,500, 2,700
Quality Score: 74, 73, 70, 66, 63, 62, 52, 68
Answer:
Step-by-step explanation:
no x y xy x²
1 2300 74 170200 5290000
2 1800 73 131400 3240000
3 2500 70 175000 6250000
4 2700 66 178200 7290000
5 2000 63 126000 4000000
6 1700 62 105400 2890000
7 1500 52 78000 2250000
8 2700 68 183600 7290000
Total 17200 528 1147800 38500000
Mean of x is
[tex]\bar x = \frac{17200}{8} =2150[/tex]
Mean of y is
[tex]\bar y = \frac{528}{8} =66[/tex]
From the table above
we find [tex]\hat B_1[/tex]
[tex]\hat B_1=\frac{\sum xy- \bar x \sum y}{\sum x^2- n \barx^2} \\\\=\frac{1147800-2150(528)}{38500000-8(2150)^2} \\\\=\frac{1147800-1135200}{38500000-36980000} \\\\=\frac{12600}{1520000} \\\\=0.008289[/tex]
so [tex]\hat b_0[/tex] is
[tex]\hat b_0=\bar y-\bar B_1 x\\\\=66-0.008289(2150)\\\\=66-17.82135\\\\=48.17865[/tex]
The line of regression is
The price x is 1900
[tex]\hat y =\hat B_0+\hat B_1x\\\\=48.17865+0.008289\times1900\\\\=48.17865+15.7491\\\\=63.928[/tex]
The line of regression is 63.928
Answer:
y=48.2+0.00829x;64
Step-by-step explanation:
Last year at a certain high school, there were 96 boys on the honor roll and 85 girls on the honor roll. This year, the number of boys on the honor roll increased by 25% and the number of girls on the honor roll increased by 20%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
22.7
Step-by-step explanation:
ok so, First we need to find new values:
96( 1 + 0.25) =120
85( 1+0.2)= 102
Boys last year girls last year total this year
96 85 181
Boys this year girls this year total this year
120 102 222
Find the overall increase:
181( 1+r)= 1.226519
THEN U SUBTRACT 1
r=0.226519
Multiply by 100 and round to nearest 10th
22.7%
Final Answer: 22.7%
HOPED IT HELPED:)
Christine has a motion detector light which gets activated an average of 16 times every 2 hours during the night. In order to find the probability that the motion detector light will be activated more than 4 times in a 25 minute period during the night using the Poisson distribution, what is the average number of activations per 25 minutes?
Answer:
The average number of activations per 25 minutes is 2.5.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!} [/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
In this question:
For 2 hours = 2*60 = 120 minutes, the mean is 16 times.
To find for 25 minutes, we use a rule of three.
120 minutes - 16 times
25 minutes - m times
[tex]120m = 12*25[/tex]
[tex]m = \frac{12*25}{120}[/tex]
[tex]m = 2.5[/tex]
The average number of activations per 25 minutes is 2.5.
Find the first 4 terms and the 10th one n+5
Answer: First 4 terms of n + 5 = 6,7,8,9
10th term = 15
Hope this is right
Step-by-step explanation:
By putting n = 1 , 2, 3 , 4 we can find first 4 terms
When n = 1
n + 5 = 1 + 5 = 6
When n = 2
n + 5 = 2 + 5 = 7
When n = 3
n + 5 = 3 + 5 = 8
When n = 4
n + 5 = 4 + 5 = 9
When n = 10
n + 5 = 10 +5 = 15