Answer:
the three boxes should be filled with
2 8 -12
respectively
Step-by-step explanation:
The general equation of the parabola in this problem is
y = a(x-h)^2 + k
vertex is at (-2, -20), => k=-20, h = 2
so the equation is
y = a(x+2)^2 - 20
To have y-intercept = -12, we set x = 0
-12 = a(0+2)^2 - 20
a(2^2) = 8
a = 2
therefore the equation of the parabola is
y = 2 (x+2)^2 -20 = 2x^2 + 8x - 12
the three boxes should be filled with
2 8 -12
respectively
Which of the following statements must be true about this diagram? Check all that apply.
Answer:
Options (D), (E) and (F) are the correct options.
Step-by-step explanation:
From the figure attached,
1). Angle 4 is the exterior angle of the given triangle having interior angles 1, 2 and 3.
Therefore, by the property of exterior angle,
∠4 = ∠1 + ∠2
2). Since ∠4 = ∠1 + ∠2,
Therefore, ∠4 will be greater than ∠1
Similarly, ∠4 will be greater than ∠2
Therefore, Options (D), (E) and (F) are the correct options.
Show all work and receive brainliest!
Answer:
Lower Quartile: 62
Upper Quartile: 81
Interquartile Range: 19
Step-by-step explanation:
To find the lower quartile, you want to find the median from the minimum to the median.
49, 55, 62, 64, 67
The median of this is 62. Therefore, 62 is the lower quartile.
To find the upper quartile, you want to find the median from the median to the maximum.
76, 79, 81, 82, 83
The median of this is 81. Therefore, 81 is the upper quartile.
To find the interquartile range, you subtract the upper and lower quartile.
81-62=19
The difference is 19. Therefore, the interquartile range is 19.
This Venn diagram represents the science subjects studied by students what is the probability chosen at random that that child does not study chemistry
Answer:
0.49
Step-by-step explanation:
From the Venn diagram:
The number of students that study biology and physics = 2
The number of students that study biology and chemistry = 6
The number of students that study chemistry and physics = 4
The number of students that study only physics = 5
The number of students that study only biology = 7
The number of students that study only chemistry = 8
The number of students that study all 3 subjects = 3
The number of students that study none = 6
Therefore the total number of students = 2 + 6 + 4 + 5 + 7 + 8 + 3 + 6 = 41 students
The number of students that study chemistry = 8 + 6 + 3 + 4 = 21 students
The number of student that does not study chemistry = 41 - 21 = 20 students
the probability chosen at random that that child does not study chemistry = number of student that does not study chemistry / total number of students = 20/41 = 0.49
Find m^4+(1/m^4) if m-(1/m)=3 Please help with this.
Answer:
m^4+(1/m^4)= 123.4641 or 118.6
Step-by-step explanation:
m-(1/m)=3
m² - 1= 3m
m² -3m -1= 0
m = (3-√13)/2 = -0.3
Or
m =( 3+√13)/2= 3.3
m^4+(1/m^4) for m = -0.3
= (-0.3)^4 + (1/(0.3)^4)
= 0.0081 + 123.456
= 123.4641
m^4+(1/m^4) for m = 3.3
= (3.3)^4 + (1/(3.3)^4)
= 118.5921 + 0.008432
= 118.6
The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. A beam with diagonal 6in will support a maximum load of 108lb. Write the equation that relates the load L to the diagonal d of the cross-section. How large of a load, in pounds, will a beam with a 10in diagonal support?
Answer:
The equation is:
[tex]L=3\,\,d^2\\[/tex]
and a beam with 10 in diagonal will support 300 lb
Step-by-step explanation:
The mathematical expression that represents the statement:
"The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. "
can be written as:
[tex]L=k\,\,d^2[/tex]
where k is the constant of proportionality
To find the constant we use the data they provide: "A beam with diagonal 6 in will support a maximum load of 108 lb.":
[tex]L=k\,\,d^2\\108 = k\,\,(6)^2\\k=\frac{108}{36} \,\,\frac{lb}{in^2}\\ k = 3\,\,\frac{lb}{in^2}[/tex]
Now we can use the proportionality found above to find the maximum load for a 10 in diagonal beam:
[tex]L=3\,\,d^2\\L=3\,\,(10)^2\\L=300 \,\,lb[/tex]
Answer:
L=3d^2 the beam will support 300 pounds
Step-by-step explanation:
108=k x 6^2
Dividing by 6^2=36 gives k=3, so an equation that relates L and d is
L=3d^2 d=10 yields
3(10)^2=300
So a beam with a 10in diagonal will support a 300lb load.
In a plane, if a line is perpendicular to one of two blank lines, then it is also perpendicular to the other
Answer:
ParallelStep-by-step explanation:
The complete statement would be "if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other".
The reason for this is because parallel lines have the same slope, that's the condition. On the other hand, parallel lines have opposite and reciprocal slopes.
So, if you think this through, if a line is perpendicular to another, then it's going to be perpendicular to all different lines which are parallel to the first one, because all their slopes are equivalent, and they will fulfill the perpendicularity condition.
Answer:
Parallel line
Step-by-step explanation:
Hope It Helps
What is the area of the circle shown below? Please
answer quickly! 20 points
Answer:
A =1017.9 cm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi * (18)^2
Using the pi button
A =1017.87602 cm^2
Rounding to 1 decimal place
A =1017.9 cm^2
Wilma can mow a lawn in 60 minutes. Rocky can mow the same lawn in 40 minutes. How long does it take for both Wilma and Rocky to mow the lawn if they are working together?
===================================================
Explanation:
Let's say the lawn is 120 square feet. I picked 120 as it is the LCM (lowest common multiple) of 60 and 40.
Since Wilma can mow the lawn in 60 minutes, her rate is 120/60 = 2 sq ft per minute. In other words, each minute means she gets 2 more square feet mowed. Rocky can do the full job on his own in 40 minutes, so his rate is 120/40 = 3 sq ft per minute.
Their combined rate, if they worked together (without slowing each other down), would be the sum of the two rates. So we get 2+3 = 5 sq ft per minute as the combined rate. The total time it would take for this 120 sq ft lawn is 120/5 = 24 minutes.
--------------------------
Another approach
Wilma takes 60 minutes to do the full job, so her rate is 1/60 of a lawn per minute. Rocky's rate is 1/40 of a lawn per minute. Their combined rate is
1/60 + 1/40 = 2/120 + 3/120 = 5/120 = 1/24 of a lawn per minute
x = number of minutes
(combined rate)*(time) = number of jobs done
(1/24)*x = 1
x = 1*24
x = 24 is the time it takes if they worked together without getting in each other's way.
Effectively, we are solving the equation
1/A + 1/B = 1/C
with
A = time it takes Wilma to do the job on her own
B = time it takes Rocky to do the job on his own
C = time it takes the two working together to get the job done
The equation above is equivalent to C*(1/A + 1/B) = 1 or (1/A + 1/B)*C = 1.
So basically you find the value of 1/A + 1/B, then find the reciprocal of this to get the value of C.
Together they can mow the lawn in 24 minutes.
What are the relation between time, work, and efficiency?Time and efficiency are inversely proportional to each other.
Time and work are directly proportional to each other.
Given, Wilma can mow a lawn in 60 minutes. Rocky can mow the same lawn in 40 minutes.
Assuming total work to be 120 as it is the LCM of 40 and 60.
So, The efficiency of Wilma is (120/60) = 2 and the efficiency of Rocky is
(120/40) = 3.
Now together their efficiency is (2 + 3) = 5.
∴ Together they can complete the work in (120/5) = 24 minutes.
learn more about time and work here :
https://brainly.com/question/3854047
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the length of a square is 16m, what is the breadth of the square
Answer:
The breadth is 16m because a square is a quadrilateral (four sided shape) that has all its side to be of equal measure.
Find the first five terms in sequences with the following nth terms. 6n+3
Answer:
33
Step-by-step explanation:
An = 6n+3
so the first five terms in sequences is A5= 6*5 +3 = 33
Please answer this correctly without making mistakes
ANSWER :
Percentage = 50%
(if it odd and even then its 100%)
Answer:
100%
Step-by-step explanation:
There is a 100% chance rolling an odd or even since all the faces of this die are odd or even.
a recipe for fruit punch calls for 1/2 liter of lemonada and 1/10 liter of cranberry juice.what is the unit rate of lemonade to cranberry juice?
Answer:
unit rate of lemonade to cranberry juice
= 5:1
Step-by-step explanation:
A recipe for fruit punch calls for 1/2 liter of lemonada and 1/10 liter of cranberry juice
1/2 liter of lemonada= 0.5
1/10 liter of cranberry juice = 0.1
unit rate of lemonade to cranberry juice
= 0.5/0.1
unit rate of lemonade to cranberry juice
= (5*10^-1)/(1*10^-1)
unit rate of lemonade to cranberry juice
= 5/1 *(10^-1)/10^-1)
unit rate of lemonade to cranberry juice
= 5/1
unit rate of lemonade to cranberry juice
= 5:1
The unit rate of lemonade to cranberry juice is 5 : 1.
1/2 liters of lemonada are to be mixed with 1/10 litres of cranberry juice.
In ratio form this is:
1/2 : 1/10
To make it a unit rate of lamonada, you should divide both sides by the ratio of lamonada to cranberry juice in order to take lomonada's ratio to 1.
= 1/2 ÷ 1/2 : 1/10 ÷1/2
= 1 : 0.2
You then need to make the decimal a whole number by dividing both sides by the decimal:
= 1 ÷ 0.2 : 0.2 ÷0.2
= 5 : 1
The unit rate of lamonada to cranberry juice is therefore 5 : 1.
Find out more at https://brainly.com/question/18314944.
What is the next number in the sequence.
1,121,12321, 1234321
The next number in the sequence is _____
Answer:
123454321
Step-by-step explanation:
it's a palendrome, made out of a number of numbers in the sqquence.
For a study regarding mean cadence, two-way ANOVA was used. The two factors were walking device (none, standard walker, rolling walker) and dual task (being required to respond vocally to a signal or no dual task required). Results of two-way ANOVA showed that there was no evidence of interaction between the factors. However, according to the article, "the ANOVA conducted on the cadence data revealed a main effect of walking device." When the hypothesis regarding no difference in mean cadence according to which, if any, walking device was used, the sample F was 30.94, with d.f.N = 2 and d.f.D = 18. Further, the P-value for the result was reported to be less than 0.05.
Required:
What is the conclusion regarding any difference in mean cadence according to the factor "walking device used"?
Answer:
Step-by-step explanation:
With regards to the factor 'walking device used', the ANOVA conducted on the cadence data revealed a main effect of walking device, and also with the results of the experiment giving rise to a p - value less than 0.05, we can reject the null hypothesis which says, there is no effect of the walking device factor.
We can thus conclude that there is not enough statistics evidence to prove that there is no interaction between the two factors or that there is no effect of the walking device given the cadence data.
4x-39> -43 and8x+31<23
Answer:
SOLUTION SET={x/x>-1} and SOLUTION SET={x/x<-1}
Step-by-step explanation:
1)4x-39>-43
evaluating the inequality
adding 39 on both sides
4x-39+39>-43+39
4x>-4
dividing 4 on both sides
4x/4>-4/4
x>-1
SOLUTION SET={x/x>-1}
2)8x+31<23
evaluating the inequality
subtracting 31 on both sides
8x+31-31<23-31
8x<-8
dividing 8 on both sides
8x/8<-8/8
x<-1
SOLUTION SET={x/x<-1}
i hope this will help you :)
Answer: There are no solutions
Step-by-step explanation:Khan Academy
What percent of this grid is unshaded?
The grid has 10 columns and 10 rows making 100 equal sized squares 5 rows are
unshaded. The sixth row has 6 squares unshaded.
Answer:
56% shaded
Step-by-step explanation:
if there are 100 boxes, then every box it 1%
5 rows (50%) + 6 extra boxes (6%) = 56%
Is f(x)=x^2-3x+2 even function
Answer:
Step-by-step explanation:
No, it is not an even function. The graph is not symmetric about the y-axis.
A simple random sample of 100 8th graders at a large suburban middle school indicated that 81% of them are involved with some type of after school activity. Find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity.
Answer:
The interval is [tex]0.7187 < p < 2.421[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 100[/tex]
The population proportion is [tex]p = 0.81[/tex]
The confidence level is C = 98%
The level of significance is mathematically evaluated as
[tex]\alpha = 100 -98[/tex]
[tex]\alpha = 2%[/tex]%
[tex]\alpha = 0.02[/tex]
Here this level of significance represented the left and the right tail
The degree of freedom is evaluated as
[tex]df = n-1[/tex]
substituting value
[tex]df = 100 - 1[/tex]
[tex]df = 99[/tex]
Since we require the critical value of one tail in order to evaluate the 98% confidence interval that estimates the proportion of them that are involved in an after school activity. we will divide the level of significance by 2
The critical value of [tex]\frac{\alpha}{2}[/tex] and the evaluated degree of freedom is
[tex]t_{df , \alpha } = t_{99 , \frac{0.02}{2} } = 2.33[/tex]
this is obtained from the critical value table
The standard error is mathematically evaluated as
[tex]SE = \sqrt{\frac{p(1-p )}{n} }[/tex]
substituting value
[tex]SE = \sqrt{\frac{0.81(1-0.81 )}{100} }[/tex]
[tex]SE = 0.0392[/tex]
The 98% confidence interval is evaluated as
[tex]p - t_{df , \frac{\alpha }{2} } * SE < p < p + t_{df , \frac{\alpha }{2} }[/tex]
substituting value
[tex]0.81 - 2.33 * 0.0392 < p < 0.81 +2.33 * 0.0392[/tex]
[tex]0.7187 < p < 2.421[/tex]
Graph on a piece of paper y= -3x-2
Hey there! :)
Answer:
To graph y = -3x - 2, we can start by solving for some points. Plug in x values for x in the equation to solve for the y value:
X Y
-2 4
-1 1
0 -2
1 -5
2 -8
Use these points to graph the line (Graphed below)
Chocolate chip cookies have a distribution that is approximately normal with a mean of 24.7 chocolate chips per cookie and a standard deviation of 2.1 chocolate chips per cookie. Find Upper P 10 and Upper P 90. How might those values be helpful to the producer of the chocolate chip cookies?
Answer:
P10 = 27.4
P90 = 22.0
It helps the producer to know the higher (P10) and lower estimates (P90) for the amount of chocolate chips per cookie.
Step-by-step explanation:
In P10 and P90 the P stands for "percentile".
In the case of P10, indicates the value X of the random variable for which 10% of the observed values will be above this value X.
In the case of P90, this percentage is 90%.
In this case, we can calculate from the z-values for each of the percentiles in the standard normal distribution.
For P10 we have:
[tex]P(z>z_{P10})=0.1\\\\z_{P10}=1.2816[/tex]
For P90 we have:
[tex]P(z>z_{P90})=0.9\\\\z_{P90}=-1.2816[/tex]
Then, we can convert this values to our normal distribution as:
[tex]P10=\mu+z\cdot\sigma=24.7+1.2816\cdot 2.1=24.7+2.7=27.4 \\\\P90=\mu+z\cdot\sigma=24.7-1.2816\cdot 2.1=24.7-2.7=22.0[/tex]
A sample of 17 items was taken, and 5 of the units were found to be green. What is the 97% upper confidence limit(one-sided) for the percentage of green items
Answer:
The 97% upper confidence limit for the proportion of green items is 0.502.
Step-by-step explanation:
We have to calculate a 97% upper confidence limit for the proportion.
The sample proportion is p=0.294.
[tex]p=X/n=5/17=0.294\\[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.294*0.706}{17}}\\\\\\ \sigma_p=\sqrt{0.01221}=0.11[/tex]
The critical z-value for a 97% upper confidence limit is z=1.881.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.881 \cdot 0.11=0.208[/tex]
Then, the upper bound is:
[tex]UL=p+z \cdot \sigma_p = 0.294+0.208=0.502[/tex]
The 97% upper confidence limit for the proportion of green items is 0.502.
suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, remove it from the box and draw another marble. What is the probability of pulling out a red marble followed by a blue marble? The multiplication rule says to use P(red) P(blue).
Describe the probability of finding a red marble?
Describe the probability of finding a blue marble?
Describe the process of finding the probability of finding a red marble followed by a blue marble if the first marble was permanently removed?
What affect did removing the first marble from the box have on the problem?
Describe the probability of finding a red marble followed by the blue marble if the first marble is removed?
Answer:
1) 2/9
2)3/9
Step-by-step explanation:
sorry,thats what i know so far
Your drawer contains 10 red socks and 7 blue socks. You pick 3 socks without replacement. What's the probability that at least two socks will be different colors?
Answer:
105/136 ≈ 0.772
Step-by-step explanation:
There are 3 socks and 2 colors, so they are either all the same color or 2 will be different colors.
P(different colors)
= 1 − P(same color)
= 1 − ₁₀C₃/₁₇C₃ − ₇C₃/₁₇C₃
= 1 − 120/680 − 35/680
= 1 − 155/680
= 1 − 31/136
= 105/136
≈ 0.772
Suppose you take a 30-question, multiple-choice test, in which each question contains 4 choices: A, B, C, and D. If you randomly guess on all 30 questions, what is the probability you pass the exam (correctly guess on 60% or more of the questions)? Assume none of the questions have more than one correct answer (hint: this assumption of only 1 correct choice out of 4 makes the distribution of X, the number of correct guesses, binomial). What is the expected number of correct guesses, from problem #19? What is the standard deviation, ? (Remember that X is a binomial random variable!) What would be considered an unusual number of correct guesses on the test mention in problem number 19 using ?
Answer:
(a) The probability you pass the exam is 0.0000501.
(b) The expected number of correct guesses is 7.5.
(c) The standard deviation is 2.372.
Step-by-step explanation:
We are given that you take a 30-question, multiple-choice test, in which each question contains 4 choices: A, B, C, and D. And you randomly guess on all 30 questions.
Since there is an assumption of only 1 correct choice out of 4 which means the above situation can be represented through binomial distribution;
[tex]P(X =x) = \binom{n}{r}\times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 30
r = number of success = at least 60%
p = probbaility of success which in our question is the probability
of a correct answer, i.e; p = [tex]\frac{1}{4}[/tex] = 0.25
Let X = Number of questions that are correct
So, X ~ Binom(n = 30 , p = 0.25)
(a) The probability you pass the exam is given by = P(X [tex]\geq[/tex] 18)
Because 60% of 30 = 18
P(X [tex]\geq[/tex] 18) = P(X = 18) + P(X = 19) +...........+ P(X = 29) + P(X = 30)
= [tex]\binom{30}{18}\times 0.25^{18}\times (1-0.25)^{30-18} + \binom{30}{19}\times 0.25^{19}\times (1-0.25)^{30-19} +.......+ \binom{30}{29}\times 0.25^{29}\times (1-0.25)^{30-29} + \binom{30}{30}\times 0.25^{30}\times (1-0.25)^{30-30}[/tex]
= 0.0000501
(b) The expected number of correct guesses is given by;
Mean of the binomial distribution, E(X) = [tex]n \times p[/tex]
= [tex]30 \times 0.25[/tex] = 7.5
(c) The standard deviation of the binomial distribution is given by;
S.D.(X) = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{30 \times 0.25 \times (1-0.25)}[/tex]
= [tex]\sqrt{5.625}[/tex] = 2.372
solve and graph the set solution. 9-2x⩽3x+24 The bottom options for what graph
Answer:
A
Step-by-step explanation:
9-2x≤3x+24
-15≤5x
-3≤x
so it's:
[-3,∞)
Last year, a soft drink manufacturer had 22% of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 100 indicated that they like the taste. We are interested in determining if more than 22% of the population will like the new soft drink. 1. Using α = .05, test to determine if more than 22% of the population will like the new soft drink. 2. What should be the critical value(s)? 3. If there is more than one, please enter the positive one. (please keep at least 4 digits after the decimal point).
Answer:
Critical value zc = 1.6449.
As the test statistic z=1.3881 is smaller than the critical value zc=1.6449, it falls in the acceptance region and the null hypothesis is failed to be rejected.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that more than 22% of the population will like the new soft drink.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.22\\\\H_a:\pi>0.22\\[/tex]
The significance level is 0.05.
The sample has a size n=400.
The sample proportion is p=0.25.
[tex]p=X/n=100/400=0.25[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.22*0.78}{400}}\\\\\\ \sigma_p=\sqrt{0.000429}=0.0207[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.25-0.22-0.5/400}{0.0207}=\dfrac{0.0288}{0.0207}=1.3881[/tex]
As this is a right-tailed test, there is only one critical value and it is, for a significance level of 0.05, zc=1.6449.
As the test statistic z=1.3881 is smaller than the critical value zc=1.6449, it falls in the acceptance region and the null hypothesis is failed to be rejected.
Please answer this correctly
Answer:
100%
Step-by-step explanation:
Total = 7
Odd or less than 7 = 6+1
=> 7
P(odd or less than 7) = 7/7
In %age:
100%
Answer:
100%
Step-by-step explanation:
Number of cards= 7
Odd or less than 7= 7
P= 7/7=1=100%
What is the constant of proportionality in the equation Y = x/9?
Answer:
1/9
Step-by-step explanation:
Separate the fraction (1/9) from the variable x:
y = (1/9)x.
1/9 is the constant of proportionality.
You are walking directly away from your house. You are 555 miles away from your house when you start walking, so you can determine your distance from your house by adding 555 to the number of miles you have walked. In the equation below, xxx represents the number of miles you have walked, and yyy represents your distance from home in miles. The relationship between these two variables can be expressed by the following equation: y=x+5y=x+5y, equals, x, plus, 5 Identify the dependent and independent variables. Dependent variable Independent variable Your distance from home Number of miles you walk
Answer:
Dependent variable is Your distance from home(y)Independent variable is Number of miles you walk(x)Step-by-step explanation:
x represents the number of miles you have walked
y represents your distance from home in miles.
The relationship between these two variables can be expressed by the following equation: y=x+5
The dependent variable is that whose value changes whenever the value of the independent variable is changed.
From the equation above:
When x=1, y=1+5=6 milesWhen x=3, y=3+5=8 milesWe can clearly see that y changes for different values of x.
Therefore:
Dependent variable is Your distance from home(y)Independent variable is Number of miles you walk(x)Answer:
1dependant
2independant
Step-by-step explanation:
Can Anyone plz help me out with a question I’m struggling question 1 in the picture
Answer:
16x^2 + 8x.
Step-by-step explanation:
To find the area of the walkway, you need to do the area of the whole thing minus the area of the pool.
The area of the whole thing is (8x - 3)(2x + 7) = 16x^2 - 6x + 56x - 21 = 16x^2 + 50x - 21.
The area of the pool is (8x - 3 - x - x)(2x + 7 - x - x) = (6x - 3)(7) = 42x - 21.
So, the area of the walkway is 16x^2 + 50x - 21 - (42x - 21) = 16x^2 + 50x - 21 - 42x + 21 = 16x^2 + 8x.
If you want, you can factor that and make it 8x(2x + 1).
Hope this helps!