Answer:
D
Step-by-step explanation:
We're looking for two numbers that have a sum of -9 and a product of 40. These 2 numbers are -4 and -5 so the answer is (x - 4)(x - 5).
Answer:
(x-4)(x-5)
Step-by-step explanation:
х^2 - 9х+ 20
What 2 numbers multiply to 20 and add to -9
-4*-5 = 20
-4+-5 = -9
(x-4)(x-5)
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.
Management at a home improvement store randomly selected 95 customers and observed their shopping habits.They recorded the number of items each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the managers of the home improvement store.
a. number of items-discrete: total time-discrete
b. number of items-continuous; total time-discrete
c. number of items-continuous; total time-continuous
d. number of items-discrete; total time-continuous
Answer:
d. number of items-discrete; total time-continuous
Step-by-step explanation:
Continuous:
Real numbers, can be integer, decimal, etc.
Discrete:
Only integer(countable values). So can be 0,1,2...
In this question:
You can purchase 0, 1, 2,...,10,...,100,... items, so the number of items is discrete.
You can spend for example, 0.5 hours in the store, or 2.5 minutes, that is, can be decimal numbers. So the total time is continuous
The correct answer is:
d. number of items-discrete; total time-continuous
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 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]
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]
Graph the system of linear equations.
-{ y = 4x+ 5 and y = 2x + 2.
Answer:
work shown and pictured
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.
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.
If x, y, and z are positive integers and 3x=4y=7z, then the least possible value of x+y+z is?
A. 33
B. 40
C. 49
D. 61
E. 84
Answer:
D
Step-by-step explanation:
3x, 4y, and 7z must be equal to the LCM of 3, 4, and 7 in order to be the smallest value. The LCM is 84 which means x = 28, y = 21 and z = 12. 28 + 21 + 12 = 61.
Answer:
61
Step-by-step explanation:
3x=4y=7z
x =4/3 y
x = 7/3 z
Since they have to be integers
y and z must be multiples of 3
y = 7/4 z
Since they have to be integers
z must be multiple of 4
Z must be a multiple of 12
Let z = 12
Then
y = 7/4 *12
y = 21
x = 7/3 *12
x = 28
x+y+z
28+ 21+12
61
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.
Chase scored 14 points on Monday, and he doubled his score each day thereafter. How many points did he score on Thursday?
Answer:
112
Step-by-step explanation:
Original Score equals 14 right?
If chase doubles his original Score daily it will be
14*2 (Tuesday)=28
28×2 (Wednesday)=56
56×2 (Thursday)=112
Therefore,
Chase's Final score Equals 112
The number of points did he score on Thursday is 112.
Given that,
Chase scored 14 points on Monday. And he doubled his score each day thereafter.Based on the above information, the calculation is as follows:
On Monday = 14
On Tuesday = (14) (2) = 28
On Wednesday = (28) (2) = 56
On Thursday = (56) (2) = 112
Therefore, we can conclude that the number of points did he score on Thursday is 112.
Learn more: brainly.com/question/24169758
In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The
longest and the shortest days of the year vary by 2 hours 53 minutes from the equinox.
In this year, the equinox falls on March 21. In this task, you'll use a trigonometric function
to model the hours of daylight hours on certain days of the year in New York City.
Identify the independent and dependent variables find amplitude and the period of the function create a trigonometric function that describes the hours of sunlight for each day of the year and then use the function you built to find how fewer daylight hours February 10 will have then March 21
Answer:
independent: day number; dependent: hours of daylight
d(t) = 12.133 +2.883sin(2π(t-80)/365.25)
1.79 fewer hours on Feb 10
Step-by-step explanation:
a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).
__
b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,
March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...
d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))
d(t) = 12.133 +2.883sin(2π(t-80)/365.25)
__
c) d(41) = 10.34, so February 10 will have ...
12.13 -10.34 = 1.79
hours less daylight.
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.
Identify the axis of symmetry of the given quadratic
y= -3x^2 - 12
Answer:
[tex]\frac{d}{dy}(-3x^{2} -12) = -6x[/tex]
0 = -6x
0 = x
[tex]-3(0)^{2} -12 = -12[/tex]
(0,-12)
Step-by-step explanation:
2a -a + 1 =
x + y + x + 2 =
2(x + 4) + 2x =
3x + 2(x - 2) =
Answer:
Step-by-step explanation:
Please, share the instructions that come with each problem. Thanks.
2a -a + 1 = can be simplified to a + 1.
x + y + x + 2 = cannot be simplified.
2(x + 4) + 2x =
3x + 2(x - 2) = can be expanded and then simplified:
3x + 2x - 4 = 5x - 4
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.
Mr. Rosenberger asked his students to use the distributive property to rewrite the expression 18 (24) by using friendlier numbers. The table below shows the expressions that four students created. Expressions Created by Students Student Expression Aaron 10 + 8 times 4 + 20 Brian 10 + 8 (4 + 20) Cece 18 (4 + 6) Diana 18 (4 + 20)
Answer:
diana
Step-by-step explanation:
Answer:
I think it’s Diana I’m sorry if I’m wrong :P
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
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
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 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.
Need help with the problem 77
Hey there! :)
Answer:
∠A = 15.6°
Step-by-step explanation:
Use trigonometry to solve for ∠A. Since this involves the opposite and adjacent sides, tangent will be used. Therefore:
24/86 = arc tan x (inverse of tangent)
0.279 = arc tan x
x = 15.59° ≈ 15.6°.
Therefore:
∠A = 15.6°
Need help with this question thanks!
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:
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.
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
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.
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,∞)
if y varies inversely as the square of x, and when y = 4/63 find y when y varies inversely as the square of x = 3, and when find y when x=5
Answer:
Step-by-step explanation:
In order to solve this, we'll set up a proportion.
Since y is inversely related to the square of x, therefore:
y=4/63 ----->9 (square of x)
y=? ---------->25 (square of x)
According to the inverse relation:
y=4/63------->25
y=?------------->9 and y=4/175