Answer:
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Which means that the first number is 104, the second number is 104 + 1 and the third number is 104 + 2. Therefore, three consecutive integers that add up to 315 are 104, 105, and 106.
Step-by-step explanation:
In a survey, participants were asked how much confidence they had in the economy.
The results were as follows:
Response Number
A great 3,187
deal
Some
9,120
Hardly 5,149
any
What is the probability that a sampled person has either some confidence or a great
deal of confidence in the economy? Write only a number as your answer. Round to
two decimal places (for example: 0.43). Do not write as a percentage.
Answer:
0.71
Step-by-step explanation:
Great Deal or Some = 12,307
Total Participants = 17,456
Probability = 12,307/17,456 = 0.71
To solve a polynomial inequality, we factor the polynomial
into irreducible factors and find all the real_______polynomial. Then we find the intervals determined by the real__________sign of the polynomial on that interval. Let
$$P(x)=x(x+2)(x-1)$$
Fill in the diagram to find the intervals on which
$P(x) \geq 0$
we see that $P(x) \geq 0$ on the
intervals_______and________.
Answer:
To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real _zeros_ polynomial. Then we find the intervals determined by the real _zeros and use test points in each interval to find the_ sign of the polynomial on that interval.
If P(x) = x(x+2)(x-1)
And P(x) ≥ 0
We see that P(x) ≥ 0 on the intervals (-2, 0) and (1, ∞).
Step-by-step explanation:
The complete question is attached to this solution
To solve inequality of a polynomial, we first obtain the solutions of the polynomial. The solutions of the polynomial are called the zeros of the polynomial.
If P(x) = x(x+2)(x-1)
The solutions of this polynomial, that is the zeros of this polynomial are 0, -2 and 1.
To now solve the inequality that arises when
P(x) ≥ 0
We redraw the table and examine the intervals
The intervals to be examined as obtained from the zeros include (-∞, -2), (-2, 0), (0, 1) and (1, ∞)
Sign of | x<-2 | -2<x<0 | 0<x<1 | x>1
x | -ve | -ve | +ve | +ve
(x + 2) | -ve | +ve | +ve | +ve
(x - 1) | -ve | -ve | -ve | +ve
x(x+2)(x-1) | -ve | +ve | -ve | +ve
The intervals that satisfy the polynomial inequality P(x) = x(x+2)(x-1) ≥ 0 include
(-2, 0) and (1, ∞)
Hope this Helps!!!
The mean weight of frozen yogurt cups in an ice cream parlor is 8 oz.Suppose the weight of each cup served is normally distributed withstandard deviation 0.5 oz, independently of others.(a) What is the probability of getting a cup weighing more than 8.64oz
Answer:
10.03% probability of getting a cup weighing more than 8.64oz
Step-by-step explanation:
Problems of normally distributed samples are solved using 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 = 8, \sigma = 0.5[/tex]
What is the probability of getting a cup weighing more than 8.64oz
This is the 1 subtracted by the pvalue of Z when X = 8.64. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8.64 - 8}{0.5}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a pvalue of 0.8997
1 - 0.8997 = 0.1003
10.03% probability of getting a cup weighing more than 8.64oz
Triangle ABC is a right triangle whose right angle is ZABC.
Find the measure of ZEBF.
ZABC and DBF are vertical angles, so they have the same
measure. Because IZABC is 90°, the sum of m2. DBE and
m2 EBF must also be 90°
Solve for x in this equation.
x + (x - 12) = 90
2x - 12 = 90
2x = 102
X51
m2 EBF = 51°
1.What is m
2.What is m
3.Explain how to find m
Answer: m is 13
m is 6
you find m by calculating!
Step-by-step explanation:
-23d + 81 <-98d + 1
Solve for d
Step-by-step explanation:
-23d + 81 < - 98d + 1
81 - 1 < - 98d + 23d
80 < - 75d
80/ - 75 < d
10/ - 3 < d
Im stuck who can help me
Answer:
Option D
Step-by-step explanation:
This question is based on the " Partition Postulate. " You might be familiar with it, it states that a whole is composed of several parts. In this case you could say that this " whole " is ∠ ABC, and the " parts " are ∠1 and ∠2. By this Theorem you could also state the following;
[tex]m< ABC = m< 1 + m< 2,\\\\Substitute,\\110 = 4x + ( 5x + 10 ),\\110 = 4x + 5x + 10,\\4x + 5x + 10 = 110 - Option D\\\\Solution - Option D[/tex]
Hope that helps!
find an angle x where sin x = cos x (I know this has been answered but I rlly don't get it..)
Answer:
45 degrees
Step-by-step explanation:
sin x=cos(90-x)
sin(45)=cos(90-45)=cos(45)
Answer:
The answer is 45.
sin45=cos45= 1/√2.
hope it helps u ...
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 7 20 14 41
Female 3 4 19 26
Total 10 24 33 67
If one student is chosen at random,
Find the probability that the student was male OR got an "A".
Answer:
46/ 67
Step-by-step explanation:
The numbers of students irrespective of grades is;
The sum of the last roll of numbers:
10+24+ 33+ 67 = 134
The number of males irrespective of grades is the sum of the numbers in the male row ;
7 +20+ 14 +41= 82
The numbers of students with grade A is the first column at the last row and is 10;
Hence;
the probability that the student was male OR got an 'A' is
the probability that the student was male plus the probability that he/she got an 'A'.
The probability that it's a male is ;
Number of males/ total number of students
=82/134
The probability that he got an A is;
The number of students that got A/ the total number of students;
10/134
Hence
the probability that the student was male OR got an 'A' is;
82/ 134 + 10/134 = 92/134 = 46/ 67
Alguien me puede ayudar con esto por favor!!!!
Answer:
8 + 15i
Step-by-step explanation:
(-2 + 3i) + 2(5 + 6i) =
= -2 + 3i + 10 + 12i
= 8 + 15i
find the area enclosed by the curve y^2=x^2-x^4
Answer: 4/3
Step-by-step explanation:
As you know this graph is a lemniscate
[tex]4\int\limits^1_0 {x\sqrt{1-x^{2} } \, dx =\frac{4}{3} =1.33$[/tex]
The most common form of color blindness is an inability to distinguish red from green. However, this particular form of color blindness is much more common in men than in women (this is because the genes corresponding to the red and green receptors are located on the X-chromosome). Approximately 79% of American men and 0.4% of American women are red-green color-blind.1 Let CBM and CBW denote the events that a man or a woman is color-blind, respectively.
(a) If an Americal male is selected at random, what is the probability that he is red-green color-blind? P(CBM) =
(b) If an American female is selected at random, what is the probability that she is NOT red-green color-blind? P (not CBW) =
(c) If one man and one woman are selected at random, what is the probability that neither are red-green color-blind? P=(neither is color-blind) =
(d) If one man and one woman are selected at random, what is the probability that at least one of them is red-green color-blind? P=(at least one is color-blind)
Answer:
(a) P(CBM) = 0.07
(b) P(not CBW) = 0.996
(c ) P(neither is color-blind) = 0.926
(d) P=(at least one is color-blind) = 0.074
Step-by-step explanation:
The correct data is that Approximately 7% of American men and 0.4% of American women are red-green color-blind.
(a) Probability that he is red-green color-blind:
[tex]P(CBM) = 0.07[/tex]
(b) Probability that she is NOT red-green color-blind:
[tex]P(not\ CBW) =1- P(CBW)\\P(not\ CBW) = 1 -0.004\\P(not\ CBW) =0.996[/tex]
(c) Probability that neither are red-green color-blind
[tex]P(neither) = P(not\ CBW)*P(not\ CBM) \\P(neither) = 0.996 *(1-0.07)\\P(neither)=0.926[/tex]
(d) Probability that at least one of them is red-green color-blind
[tex]P(at\ least\ one) = 1- P(neither) \\P(at\ least\ one) = 1-0.926\\P(at\ least\ one) = 0.074[/tex]
Please answer this correctly
Answer:
A = 1/2 b*h
A = 24
b = 8
h = ?
24 = 1/2 * 8 * h
24 = 4h
h = 6
The height is 6 cm.
Hope this helps.
find the quotient of 25.5÷0.5
Answer:
[tex]51[/tex]
Step-by-step explanation:
[tex]\frac{25.5}{0.5}[/tex]
[tex]\frac{255}{5}[/tex]
[tex]=51[/tex]
It is believed that approximately 12% of the population of the United States is lefthanded. Suppose researchers suspect that the proportion of left-handed people is higher in certain states than the national average. The researchers conduct a sample of 200 randomly selected people in the state of Maine and find that 29 people in the sample are left-handed.
a. Write the null hypothesis and alternative hypothesis and define your parameter.
b. Show that the necessary conditions (Randomization Condition, 10% Condition, Sample Size Condition) are satisfied to perform a hypothesis test. Briefly explain how each condition is satisfied.
c. Perform the hypothesis test and find the P-value. (To show your work: Write down what values you are entering into the hypothesis testing calculator.)
d. Is there strong evidence that the left-handed rate in the state of Maine is higher than the national average? Briefly explain how you know.
Answer:
Step-by-step explanation:
a. Null hypothesis: P = p
Alternatives hypothesis: P =/ p
Where P is the hypothesized population proportion and p is the sample proportion
b. Performing a test of proportions
Randomization: the sample was randomly selected in the study
The population size is at least 20 times as big as the sample size.
The sample includes both successes and failures with 29 success and 171 failures.
c. To perform the hypothesis test: we have to find the standard deviation first
Sd = sqrt[ P * ( 1 - P ) / n ]
where P is the hypothesized value of population proportion, n is the sample size.
Sd = √[0.12*(1-0.12)/200]
Sd = √[0.12*(0.88/200]
Sd = √[0.12*(0.0044)]
Sd = √0.000528
Sd = 0.023
Then we can find the z score
z = (p - P) / σ where p = 29/200 = 0.145
z = (0.145-0.12)/ 0.023
z = 0.025/0.023
z = 1.09
Calculation the p value using 0.05 level of significance and a two waited test (p value calculator),
A p-value of 0.2757 which is greater than 0.05, thus we will fail to reject the null stating that there is not enough strong evidence that the left-handed rate in the state of Maine is higher than the national average.
one car takes half a minute to complete a circuit.
the other car takes 1 minute and 10 seconds to complete a circuit.
if they start side by side, how long will it be before they are next side by side on the start line? state the units in your answer!
please help me I just need the answer
Answer:
7 laps
Step-by-step explanation:
Draw a model of square root of 12 using perfect squares
Answer:
The answer is "[tex]\sqrt{12}[/tex] is not a perfect square".
Step-by-step explanation:
12 is not a perfect square because it is the natural number, and no other natural number would square the number 12, that's why it is not a perfect square.
If we calculate the square root of [tex]\sqrt{12}[/tex]. so, it is will give [tex]2\sqrt{3}[/tex] that is not a perfect square root which can be described as follows:
[tex]\Rightarrow \sqrt{12}= \sqrt{2\times 2\times 3}[/tex]
[tex]= \sqrt{2^2\times 3}\\\\= 2\sqrt{3}\\\\[/tex]
[tex]\bold{\sqrt{12}}[/tex] is not a perfect square root.
Answer:
Here's a picture
Step-by-step explanation:
find the slope of the line through points 8,2 and -1,-4
Answer:
2/3
Step-by-step explanation:
We can find the slope by using the slope formula
m= (y2-y1)/(x2-x1)
= (-4-2)/(-1-8)
= -6/ -9
= 2/3
Graph the equation below by plotting the
y-intercept and a second point on the
line.
Answer:
Step-by-step explanation:
On the y-axis, graph the point on (0,4). Then from there, go up one, and to the right 4.
what is the radius of the circle that has an area of [tex]81*x*pi[/tex] degrees
Answer:
R=9
Step-by-step explanation:
the formula for area of a circle is pi r squared
where r denotes the radius of the circle
equating the formula for area with the area of the circle provided
p\i r squared = 81 p\i
r squared = 81
r = radical 81
r =9 inches
A train is traveling at a constant speed and has traveled 67.5 miles in the last 11 hours.
Which equation shows the proportional relationship between the distance, d, and the time, t,
that the train has traveled?
A.d=45t
B.d=50t
C.d = 690
D.d=67.5t
Answer:
A. d= 45t
Step-by-step explanation:
(assuming that you meant 67.5 in the last 1.5 hours)
67.5 miles = distance
1.5 hours = time
therefore:
[tex]\frac{d}{t\\}[/tex] = 67.5/1.5
making your answer 45
leaving a as your correct answer:
d= 45t
The proportion relationship between the distance d, and the time t, that the train has travelled is, d = 45t. So the correct option is A).
What is a proportion relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
Given that, A train travels at a constant speed and has travelled 67.5 miles in the last 1.5 hours. (assuming that you meant 67.5 in the last 1.5 hours)
67.5 miles = distance
1.5 hours = time
We know that, speed = distance / time
s = 67.5/1.5
s = 45 mph
Now, distance = speed × time
d = 45t
Hence, the proportion relationship between the distance d, and the time t, that the train has travelled is, d = 45t. So the correct option is A).
For more references on proportion relationship, click;
https://brainly.com/question/29765554
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The point A (-7,5) is reflected over the line x = -5, and then is reflected over the line x= 2. What are the coordinates of
A?
o (7, 19)
O (10,5)
(7,5)
(10, 19)
Answer:
(7, 5) is the final reflection of the point.
Step-by-step explanation:
We are given point A(-7, 5) which is first reflected over the line [tex]x= -5[/tex].
The minimum distance of the point A(-7, 5) from the line [tex]x= -5[/tex] is 2 units across the horizontal path (No change in y coordinate).
Point A lies 2 units on the left side of the line [tex]x= -5[/tex].
So, its reflection will be 2 units on the right side of [tex]x= -5[/tex].
Let its reflection be A' which has coordinates as (-5+2,5) i.e. (-3, 5).
Now A'(-3, 5) is reflected on the line [tex]x=2[/tex].
The minimum distance of the point A'(-3, 5) from the line [tex]x=2[/tex] is 5 units across the horizontal path (No change in y coordinate).
Point A' lies 5 units on the left side of the line [tex]x=2[/tex].
So, its reflection will be 5 units on the right side of [tex]x=2[/tex].
Let its reflection be A'' which has coordinates as (2+5, 5) i.e (7, 5) is the final reflection of the point..
Please find attached image.
(7, 5) is the final reflection of the point.
If 9: x= x-4, then x=
0 36
18
0 24
6
Answer:
2±√13
Step-by-step explanation:
9/x=x-4
x² -4x - 9=0
x² -4x +4- 13=0
(x -2)²=13
x-2= ±√13
x= 2±√13
What is the approximate value for the modal daily sales?
Answer:
Step-by-step explanation:
Hello!
The table shows the daily sales (in $1000) of shopping mall for some randomly selected days
Sales 1.1-1.5 1.6-2.0 2.1-2.5 2.6-3.0 3.1-3.5 3.6-4.0 4.1-4.5
Days 18 27 31 40 56 55 23
Use it to answer questions 13 and 14.
13. What is the approximate value for the modal daily sales?
To determine the Mode of a data set arranged in a frequency table you have to identify the modal interval first, this is, the class interval in which the Mode is included. Remember, the Mode is the value with most observed frequency, so logically, the modal interval will be the one that has more absolute frequency. (in this example it will be the sales values that were observed for most days)
The modal interval is [3.1-3.5]
Now using the following formula you can calculate the Mode:
[tex]Md= Li + c[\frac{(f_{max}-f_{prev})}{(f_{max}-f_{prev})(f_{max}-f_{post})} ][/tex]
Li= Lower limit of the modal interval.
c= amplitude of modal interval.
fmax: absolute frequency of modal interval.
fprev: absolute frequency of the previous interval to the modal interval.
fpost: absolute frequency of the posterior interval to the modal interval.
[tex]Md= 3,100 + 400[\frac{(56-40)}{(56-40)+(56-55)} ]= 3,476.47[/tex]
A. $3,129.41 B. $2,629.41 C. $3,079.41 D. $3,123.53
Of all options the closest one to the estimated mode is A.
14. The approximate median daily sales is …
To calculate the median you have to identify its position first:
For even samples: PosMe= n/2= 250/2= 125
Now, by looking at the cumulative absolute frequencies of the intervals you identify which one contains the observation 125.
F(1)= 18
F(2)= 18+27= 45
F(3)= 45 + 31= 76
F(4)= 76 + 40= 116
F(5)= 116 + 56= 172 ⇒ The 125th observation is in the fifth interval [3.1-3.5]
[tex]Me= Li + c[\frac{PosMe-F_{i-1}}{f_i} ][/tex]
Li: Lower limit of the median interval.
c: Amplitude of the interval
PosMe: position of the median
F(i-1)= accumulated absolute frequency until the previous interval
fi= simple absolute frequency of the median interval.
[tex]Me= 3,100+400[\frac{125-116}{56} ]= 3164.29[/tex]
A. $3,130.36 B. $2,680.36 C. $3,180.36 D. $2,664
Of all options the closest one to the estimated mode is C.
Please help. I keep getting this problem wrong . I need help please . I’ll mark you as brainliest if correct . Only answer if you know. Thank you
Answer:
The real number 'a' = 32
The real number 'b' = 0
Step-by-step explanation:
Product of a number of a number and its conjugate = a + bi
The number is = -4 + 4i
Conjugate of this number is = -4 - 4i
Product of the number and it's conjugate
= (-4 + 4i)(-4 - 4i)
= -4(-4 - 4i) + 4i(-4 - 4i) [By distributive property]
= 16 + 16i - 16i - 16i²
= 16 - 16(-1)
= 16 + 16
= 32
a + bi = 32 + (0)i
By comparing both the sides,
a = 32
b = 0
What is the length of AC
Answer:
5.8
Step-by-step explanation:
The angle bisector makes the triangle sides on either side of it proportional.
AC/CD = AB/BD
AC = CD·AB/BD
AC = 2(8.1/2.8) = 8.1/1.4 ≈ 5.7857 . . . . substitute shown values, evaluate
AC ≈ 5.8
4. In the Department of Natural Sciences, 14 faculty members have a PhD, and 30 faculty
members do not have a PhD. In the Department, the number of female faculty who do not
have a PhD is 10 more than the number of females who have a PhD. If a third of the male
faculty in the Department have a PhD, then what is the number of female faculty in the
Answer:
8
Step-by-step explanation:
We can start by making the table below to show the given numbers (red) and to assign a variable (x) to the number we want to find: female PhDs.
By subtracting the female numbers from the totals, we can find the corresponding numbers of male PhDs and non-PhDs.
The number of male non-PhDs is twice the number of male PhDs, so we have ...
2(14 -x) = 20 -x
28 -2x = 20 -x . . . . eliminate parentheses
8 = x . . . . . . . . . . . .add 2x-20
The number of female faculty with PhDs is 8.
What is the MEDIAN of this data?
Answer:
I think the median is 7
if it is not im so sorry
The median of the data is 7.
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Show the frequency distribution for the Gross Profit Margin using the five intervals below:, , , , and Gross Profit MarginFrequencyA. B. C. D. Choose the correct histogram from the above diagrams.e. What is the average price/earnings ratio (to 1 decimal)
Answer:
Step-by-step explanation:
a) Number of variables in the data set : 5
b) A quantitative variable is the one which can be quantitatively measured. i.e. it is a numerical value.
A categorical variable is the one that can take one value from a limited number of fixed values.
Exchange is a Categorical Variable. Price/Earnings Ratio is a Quantitative Variable. Gross Profit Margin (%) is a Quantitative Variable.
c. Out of the 25 stocks, AMEX is the exchange for 5 stocks. So percent frequency is 5/25 = 0.2 = 20%.
NYSE is the exchange for 3 stocks. So percent frequency is 3/25 = 0.12 = 12%.
OTC is the exchange for 17 stocks. So percent frequency is 17/25 = 0.68 = 68%.
These percentages are correctly shown in graph a. So the answer is a.
d) The frequency distribution is
Gross Profit Margin Frequency
0-14.9 2
15-29.9 6
30-44.9 8
45.59.9 6
60.74.9 3
As we come across the Gross Profit Margin values in the table, we add a | next to its respective interval and build the above table. E.g. the first value in the table under Gross Profit Margin is 36.7 which lies in the interval 30–44.9. So we add one | in fromt of that interval and so on until we cover the entire table. The number of | shows the frequency distribution of the values.
The correct histogram is A.
e. The average price/earnings ratio is found by adding all the 25 values in the table and dividing the answer by 25.
= 505.40/25
= 20.2Find the third-degree polynomial function that has zeros −2 and −15i, and a value of 1,170 when x=3.
Answer:
The third degree polynomial function = x³ + 27x² + 200x + 300
Step-by-step explanation:
The third-degree polynomial function has zeros −2 and −15.
From the above, we have been given two factors of the polynomial function. Let's derive the factors from the two zeros of the polynomial given.
The two given zeros of the polynomial can be written as:
x= -2
x+2 = 0
(x+2) is a factor of the polynomial
x= -15
x+15 = 0
(x+15) is a factor of the polynomial
So we have two factors of the polynomial (x+2) and (x+15). But since it is a third degree polynomial, we have to find the third factor.
Let (x-b) be the third factor and f(x) represent the third degree polynomial
f(x) = (x-b) (x+2) (x+15)
Expanding (x+2) (x+15) = x² + 2x + 15x + 30
(x+2) (x+15) = x² + 17x + 30
f(x) = (x-b) (x² + 17x + 30)
From the given information, a value of 1,170 is obtained when x=3
f(3) = 1170
Insert 3 for x in f(x)
f(3) = (3-b) (3² + 17(3) + 30)
1170 = (3-b) (9 + 51 + 30)
1170 = (3-b) (90)
1170/90 = 3-b
3-b = 13
b = 3-13 = -10
Insert value of b in f(x)
f(x) = [x-(-10)] (x² + 17x + 30)
f(x) = (x+10) (x² + 17x + 30)
f(x) = x³ + 17x² + 30x + 10x² + 170x + 200x + 300
f(x) = x³ + 27x² + 200x + 300
The third degree polynomial function = x³ + 27x² + 200x + 300
someone plz help asap plz
Answer:
a) 6
b) 10
Step-by-step explanation:
a) The area of a rhombus is half the product of the diagonals, meaning that the area of the shaded part is 4*3/2=6 square meters.
b) To find the area of the white background, you need to find the area of the full rectangle, and then to find the area of both rhombii. The area of the black rhombus is 2*4/2=4 square meters. The area of the full rectangle is 4*5=20 units. Subtracting the areas of the two rhombii, you get an area for the white background of 20-6-4=10 square meters. Hope this helps!
