The likelihood that at least 150 people will collaborate and react in a fresh sample of 400 telephone numbers is 0.9953.
Describe probability?The probability informs us of the likelihood that an event will occur. It is necessary for the likelihood to fall between 0 and 1. The likelihood of success is 1, whereas the probability of failure is 0.
Given, that the market research company has a history of having a 44% response rate for its telephone surveys.
Therefore, p=44%=0.44=μ
n=400
p=150/400
p=0.375
The standard deviation is then equal to,
σ=√(p(1-p))/n
σ=√(0.44(1-0.44))/400
σ=√(0.44×0.56)/400
σ=0.025
Using the z-table, the values are as follows:
z=(p-μ)/σ
z=(0.375-0.44)/0.025
z=-2.6
p(p>0.375)
=p(z>-2.6)
=1-p(z<-2.6)
=1-0.0047
=0.9953
=99.53%
Therefore, the likelihood that at least 150 people will participate and provide information in a new sample of 400 telephone numbers
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a shipment of 12 television sets contains 3 defective sets. in how many ways can a hotel purchase 5 of these sets and receive at least 2 of the defective sets?
The hotel can acquire 5 of these sets in 119/792 different ways and still expect to receive 2 of the defective sets.
Define the term combination?Combinations are mathematical operations that count the total number of possible configurations for a set of elements is when order of said selection is irrelevant.As per the stated question.
You can select five television from a possible twelve in the sample space.
To acquire at least 2 faulty, therefore:
¹²C₅ = 12!/(7!)(5!) =12*11*10*9*8/(5*4*3*2*1)
¹²C₅ = 11*9*8
Obtaining two or three defective items. (At least 2).
2 defective items are-
(³C₂)(⁹C₄) = 3*9*8*7*6/(4!)
(³C₂)(⁹C₄) =9*7 =63
Three defective items equal -
(³C₃)(⁸C₂) = 1*8*7/2!
(³C₃)(⁸C₂) = 56
Total defective items is 63+56= 119 ways.
Probability = 119/(11*9*8)
Probability = 119/792
Thus, a hotel can acquire 5 of these sets in 119/792 different ways and still expect to receive 2 of the flawed sets.
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This rectangular design is made from 6 squares. there are 2 small squares surrounded by 4 larger squares. the area of each small square of 1sq.cmwhat is the total area of the design?
The total Area the design is 8 square cm.
Area of rectangular design is product of length and breadth of rectangular design.
In the given question we have,
Rectangular design is made up from 6 squares .
there is 2 small squares surrounded by 4 large squares.
Area of each small square = 1 sq.cm
let the length of rectangular design be l cm
and breadth is b cm.
Area of rectangular design= l×b sq.cm
from the given statement, we can see that side of small square is 1 cm and small squares surrounded by 4 large squares i.e side of large square is sum of side of small squares or 2cm .
Also , length of rectangular design is sum of sides of two large squares and breadth is same as side of one large square.
so, length of rectangular design= 4 cm
breadth of rectangular design= 2cm
Area of rectangular design= 4×2 = 8sq. cm
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Example of a slope intercept form equation with a negative slope and y-intercept of 0
Answer:
An example would be y = -x.
Step-by-step explanation:
Since the y-intercept is 0, we don't have to write it out. The slope has to be negative, so I chose -1 as the slope. We don't have to write 1 when we use it as a coefficient, so that is why I wrote it as -x. Now to put it all together in slope intercept form, we get y = -x.
Hope this helps.
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Someone help
Given the function f(x) = 1 + 1/2x³, find the value of f(-4) in simplest form.
Answer: -62.5
PLEASE GIVE BRAINLIEST THANK YOU!!!
Step-by-step explanation:
help me please
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The values of x after applying congruency to solve the complete shape is 3.5.
What are congruent shapes?Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. The symbol to represent two congruent shapes is ≅.
To calculate the values of x in the diagram, we need to first join point Q to point H and point G to form ΔQHG also, we join point Q to point E and point F to form ΔQFE.
Comparing ΔQHG and ΔQFE, we can deduce that
ΔQHG ≅ ΔQFETherefore,
x+8 = 3x+13x-x = 8-12x = 7x = 7/2x = 3.5Hence, the values of x in is 3.5.
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Write the equation of a line in point slope form that has a slope of 1/3 and passes through the point (6,-2)
The equation of a line in the point-slope form that has a slope of 1/3 and passes through the point (6,-2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex].
What is point-slope form?A straight line is represented using its slope and a point on the line using point slope form. In other words, the point-slope form is used to determine the equation of a line whose slope is "m" and passes through the point ([tex]x_{1}, y_{1}[/tex]). The equation of a straight line can be expressed in various ways, Point slope shape is one of them. The point slope form's equation is as follows:[tex]y-y_{1} =m(x-x_{1} )[/tex]where (x, y) is a chance point on the line that should be treated as a variable when using the formula.A fixed point on the line is ([tex]x_{1}, y_{1}[/tex]).The slope of the line is m.Calculation
[tex]y-y_{1} =m(x-x_{1} )[/tex]
[tex]y-(-2) =\frac{1}{3} (x-6 )[/tex]
[tex]y+2 =\frac{1}{3} (x-6 )[/tex]
Therefore, the equation of a line in the point-slope form that has a slope of 1/3 and passes through the point(6, -2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex]
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The solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 side touching. What is the total number of white cubes that were used to build the prism?
Answer:34?
Step-by-step explanation: not too sure but yeah
according to a wired magazine article, of e-mails that are received are tracked using software that can tell the e-mail sender when, where, and on what type of device the e-mail was opened (wired magazine website). suppose we randomly select received e-mails. a. what is the expected number of these e-mails that are tracked?
There should be 12 emails total.
7.200 and 2.683 are the variance and standard deviation, respectively.
What is varience?The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: 2. Both analysts and traders use it to assess market volatility and security.The standard deviation (SD or ), which aids in determining the consistency of an investment's returns over time, is the square root of variance.Calculation of expected number of emails, variance and standard deviation:
Given thatP = 0.40 and n = 30a)The expected value of received e-mails is= n × p= 30 × 0.4= 12 b)The variance of emails received is= n × p × (1 - p)= 30 × 0.4 × 0.6= 7.200NowThe standard deviation of emails received is= sqrt(variance)= 2.683Learn more about variance here:
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Triangles UVW and VUX are congruent identifier common sides are angles.
Answer:
Common side: UV
Step-by-step explanation:
What is the value of z where distance of between two point R(6, - 1, - 3) and S(3, 3, z) is 13?
Answer:
-15, 9
Step-by-step explanation:
Substituting into the distance formula,
[tex]\sqrt{(6-3)^2+(-1-3)^2+(-3-z)^2}=13 \\ \\ \sqrt{25+(3+z)^2}=13 \\ \\ 25+(3+z)^2=169 \\ \\ (3+z)^2=144 \\ \\ 3+z=\pm 12 \\ \\ z=-3 \pm 12 \\ \\ z=-15, 9[/tex]
2. The lengths of a certain species of fish was
found to be normally distributed. The mean
length is 78 cm with a standard deviation
of 14 cm. In a school of 370 of these fish,
how many would be longer than than
92 cm
So, approximately 59 fish in the school would be longer than 92 cm.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, logarithms, etc.
Here,
We can solve this problem using the normal distribution formula, which states:
z = (x - mu) / sigma
where z is the standard score, x is the raw score, mu is the mean, and sigma is the standard deviation.
To find the number of fish longer than 92 cm, we need to find the proportion of fish in the population with lengths greater than 92 cm. We can then multiply this proportion by the total number of fish in the school to get the number of fish longer than 92 cm.
First, we calculate the standard score for 92 cm:
z = (92 - 78) / 14
z = 1
Next, we look up the proportion of the standard normal distribution that corresponds to a z-score of 1. We can use a standard normal distribution table or calculator to find this value. The proportion of the distribution that is greater than z = 1 is approximately 0.1587.
Therefore, the proportion of fish in the population with lengths greater than 92 cm is 0.1587. To find the number of fish longer than 92 cm, we multiply this proportion by the total number of fish in the school:
370 * 0.1587 = 58.8
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Calculate (8.42 x 109) − (2.35 x 108).
Answer:
Step-by-step explanation:
663.98
Answer: 663.98
Step-by-step explanation:
(8.42*109)=917.78
(2.35*108)=253.8
917.78-253.8=663.98
Write an equation for the transformation of y=x; vertical by a factor of 1/10
The equation the function after the transformation is g(x) = x/10
How to determine the transformation of the function?The equation of the function is given as
y = x
Express as a function
f(x) = x
The sequence of transformations is given as follows:
Vertically stretched by a factor of 1/10
When the above transformations are combined, we have:
Vertically stretched by a factor of 4: g(x) = 1/10f(x)
So, we have
g(x) = 1/10f(x)
Substitute x for f(x)
So, we have
g(x) = 1/10 * x
Evaluate
g(x) = x/10
Hence, the function g(x) is g(x) = x/10
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Use the real number line shown below to complete each statement.
The letter best represents −0.1525.
The letter best represents 9
5
.
The letter best represents −1
5
.
A number line goes from negative 0.5 to positive 1.8 and shows points negative 0.5, 0, positive 0.5, 1, and 1.5. Marks divide the space between each number into 5 equal parts. Point a is on the third mark and point b is halfway between the third and fourth mark to the right of negative 0.5, point c is on the second mark after 0, point d is between the second and third mark after positive 1, point e is on positive 1.5, and point f is on the third mark after positive 1.5.
Based on the real number line shown below, each statement should be completed as follows:
The letter b best represents −0.1525.The letter f best represents 9/5.The letter a best represents −1/5.What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Therefore, both -0.1525 and -1/5 would be represented by the letters that are on the left hand side of the real number line while 9/5 would be represented by a letter that is on the right hand side, which are letters b, a, and f respectively;
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Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answer:
0.86 pounds of fruit is left.
Step-by-step explanation:
If Stacey bought 8.3 pounds and the class ate 7.44 pounds, the amount of fruit that's left is 8.3-7.44=0.86
The sum of the squares of two consecutive positive numbers is 1,105. Find the numbers.
Answer:
23 and 24
Step-by-step explanation:
let the 2 consecutive numbers be n and n + 1 , then
n² + (n + 1)² = 1105
n² + n² + 2n + 1 = 1105 ( subtract 1105 from both sides )
2n² + 2n - 1104 = 0 ( divide through by 2 )
n² + n - 552 = 0 ← in standard form
(n + 24)(n - 23) = 0 ← in factored form
equate each factor to zero and solve for n
n + 24 = 0 ⇒ n = - 24
n - 23 = 0 ⇒ n = 23
However, n > 0 , then n = 23 and n+ 1 = 23 + 1 = 24
the numbers are 23 and 24
find the slope through(0,10) and (24, 6)
Answer:
slope = - [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 10 ) and (x₂, y₂ ) = (24, 6 )
m = [tex]\frac{6-10}{24-0}[/tex] = [tex]\frac{-4}{24}[/tex] = - [tex]\frac{1}{6}[/tex]
What is the value of x?
1.9x+0.1x=0.6
Enter your answer as a decimal in the box.
x = ???
Answer:
x = 0.3
Step-by-step explanation:
[tex] \sf1.9x + 0.1x = 0.6[/tex]
Combine like terms.
[tex] \sf2x = 0.6[/tex]
Divide both sides by 2.
[tex] \sf \: x = 0.3[/tex]
Which statement is true about 67?
A. its a prime number
B. its a composite number
C. its neither prime or composite
Answer:
a. its a prime number cuz as far as ik 67 has one factor 67x1
Answer:
Number 67 is prime because it doesn't have proper factors. In other words, the only factors of 67 are 1 and itself
x³+10<9 help pls pls pls pls pls pls
Answer:
x< -1
Step-by-step explanation:
x^3 < 9 - 10
x^3 < -1
x< -1
Answer:
x < -1
Step-by-step explanation:
x³<9-10
x³<-1
x < -1
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Find the value of the variables in each figure. Explain your reasoning.
The value of the variables x and y in each figure are 28 and 46.3 respectively.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line.
Therefore,
5x + 40 = 180,
5x = 180 - 40
5x = 140
x = 28
Also,
(3y-1 ) and 40 are corresponding angles, thus
40 + 3y - 1= 180 ,
3y = 180 - 40 + 1
3y = 139
y = 46.3
Thus, the value of the variables x and y in each figure are 28 and 46.3 respectively.
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Evaluate f(x) = 2|x – 5| for f(–5) and f(0).
Question 20 options:
f(–5) = 10, f(0) = 0
f(–5) = 12, f(0) = 5
f(–5) = –20, f(0) = –2
f(–5) = 20, f(0) = 10
Answer:
D
Step-by-step explanation:
f(-5) = 2|-5-5|
f(-5) = 2|-10|
f(-5) = 2 * 10
f(-5) = 20
f(0) = 2|0-5|
f(0) = 2|-5|
f(0) = 2 * 5
f(0) = 10
to test whether the overall regression equation is statistically significant one uses a. the r2-statistic. b. the standard error statistic. c. the f-statistic. d. the t-statistic.
One can use the f-statistic to test whether the overall regression equation is statistically significant, one uses the f-statistic.
A reasonably high R-squared score makes sense if your regression model includes independent variables that are statistically significant. According to the statistical significance, shifts in the dependent variable are correlated with changes in the independent variables.
The ratio of two variances is known as an F-statistic, and it bears Sir Ronald Fisher's name. Variances gauge how widely apart the data points are from the mean. When the individual data points tend to deviate further from the mean, there are more variances.
The F-test determines that it is unlikely that all of the coefficients will equal zero by adding the predictive power of all independent variables. But it's likely that none of the variables are individually important enough to be statistically significant.
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What is a counterexample for the conjecture?
If the area of a rectangle is 80 square units, the perimeter must be greater than 35.9 units.
A) A rectangle with length 39.5 units and width 0.5 unit has a perimeter of 80 units and an area of 19.75 square units.
B) A rectangle with length 8 units and width 10 units has a perimeter of 36 units and an area of 80 square units.
C) A rectangle with length 8 units and width 9 units has a perimeter of 34 units and an area of 72 square units.
D) A square with a side length of √80 units has a perimeter of approximately 35.8 units and an area of 80 square units.
The argument against the conjecture The area of a rectangle with a perimeter of 40 units must be at least one square unit. A rectangle with dimensions of 19.99 units long and 0.1 units wide has a 40 unit perimeter and an area of 0.1999 square units.
What is counterexample?An instance or example that refutes the proposition is referred to as a counterexample. To determine if a statement is true or not, logic uses this. Counterexamples typically offer strong arguments in opposition to the assertion under discussion.The goal of the inquiry is to demonstrate any possible relationship between the area and perimeter of a rectangle.acc to our question-
The goal of the inquiry is to illustrate any potential connections between a rectangle's perimeter and area.
The counterexample presented dimensions that revealed the perimeter, which is 40, but omitted to provide the area, which is 1 square unit.
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write the inverse: if the 2 smallest sides sum to be larger than the 3rd side, then it is a triangle.
Using the properties of conditional statements we can write the inverse of the statement as ": if the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle."
The statement is given as if the sum of two sides is greater than the third side then it is a triangle.
Now for the inverse we have to convert the given line into double negative.
Hence we get:
If the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle
Conditional statements are part of mathematical reasoning, a vital skill that enables students to evaluate a given hypothesis without reference to a particular context or meaning. Simply put, when a scientific research or allegation is studied, the logic isn't truly founded on an individual's perspective. Deductions and evidence must have factual and scientific foundations.
the various types of conditional statements are:
When the conditional statement's hypothesis and conclusion are both untrue, it is referred to as an inversion of the statement.If both a hypothesis and a conclusion are false at the same time, the statement is contrapositive.A statement is said to be biconditional when it is both conditional and converse at the same time, satisfying both conditions as true.Top learn more about inverse of a statement visit:
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Heeelllllllllllp Simplify the expression completely.
√144 +18 √12-5√64
Answer:
A
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{12}[/tex]
= [tex]\sqrt{4(3)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]
= 2[tex]\sqrt{3}[/tex]
Then
[tex]\sqrt{144}[/tex] + 18[tex]\sqrt{12}[/tex] - 5[tex]\sqrt{64}[/tex]
= 12 + 18(2[tex]\sqrt{3}[/tex] ) - 5(8)
= 12 + 36[tex]\sqrt{3}[/tex] - 40
= - 28 + 36[tex]\sqrt{3}[/tex]
Write an equation of the line in slope-intercept form.
Ay
4
y =
(0, 2)
2
(3, 3)
4
AX
Equation of line in slope-intercept form is [tex]y = (\frac{1}{3})x + 2[/tex].
Given in graph,
A(0,2) and B(3,3)
Slope-intercept form => y = mx + c
Slope, m = [tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{3-2}{3-0}[/tex]
= [tex]\frac{1}{3}[/tex]
Therefore, y = (1/3)x + c
Put A(0,2) in above equation
2 = (1/3)*0 + c
2 = c
Hence, y = (1/3)x + 2.
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What is the product of (4i-5)(4i+5)
The product of (4i-5)(4i+5) is -41.
What are complex numbers?
Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted i, also known as the imaginary unit, and satisfies the equation i² = - 1.
Here, we have
Given function
= (4i-5) (4i+5)
After applying the product rule, we get
= 16i² + 20i - 20i - 25
= 16i² - 25
after putting i² value, we get
= 16(-1) - 25
= -41
Hence, the product of (4i-5)(4i+5) is -41.
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Match the following definitions with the correct term.
Answer:
that's biology but
Step-by-step explanation:
autotrophs make their owner food
heterotrophs can't make their own food
photosynthesis is the 3rd one
photosynthesis happens in the chloroplast
photosynthesis makes glucose
I can go in depth about any of these, ask me if needed
What is the
y-intercept of the function f(x)=-2/9x+1/3?
Answer:
1/3
Step-by-step explanation
We can immediately tell the y-intercept is 1/3.
Slope intercept form:
y = mx + b
m = slope
b = y-intercept.
Answer: the y - intercept is 1/3
Step-by-step explanation: trust