As per the standard distribution, the lowest test score is 27.76%
Standard distribution:
In statistics, standard distribution means a normal distribution with a mean of zero and standard deviation of 1.
Given,
The top 5% of applicants on a test will receive a scholarship. if the test scores are normally distributed with a mean of 76 and a standard distribution of 12.
Here we need to find the lowest test score that still qualifies for a scholarship.
As per the given question, we have identified the value of
=> μ = 76 (mean)
=> σ = 12 (standard deviation)
Then we need to take the value of x as,
x < 5% (find the probability)
Now, converting the problem in standard form
=> Z = (5 − 76) / 12
=> Z = -5.91
Then as per the z table the value is 0.2786
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Last year, Pinwheel Industries introduced a new toy. It cost $2500 to develop the toy and S25 to manufacture each toy. Fill in the blanks below as appropriate.
A.) Give a linear equation in the form Cmn + b that gives the total cost, C, to produce n of these toys Preview
B.) The total cost to produce n 3000 toys is S
C.) With $32500, a total of toys can be produced.
a)The linear equation is C=25n + 2500 to produce n 3000 toys, b) The total cost to produce 3000 toys is $77,500, c) With $32500, a total of 1200 toys can be produced in Pinwheel Industries.
What is meant by the term linear equation?An equation is a mathematical statement with an equal symbol (=) between the algebraic expression. Equations with a degree of one are called linear equations. It is the straight line's equation. Whenever values are substituted for the unknown values in linear equations, the solutions produce values that make the equation true. Since there is only one variable, there is only one solution. For instance, the equation x + 2 = 0 has just one solution, which is x = -2. In the case of the two-variable linear equation, however, the solutions are determined as the Cartesian coordinates of a point on the Euclidean plane.
The three different types of linear equations are: 1) Standard Form
2) The slope intercept form
3)Point Slope Form
How to solve?
A) Linear equation y=mx+b,
C (total cost) = y and n (number of toys) =x.
C=25n + 2500
B) Put n=1750
C= 25(3000) + 2500
C= $77,500
C)
32500= 25n +2500
30000=25n
n = 1200
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Suppose that y varies directly with x, and y= 8 when x = 2. find y when x is -5
The required value of y is -20, when x is -5.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given that,
y varies directly with x,
implies that,
y = k x (1)
Substitute the values x = 2 and y = 8,
8 = k x 2
k = 4
Substitute x = -5 and k = 4, to find the values of y,
y = -5 x 4
y = -20
The value of y is -20, when x is -5.
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Work out the length of ab a=-1.6 b=5.3 give your answer
Answer: 6.708
Step-by-step explanation:
a(-1,6)
b(5,3)
ab =( (-1-5)^2+(6-3)^2)^(1/2)
ab=(36+9)^(1/2)
ab=6.708
Which of the following constructions can be accomplished with paper
folding?
Check all that apply.
A. Drawing a line through a given point parallel to a given line
B. Drawing a perpendicular line segment from a given point to a
given segment
C. Finding the midpoint of a segment
D. Drawing a perpendicular line segment through a given point on a
given segment
The steps are given in option B and option C are used in paper folding.
What is Paper Folding?When we simply fold the paper in such a manner that we can achieve our objectives, the method is called Paper Folding.
Now, WE get;
Option A can not be accomplished as we need the proper equipment to construct the circle.
Option B can be done by folding the paper along the point.
Option C can be done by folding the paper in the exact half measure.
Option D can not be done.
Hence, the steps are given in option B and option C are used in paper folding.
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a pet store has 16 1/2 pounds of dry cat food. the manager divides the food into containers, putting 2 3/4 pounds in each container how many containers does the manager fill
#10 i need help with my math
Answer: √6 -8√5
or 15.43905
Step-by-step explanation:
a runner competed in a 5 mile run. how many yards did she run (1 mile =1760 yards)
Answer:8,800
Step-by-step explanation:
1760 times 5 = 8,800
a worn, poorly set-up machine is observed to produce components whose length x follows a normal distribution with mean 14 centimeters and standard deviation 3 centimeters. find the probability that the length of a component lies between 19 and 21 centimeters. round your answer to four decimal places.
The probability that the length of a component lies between 19 and 21 centimeters is 0.0376.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
Population mean, µ = 14
Population standard deviation, σ = 3
Probability that the length of a component lies between 19 and 21 centimeters
= P(19 < X < 21)
= P( (19 - 14) / 3 < (X - µ) / σ < (21 - 14) / 3)
= P(1.67 < z < 2.33)
= P(z < 2.33) - P(z < 1.67)
Using excel function:
= NORM.S.DIST(2.33,1) - NORM.S.DIST(1.67,1)
= 0.9901 - 0.9525
= 0.0376
Hence, the probability that the length of a component lies between 19 and 21 centimeters is 0.0376.
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Jakobe earns a bi-weekly mean gross pay of $1,592. 0. What percent of his total salary will he pay if his student loan payments are $130. 00 per month for 180 months? round to the nearest tenth. (4 points) 3. 9% 3. 8% 3. 6% 3. 7%
Answer:
Step-by-step explanation:
Which logarithmic equation is equivalent to 32 = 9?
The equivalent equation to the given logarithm is log₃9=2.
Define the term logarithmic equation?An equation using the logarithm of just an expression involving a variable is referred to as a logarithmic equation. Check to verify if you can write two aspects of the equation as powers of a similar number before attempting to solve an exponential equation.A log function can be used to determine how much a given number must always be raised to reach the desired result.
aˣ = b
This can be written as;
logₐ b = c
Where an is the starting point from which the power will be raised,When power is increased, we want b to be the appropriate number,To obtain b, c must be increased to a power.For the expression;
3² = 9
Given what we know about just the logarithm, the following is how we can represent the given equation:
3² = 9
log₃9 = 2
Consequently, the equivalent equation of 3² = 9 could be expressed as log₃9=2.
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The correct question is-
Which logarithmic equation is equivalent to 3^2 = 9?
12 is 30% of what number?
Answer: 40
Step-by-step explanation: the answer is 40
Answer:
40
Step-by-step explanation:
12=[tex]\frac{30}{100}[/tex]*x
12=[tex]\frac{3}{10}[/tex]x
multiply both sides by 10/3
x=40
a researcher developing a regression equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3). educational status is a dummy variable with 0
A substantial interaction between age and educational status was discovered by a researcher who was creating a regression equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) (x3)
A dummy variable, educational status has the values 0 for no college degree and 1 for a college degree.
The regression formula is y = 0 + 1x1 + 2x2 + 3x1x2 where 0 is the intercept, 1 is the age regression coefficient, 2 is the educational status regression coefficient, and 3 is the regression coefficient for the interaction between age and educational status.
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A bake sale committee wants to raise $189 for a donation to a local charity. They set aside $14 of their profit at the end of each day. How many days will it take them to raise enough money for the whole donation?
Answer:
Step-by-step explanation:
14x=189 (x represents the number of days)
189 divided by 14 = 13.5
Answer or X: Approximately = 14 days
A new movie streaming service opens and it charges a $9 sign up fee. Streaming 10 movies costs a total of $14, including the sign up fee.
Answer:
33 I guess I don't really know
Answer: ok expensive
Step-by-step explanation:
what would happen to the width of a confidence interval if the size of the population being sampled was doubled, from 25 million to 50 million?
50 million people instead of 25 million people make up the population. The degree of assurance is reduced from 95% to 90%.
What is confidence interval?
A confidence interval in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 95%, but other levels, such 90% or 99%, are occasionally used.
Because the standard error is reduced as sample size increases, confidence intervals are narrower.
Therefore, we may state that when the population standard deviation rises, the width of the confidence interval will also rise.
Hence, 50 million people instead of 25 million people make up the population. The degree of assurance is reduced from 95% to 90%.
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what is the degrees of freedom for the t distribution? (round your answer down to the nearest integer.) (c) what is the p-value? (round your answer to four decimal places.) p-value
By using t distribution, it can be calculated that
b) Degree of freedom is 65
c) P value of 2.115 at 65 degrees of freedom = 0.0383
What is t-distribution?
t - distribution is used to find the distance between two sample means if the population standard deviation is unknown and it is assumed that the observation comes from a normally distributed population.
b) Here,
Degree of freedom =
[tex]=\frac{(\frac{s_1^2}{n_1} + \frac{s_1^2}{n_2})^2}{\frac{s_1^4}{n_1^2(n_1 -1)} + {\frac{s_2^4}{n_2^2(n_2 -1)}}}\\\\=\frac{(\frac{5.3^2}{35} + \frac{8.8^2}{40})^2}{\frac{5.5^4}{35^2(35 -1)} + {\frac{8.8^4}{40^2(40 -1)}}}[/tex]
= 65
c) The value of test statistic obtained is 2.115
P value of 2.115 at 65 degree of freedom = 0.0383
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Complete Question
The complete question has been attached
1. Explain what a polygon is and how it is classified. Give more than one example to justify your answer.
2. What is a one-hundred sided polygon called? Why?
3. Tell whether the following is or is not a polygon and justify your answer:
Answer:
1. Polygons are flat figures formed by a closed polygonal line and its interior. Any plane figure that is made up of “straight sides” is a polygon.
2.A 100-sided polygon is called a hectogon, centagon or 100-gon. In general, any n-sided polygon with over 12 sides is called an n-gon. While there are other conventions for naming polygons with any number of sides, it is most common to use the n-gon form.
Step-by-step explanation:
Augusto wants to prove to his parents that watching TV while he does his homework will help him get better grades. He decides to ask 20 of his friends if they watch while they do their
homework and what their grades are. He finds that his friends who have high grades also watch TV while they do their homework. He tells his parents that he has proven that watching TV
while doing homework will cause his grades to improve. What mistake has Augusto made? (6 points)
© He did not use a random sample, and he tried to show cause and effect with an observational study.
O He did not use random sample, and he tried to show cause and effect with an experiment.
© He did not separate his friends into different groups, and he didn't apply a treatment.
© He did not separate his friends into different groups, and he used survey to collect data.
Answer:
A. He did not use a random sample, and he tried to show cause and effect with an observational study
Hope this helps! : D
Step-by-step explanation:
8.
(08.05 MC)
Augusto wants to prove to his parents that watching TV while he does his homework will help him get better grades. He decides to ask 20 of his friends if they watch TV while they do their homework and what their grades are. He finds that his friends who have high grades also watch TV while they do their homework. He tells his parents that he has proven that watching TV while doing homework will cause his grades to improve. What mistake has Augusto made? (6 points)
In exercises 4 and 6 tell whether the ordered pair is a solution to the linear inequalities.
Just Question 4 and 6.
Answer:
3
Step-by-step explanation:
if you look at the graph, you can see that the line intercepts where the points are
Find f (5)
quick can someone answer meee
Answer:
f (5) = 4
Step-by-step explanation:
First we need to find f(x)
To do this we can find the gradient of the line then plug it into the formula for an equation of a line.
using the points on the line, (3,0) (0,-6)
gradient, m :
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
[tex] \frac{0 - ( - 6)}{3 - 0} = \frac{6}{3} = 2[/tex]
therefore the gradient was found to be 2.
Equation of a line:
y - y1 = m( x - x1)
y - 0 = 2( x - 3)
y = 2x - 6
Therefore the function of the line was found to be:
f(x) = 2x -6
so to find f(5) we substitute 5 in the place of x:
f(5) = 2(5) - 6
f(5) = 10 - 6
f(5) = 4
does anyone know?? please help
Check the picture below.
if an open rectangular box is to have a fixed volume v, what relative dimensions will make the surface area a maximum
Relative dimensions which will make the surface area a maximum is
x=y = \sqrt{area/3 }
z = 1/2( \sqrt{area/3 })
Volume = 2xh
Let the box have dimensions x,y,z>0.
The surface area is A=xy+2xz+2yz
The volume is V=xyz
The Lagrangian is L=V−λ(A−constant)=xyz−λ(xy+2xz+2yz−constant).
∂L∂x=yz−λ(y+2z)=0
∂L∂y=xz−λ(x+2z)=0
∂L∂z=xy−λ(2x+2y)=0
Hence, λ=yzy+2z=xzx+2z=xy2x+2y
On cross multiplication,
xyz+2yz2=xyz+2xz2which implies x=y.
Cross-multiplying the middle and the right expressions ,2x2z+2xyz=x2y+2xyzwhich implies z=12y.
So, optimal volume with fixed surface area is to have the width and the depth equal and the height to be half the width and depth.
To find x,y,z given a fixed surface area Area one would use x=y=2z in the equation
Area=xy+2xz+2yz=x2+x2+x2 so
x=y = \sqrt{area/3 }
z = 1/2( \sqrt{area/3 })
Volume is a measurement of three-dimensional space that is occupied. Numerous imperial units or SI-derived units, such as the cubic metre and litre, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship.
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One of the same side interior angles of two parallel lines is 20* less than the other same side interior angle. Find the measures of the two angles
The measure of both the angles will be x = 80° and y = 100°.
What is Parallelogram? What are parallel lines?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. Two lines are said to be parallel if they have same slope. These lines never intersect each other and have no common point of intersection.
Given is the same side interior angles of two parallel lines is 20° less than the other same side interior angles.
Same side interior angles are supplementary, we can write -
x + x + 20 = 180
2x = 160
x = 80°
Other angle will be -
y = x + 20 = 100°
y = 100°
Therefore, the measure of both the angles will be x = 80° and y = 100°.
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all problems concern the following wheel, which we shall call q. 1 4 16 64 (a) estimate the probabilities of the outcomes of q. (b) estimate the expected value of q. (c)
Probabilities of Q are 1,4, 16, 64 are 312 2 8181818 , E(Q)=20.88 and 12.5% information revealed. Wheel is spin twice 0.2815.
When we are not sure about the outcome we can make possible probabilities about the situation. Therefore, it is the maximum and possible chances of something to be happen.
Step 1
Angle of one complete spin = 360°
Q=16=90° Q=6490"
Q=4-450
Q=1=135°
Here
P(Q16) = P(Q= 64)
=90/36
=1/4
Step 2
Expected value E(Q) = xP(x) E(Q) = 1x+4x+16x+64 x2/8
Step 3
c)
We learn Q=4
P(Q=4)=1/8=0.125
12.5 % information is revealed.
Please refer to solution in this step.
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A survey of all beings on planet Boondin found that 75% preferred alaber juice to all other juices. If 12 beings were surveyed altogether, how many of them preferred alaber juice?
The number of people who preferred alaber juice is 9 people
How many of them preferred alaber juice?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, the survey of all beings on planet Boondin found that 75% preferred alaber juice to all other juices. If 12 beings were surveyed altogether
Those who preferred alaber juice will be:
= 75% × 12
= 0.75 × 12
= 9
The number of people is 9.
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problem 3.7. suppose integer polynomials p and q satisfy that p ( x)/ q ( x ) is an integer for infinitely many integer inputs x. does it follow that q ( x ) divides p ( x ) ?
Integer polynomials p and q fulfill that for an unlimited number of inputs of integers x, p (x)/q (x) is an integer. q (x) does not necessarily divide p. (x)
Sums of terms of the form k^xn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.This section covers the ideas of degree, standard form, monomial, binomial, and trinomial.
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What is the equation of the line that passes through (0, 3) and is perpendicular to y = 3/4x + 5?
Answer:
3/4x + 3
Step-by-step explanation:
they both need to have the same gradient but different y intercepts and in this case the y intercept is 3
The equation of line passing through the point P ( 0 , 3 ) is given by
y = ( -4/3 )x + 3
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 3 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
The slope of the line we want to find will be the negative reciprocal of this slope, which is -4/3
Slope m = -4/3
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 3 = ( -4/3 ) ( x - 0 )
Adding 3 on both sides , we get
y = ( -4/3 )x + 3
Hence , the equation of line is y = ( -4/3 )x + 3
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HELP ASAP! Linear function k has a zero at 3 and a y-intercept of 9. Which graph best represents k?
-2m + 11m + m + 11 = -19
Answer:
m= -3
Step-by-step explanation:
-2m+11m+m+11= -19
9m+m+11=-19
10m+11=-19
-11. -11
10m=-30
/10. /10
m= -3
Hopes this helps please mark brainliest
Answer:
hop this helps
Step-by-step explanation:
you should use the step by step calculator Symbolab
How many baseballs are in the next picture in this pattern?
A. 64
B. 30
C. 32
D. 24
E. 25