Answer:
what is the monthly payment or ask for the mileage use for the car
A genetic experiment with peas resulted in one sample of offspring that consisted of 427 green peas and 161 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%
O Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%
a. Construct a 90% confidence interval. Express the percentages in decimal form.
Using the z-distribution, we have that:
a) The confidence interval is: (24.33%, 30.37%).
b) The correct option is: No, the confidence interval includes 0.25, so the true percentage could easily equal 25%.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The other parameters are given as follows:
[tex]n = 427 + 161 = 588, \pi = \frac{161}{588} = 0.2735[/tex]
Then the bounds of the interval are:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2735 - 1.645\sqrt{\frac{0.2735(0.7265)}{588}} = 0.2433[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2735 + 1.645\sqrt{\frac{0.2735(0.7265)}{588}} = 0.3037[/tex]
As a percentage, the interval is: (24.33%, 30.37%).
25% is part of the interval, hence the correct statement is:
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%.
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Construct a right angled traiangle ,choosing whole numbers of centimeters for the lengths of the two shorter sides, such that the hypotenuse will be √65 long.Check the accuracy of your drawing by measuring the hypotrnuse and by calculating √65.
Please give me a correct answer.
Answer:
1. Shorter Side: 4
2. Longer Side: 7
3. Hypotenuse: [tex]\sqrt{65}[/tex]
Step-by-step explanation:
[tex]4^{2} +7^{2} =65[/tex]
This is so confusing please help asap !
Tyler wants to have $250,000 in his retirement account by the time he retires in 30 years. The interest rate is 5%. Use the annuity formula to calculate the amount Tyler needs to deposit on a monthly basis in order to reach his goal. When solving, round numbers to the nearest hundred-thousandth. Round your final answer to the nearest cent.
Using the monthly payment formula, he needs to deposit A = $1,342.12 a month to reach his goal.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are:
P = 250000, r = 0.05, n = 12 x 30 = 360.
Then:
r/12 = 0.05/12 = 0.004167.
Then:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 250000\frac{0.004167(1+0.004167)^{360}}{(1+0.004167)^{360} - 1}[/tex]
A = $1,342.12
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A matrix A has x rows and x+5 columns. B has y rows and 11−y columns. Both AB and BA exist. Find x and y.
Answer:
x = 3
y = 8
Step-by-step explanation:
A matrix product exists if and only if the number of columns in the left matrix is equal to the number of rows in the right matrix.
SetupFor AB to exist, we must have ...
columns of A = rows of B
x +5 = y
For BA to exist, we must have ...
columns of B = rows of A
11 -y = x
SolutionUsing the second equation to substitute for x in the first equation, we have ...
(11 -y) +5 = y
16 = 2y
8 = y
Then the value of x is ...
11 -8 = x = 3
The values of x and y are ...
x = 3y = 8__
Additional comment
The dimensions are A = 3×8; B = 8×3.
How did the temperature change if it increased by 50% and then decreased by 33 1/3%
The temperature does not change after the percentage increase and decrease.
What is the change in the temperature?
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
Assume the initial temperature is 10.
Temperature after the 50% increase : (1 + 0.5) x 10 = 15
Temperature after the 33 1/3% decrease : (1 - 0.333) x 15 = 10.00
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Is the answer e? I think it is
Answer: I am pretty sure you are correct from my standpoint
Step-by-step explanation:
If you look closely he is pretty close to the answer or it is the answer or this is just answer on my point or if its wrong try b
The graph shows a system of equations:
What is the solution to the system of equations?
y = -x + 5
y=x-1
(-3,2) (3,-2) (3,2) (-3,-2)
The solution to the system of equations is (3, 2)
System of equationGive the system of equation below
y = -x + 5
y=x-1
Equate both expression
-x+5 =x - 1
Equate
-x - x = -1 - 5
-2x = -6
x = 3
Since y = x - 1
y = 3 - 1
y = 2
Hence the solution to the system of equations is (3, 2)
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cual es el vaolor de t-19=1
Answer:
t=20
Step-by-step explanation:
t-19=1
t-19(+19)=1+19
t=20
Women appear to marry about 3 years younger than men, but the two distributions are very similar in shape and spread.
The brief report about what the attached data in the box plot shows that: "Women appear to marry around three years younger than males, although the shape and dispersion of the two distributions are extremely comparable."
What is a box plot?A boxplot is a type of graph that shows how the values in the data are distributed.
A boxplot is a standardized technique of representing data distribution based on a five-number summary ("minimum", first quartile (Q1), median, third quartile (Q3), and "maximum").
It can provide information about your outliers and their values.
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Full Question:
In 1975, did men and women marry at the same age? Here are boxplots of the age at first marriage for a sample of U.S. citizens then. Write a brief report discussing what these data show.
Find the ratio of 700m to 2 km
Answer:
7 : 20
Step-by-step explanation:
2km = 2000m
Then the ratio of 700m to 2 km is :
700 / 2000
Then the ratio in simplest form is :
7 / 20
Question 13 (5 points)
Find the greatest common factor of 48a²b7 and 48a6b5z.
a.) 12a²b5
b.) 12a8b¹2
c.) 18a6b7
d.) 48a²b5
The greatest common factor of 48a²b⁷ and 48a⁶b⁵z is the number 48a²b⁵
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The greatest common factor is the highest number that all the numbers share.
The greatest common factor of 48a²b⁷ and 48a⁶b⁵z is the number 48a²b⁵
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SKETCHPAD
Question 5
Given AABC shown on the coordinate plane below.
AA"B"C" = Ro (T(-4,3)(ABC))
90°
Draw AA'B'C'' if
You may use different colors for the separate transformations. Indicate your final
answer. Feel free to use the Dynamic Geometry Tool to complete the
transformations.
The attached figure represents the image of A"B"C" after the transformation
How to transform the triangle?The transformation rule is given as:
A"B"C" = Ro90° (T(-4,3)(ABC))
This means that we rotate the triangle 90 degrees clockwise, and then translate the triangle
From the figure, the coordinates of ABC are
A = (-1, 2)
B = (1, 4)
C = (3, -1)
The rule of 90 degrees clockwise rotation is
(x,y) ⇒ (y,-x)
So, we have
A' = (2, 1)
B' = (4, -1)
C' = (-1, -3)
The translation of the triangle by T(-4,3) is
(x,y) ⇒ (x - 4, y + 3)
So, we have
A'' = (-2, 4)
B'' = (0, 2)
C'' = (-5, 0)
See attachment for the image of the transformation
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A board is 59.69cm long. How long is the board in inches ? Use the following conversion 1in is 2.54cm
Answer:
Given,
1in= 2.54cm
59.69cm=
[tex] \frac{59.69}{2.45} in[/tex]
=23.5 in
in the diagram , what is the value of x
The value of x from the given diagram is 100 degrees
Sum of interior angleFrom the given diagram, we will use the theorem "angle at the vertex is half that at the centre.
<50 = 1/2 x
Cross multiply
50 * 2 = x
x = 50 * 2
x = 100 degrees
Hence the value of x from the given diagram is 100 degrees
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I run 3 miles in 20 minutes. What was my average speed in miles per hour?
what is the inverse of the function f(x)=x/5-2
Answer:
[tex]\huge\boxed{\sf f^{-1}(x)=5x+10}[/tex]
Step-by-step explanation:
Given function:[tex]\displaystyle f(x)=\frac{x}{5} -2[/tex]
Put f(x) = y
[tex]\displaystyle y=\frac{x}{5} -2[/tex]
Swap x and y
[tex]\displaystyle x = \frac{y}{5} -2[/tex]
Now, solve for y
[tex]\displaystyle x = \frac{y}{5} -2[/tex]
Add 2 to both sides
[tex]\displaystyle x + 2 =\frac{y}{5}[/tex]
Multiply 5 to both sides
[tex]5(x+2)=y[/tex]
Distribute
[tex]5x + 10 =y[/tex]
Put y = f⁻¹(x)
[tex]\boxed{f^{-1}(x)=5x+10}[/tex]
[tex]\rule[225]{225}{2}[/tex]
f(x)=2^x. What is g(x)?
The function g(x) is g(x)= (3x)^2
How to solve for g(x)?The complete question is in the image
From the graph in the image, we have:
f(x) = x^2
The function f(x) is stretched by a factor of 3 to form g(x).
This means that:
g(x) = f(3x)
So, we have:
g(x)= (3x)^2
Hence, the function g(x) is g(x)= (3x)^2
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pls help with both of the questions
The number of solutions there are for the functions, -f(x) and f(-x) are; 2 and 2 respectively.
How many solutions are there to each function?According to the task content, the function given initially is; f(x).
Hence, the function -f(x) represents a reflection of the function f(x) over the x axis. And in this case scenario, the reflection also has 2 solutions as it only cuts the x-axis at two points.
Also, the function f(-x) represents a reflection of the function f(x) over the y-axis. And in this case scenario, the reflection also has 2 solutions as it only cuts the x-axis at two points.
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Question 2 of 5
Select the correct answer.
After buying a car, Sarah decides to get it appraised every few years. After owning the car for two years, its value is $5,000. After own
the car for five years, its value is $2,000.
What is the equation that models this inverse variation?
Oy=
O y = 2,500
O
O
5,000
y = 2,000
y =
10,000
Submit
Reset
The inverse proportional relationship that models this variation is given as follows:
[tex]y = \frac{10,000}{x}[/tex]
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
An inverse proportional relationship is given as follows:
[tex]y = \frac{k}{x}[/tex]
In this problem, we have an inverse relation in which y(2) = 5000, hence the constant k is found as follows:
[tex]y = \frac{k}{x}[/tex]
[tex]5000 = \frac{k}{2}[/tex]
k = 10,000
Hence the relation is:
[tex]y = \frac{10,000}{x}[/tex]
As stated in the problem, when x = 5, y = 2,000, which we can verify replacing in the relation.
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2. State two (2) values of θ (theta) to the nearest degree for
sin θ = − 0. 966
Using equivalent angles, the solutions to the equation are given as follows:
[tex]\theta = 255^\circ, \theta = 285^\circ[/tex]
What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
In this problem, the equation is:
[tex]\sin{\theta} = -0.966[/tex]
Applying the inverse relation:
[tex]\theta = \arcsin{-0.966} = 255^\circ[/tex]
Which is on the third quadrant. The equivalent angle on the fourth quadrant is given as follows:
[tex]270^\circ + (270^\circ - 255^\circ) = 285^\circ[/tex]
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centered at the origin given its...
Give the equation of the circle centered at the origin and passing through the point (0, -5).
Step-by-step explanation:
the equation of a circle centered at the origin is
x² + y² = r²
r being the radius (the distance of the center to every point on the circle's arc).
so, we get a point on the arc : (0, -5).
what is its distance to the origin ?
the origin is (0, 0).
we see, both points have the same x coordinates. they are therefore on the same vertical line going through x=0.
that means there is no distance between them in x direction.
the only distance is in y direction : 0 to -5.
a distance is always positive (no matter in what direction).
so, the distance from 0 to -5 is : 5 units.
that means r = 5.
and our equation is
x² + y² = 5² = 25
Which equation can be used to solve for b?
Triangle A B C is shown. Angle B C A is a right angle and angle C A B is 30 degrees. The length of side B C is 5 centimeters, the length of B A is 10 centimeters, and the length of C A is b.
tan(30o) = StartFraction 5 Over b EndFraction
tan(30o) = StartFraction b Over 5 EndFraction
tan(30o) = StartFraction 10 Over b EndFraction
tan(30o) =
Answer:
[tex]tan(30) = \frac{5}{b} [/tex]
Step-by-step explanation:
Trigonometric Ratios.
To solve for b, we check the parameters that are given in the triangle.
If we're considering 30°, we can see that the opposite is given as 5cm and the adjacent is b.
Applying:
[tex]tan \alpha = \frac{oppsite}{adjacent} \\ \\ tan \: (30) = \frac{5}{b} [/tex]
Answer:
a
Step-by-step explanation:
just did the quiz!!!!
Please help!!! 24 points!!!
Answer:
-24
Step-by-step explanation:
-6 × f(3) - 6 × g(-1) = ?
to answer this we need to find the functional values of the functions at the specified points.
f(3) = -2
we find this easily : we go to x = 3 on the x-axis, and then see there at what y value a vertical line is intersecting the functional graph. the intersection is below the x-axis, so the y value is negative.
g(-1) = 6
we go to x=-1, and we find that a vertical line there will intersect the g curve at y = 6.
and that's really it.
now we need to calculate it all in the main expression :
-6 × -2 - 6 × 6 = 12 - 36 = -24
you remember, that multiplications and divisions have to happen before any addition of subtraction ?
Use the figure below to complete the following problem.
Given:
ZH=2x+60
LT=x+30
HALT is a
H
2T=
1. 30
2. 60
3. 90
Answer:
Step-by-step explanation:
ascxne rdsjazs bcbnnnncccd
Please help me quick
The product of the ages 2 years from today is 924
System of equationLet the ages of the three cousins be x, y and z. If the product of their ages is 1716, hence;
xyz = 1716
If the product of their ages last year is 1320, then;
(x-1)(y-1)(z-1) = 1320
Two years ago, the product of their ages will be;
(x-2)(y-2)(z-2) = 1320- (1716-1320)
(x-2)(y-2)(z-2) = 1320-396
(x-2)(y-2)(z-2) =924
Hence the product of the ages 2 years from today is 924
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Please help me with this math quickly
The area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches
Calculating AreaFrom the question, we are to determine the area of the shaded part
In the given diagram, the shaded part is a rectangle
Area of a rectangle = Length × Width
Length of the shaded part = 18 inches - 4 inches - 1 inch = 13 inches
Width of the shaded part = 6 inches - 2inches = 4 inches
Then,
Area of the shaded part = 13 inches × 4 inches
Area of the shaded part = 52 sq. inches
Hence, the area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches
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What is the range of y = log Subscript 8 Baseline x?
The range of [tex]y =\log_8(x)[/tex] is the set of all real values
How to determine the range?The function is given as:
[tex]y =\log_8(x)[/tex]
The above function is a parent logarithmic function.
The parent logarithmic function have a range of the set of all real values
Hence, the range of [tex]y =\log_8(x)[/tex] is the set of all real values
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Answer:
D
Step-by-step explanation:
on edg
A bag contains 2 yellow balls, 3 green balls, 5 red balls and 6 black balls.
What is the probability of either a yellow ball or a red ball being drawn if
only one ball is drawn?
Answer:
7/16
Step-by-step explanation:
(2+5)/(2+3+5+6) = 7/16
The probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.
What is probability?The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total outcomes.
According to the given question.
Numnber of yellow balls = 2
Number of green balls = 3
Number of red balls = 5
Number of black balls = 6
So,
The total number of balls in a bag = 2+ 3+ 5 + 6 = 16
And,
The sum of yellow and red ball = 2 + 5 = 7
Therefore,
The probability of either a yellow or a red ball being drawn if only one ball is drawn
= [tex]\frac{total\ number\ of \ red \ and \ yellow\ balls }{Total\ number\ of \ balls}[/tex]
[tex]= \frac{7}{16}[/tex]
Hence, the probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.
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Which of the relations given by the following sets of ordered pairs is a function?
O {(2,-8), (1, — 4), (0, 0), (1, 4), (2, 8)}
O {(3, -3), (3, -1), (3, 1), (3, 3), (3,5)}
O {(1, 2), (2, 3), (3, 4), (5, 6), (2, 1)}
O {(-2,5), (7,5), (-4, 0), (3, 0), (1, -6)}
Answer:
Option (4)
Step-by-step explanation:
Each value of x maps onto only one value of y, so it is a function.