Since there are 3 white horses in a total of 15 horses, the ratio of white horses, to the total number of horses are 1 : 5 So for 20 total number of horses, the number of white horses should be 4. The ratio of white horses to the total number of horses is 4 : 20 which is 1: 5
Therefore, 4 of the next 20 horses that come to board should you expect to be white horses
Can anybody help me quick 21 points
According to a recent poll, 22% of US adults get an average of 7 or more hours of sleep per night. Assume this is the parameter value for the population. Suppose you select a simple random sample of 50 US adults and find that 10 of them get an average of 7 or more hours of sleep per night. Let p(hat) = the proportion in the sample who get an average of 7 or more hours of sleep per night.
Assuming the polling information is true, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night is ?
answer is .3664
If needed, use the z-table to answer the question.
assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
The mean of the sample proportion distribution is given by:
μp(hat) = p = 0.22
The standard deviation of the sample proportion distribution is given by:
σp(hat) = sqrt((p*(1-p))/n) = sqrt((0.22*0.78)/50) = 0.0802
To find the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night, we need to find the z-score corresponding to this value:
z = (0.20 - 0.22) / 0.0802 = -0.2494
Using a standard normal table or calculator, we find that the probability of obtaining a z-score of -0.2494 or less is 0.4019. Therefore, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night,
Hence assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.
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given that ab is the diameter of a circle o find the missing angle and arc measures show your work look at the photo of the circle
The given angles are:
M arc CB=64°,M<AOC= 116° ,M arc AD=26°,M arc DFB=154°,M<CDB=32°.
How to solve thisFirst, we use the property that the measure of a central angle is equal to the measure of the intercepted arc.
Given that <COB = 64°, we know that the measure of arc CB is also 64°.
Next, we use the fact that the measure of an angle made on the circumference is half the measure of the angle made at the center.
We know that the measure of intercepted arc AD is 26°, and since the angle made at the center, <ABD, is 13°, we can calculate that the measure of arc AD is 2 x 13° = 26°.
Using the fact that a semicircle has a measure of 180°, we know that the measure of arc DFB is 180° - 26° = 154°.
Finally, we can use the angle CDB to find the missing angle.
We know that <CDB is an angle made on the circumference and that the measure of arc CB is 64°.
Thus, we can calculate that <CDB = 64°/2 = 32°.
Therefore, the missing angle is 32°.
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7
35cm
42cm
X =
6cm
cm
N
HELP ME FAST GUYS!! Asap
The value of x in the polygon is 5 centimetres.
How to find the side of similar polygon?A polygon is a two-dimensional geometric figure that has a particular number of sides.
Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio .
Therefore, using the ratio of the similar polygon, let's find the value of x as follows:
35 / x = 42 / 6
cross multiply
35 × 6 = 42x
210 = 42x
divide both sides of the equation by 42
x = 210 / 42
x = 5 cm
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Piston movement compresses air in this type of air compressor. Medium size compressors Industrial compressors Small compressors Horizontal compressors
Piston movement compresses air in Small compressors type of air compressor
Piston movement compresses air in small compressors. Small compressors, also known as portable compressors, are commonly used for home improvement projects, powering tools, and inflating tires or other objects. The piston moves back and forth inside a cylinder, compressing air and increasing its pressure. The compressed air is then stored in a tank until it is needed to power a tool or inflate an object.
Small compressors are generally less powerful than medium or industrial compressors, but they are more affordable, portable, and easier to use for smaller tasks. They can be powered by electricity or gasoline, and they come in a range of sizes and capacities to meet different needs. Overall, piston-driven small compressors are an efficient and cost-effective way to compress air for various applications.
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What is the relation between the variables in the equation
The equation x⁴/y = 7 represents a relationship of direct proportionality between x and y, where x⁴ and y are inversely proportional to each other.
The equation x⁴/y = 7 represents a relationship between the variables x and y. Specifically, it shows that the fourth power of x divided by y is equal to 7.
This equation can be rewritten as x⁴ = 7y, which means that if we know the value of y, we can determine the corresponding value of x that satisfies the equation. For example, if y = 1, then x⁴ = 7, and taking the fourth root of both sides of the equation gives us x = ± √7.
Conversely, if we know the value of x, we can solve for y by rearranging the equation as y = x⁴/7. This shows that y is directly proportional to x raised to the fourth power, meaning that as x increases, y will also increase, but at a faster rate due to the exponent of 4.
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Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
-409-8
Click twice to plot each segment.
Click a segment to delete it.
Slope of the Line:
-3 -2 7
10
9
Submit Answer
5
4
7
9
10
The rise and run of the line is shown in the image below, where: slope of the line (m) = -3/4.
What is the Slope of a Line?The slope refers to how steep a line is. To find the slope of a line on coordinate plane, find the rise and the run of the line, then find their ratio.
Slope of a line (m) = change in y / change in x = rise / run
The red line in the image below represents the rise of the line while the blue line represents the run of the line.
The rise = 3 units
The run = 4 units
Therefore, we have:
Slope (m) = rise/run = -3 units / 4 units
Slope (m) = -3/4.
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A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=918 and x=592 who said "yes." Use a 90% confidence level.
The values received after utilizing confidence interval are (0.614, 0.674)
Poll = n = 918
X = 592
Calculating the value of p -
p = x/n
= 592/918
= 0.644
The mean of an estimate plus and minus the range of that estimate constitutes a confidence interval. inside a specific degree of confidence, this is the range of values that anticipates the estimate to fall inside if the test is repeated.
Using the formula of confidence interval -
[tex]CI = p + z\sqrt{} p ( 1-p/n)[/tex]
Substituting the values -
[tex]CI = 0.644 + 1.645 \sqrt{} ( 0.644 ( 1 - 0.644) / 918)[/tex]
= 0.644 ± 0.030
Thus, the interval values are -
= 0.644 + 0.030 = 0.674
= 0.644 - 0.030 = 0.614
With 90% certainty that this range represents the true percentage of the population who feel vulnerable to identity theft.
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I know is blurry just pls help
12 - 2^2 x 2
---Remember: PEMDAS
---In this case exponents are first, then multiplication, then subtraction
12 - 4 x 2
12 - 8
4
Answer: 4
Hope this helps!
I need help i don't know how to do this please
The size of matrix cM is given as follows:
9 x 10.
What happens when a matrix is multiplied by a constant?When a matrix is multiplied by a constant, we have that every element in the matrix is multiplied by the constant. Hence, the dimension of the matrix remains constant.
The parameters for this problem are given as follows:
Constant c.Matrix M of dimensions 9 x 10.Hence the size of matrix cM is given as follows:
9 x 10.
(same size as the original matrix, as we simplify multiply each element in the matrix by the constant, hence the dimensions remain the same).
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OAB is a minor sector of the circle below.
Calculate the length of the minor arc AB in terms of pi
Not drawn accurately
AWARDING BRAINLIEST TO FIRST ANSWER
The Length of the arc in the circle shown is calculated to one decimal place, in terms of pi, as approximately 3.6π cm.
How to Calculate the Length of an Arc?The length of an arc in a given circle can be calculated by applying the formula as expressed below:
Length of arc (s) = ∅/360 * 2πr, where:
Reference angle = ∅
Radius of the circle = r.
Given the parameters:
Radius (r) = 16 cm
Reference angle (∅) = 40 degrees.
Plug in the values:
Length of the arc (s) = 40/360 * 2 * π * 16
Length of the arc (s) = 3.6π cm
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Answer:
To calculate the length of the minor arc AB in terms of pi, you need to know the measure of the central angle that intercepts the arc and the radius of the circle. Do you have that information?
Step-by-step explanation:
Jerome buys 4 pints of milk for the baby goats and has pint of milk left from yesterday. If each baby goat gets pint of milk, how many goats can Jerome
feed?
Jerome can feed (blank) baby goats.
Answer:
5 baby goats
Step-by-step explanation:
4 + 1 = 5 pints total
each baby goat gets 1 pint
Elin chose C as the correct answer. Explain how she got her answer.
Answer:
Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.
Step-by-step explanation:
My apologies for the confusion. Let's analyze how Elin arrived at her answer.
According to the given information, car A travels 221.5 km at a given time. Elin interpreted the statement "car B travels 1.2 times the distance car A travels at the same time" to mean that the distance traveled by car B is 1.2 times the distance traveled by car A.
To calculate the distance traveled by car B, Elin multiplied the distance of car A (221.5 km) by 1.2:
Distance of Car B = 1.2 * Distance of Car A
Distance of Car B = 1.2 * 221.5 km
Distance of Car B = 265.8 km
Therefore, Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.
Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items.
Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.
How to solve for the costB = 1/4 * S
S = 2/3 * P
B + S + P = 23.75 - 4.50
Emma spent 23.75 - 4.50 = $19.25 on the brush, sketchbook, and paint set.
Now we have the equation:
B + S + P = 19.25
Substitute the expressions from relationships 1 and 2 into the equation:
(1/4 * S) + S + (3/2 * S) = 19.25
Now combine the terms:
(1/4 * S) + (4/4 * S) + (6/4 * S) = 19.25
(11/4 * S) = 19.25
Now, to solve for S, multiply both sides of the equation by the reciprocal of the fraction (4/11):
S = (4/11) * 19.25
S = 7
The sketchbook cost $7. Now we can find the costs of the brush and the paint set using relationships 1 and 2:
B = 1/4 * S = 1/4 * 7 = 1.75
P = 3/2 * S = 3/2 * 7 = 10.5
Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.
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Complete question
Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items. What is the total cost for each item
3. Point F(21, -14) is rotated-90° clockwise about the origin. What are the coordinates of F’
Answer: The coordinates of F' are (14, 21).
Step-by-step explanation:
Since we are rotating -90° clockwise about the origin (or 90° counterclockwise), we will apply (x, y) becoming (-y,x). I have also graphed this, see attached.
(21, -14) ➜ (14, 21)
The coordinates of F' are (14, 21).
For any positive values x and y, f(xy) = f(x) + f(y). f(1/2021) = 1.
Find f(2021).
I will give BRAINLIEST to correct answer.
In a class of 26 students, a teacher chooses a different student to each present five different homework problems. Which statement describes the number of ways the students can be chosen to present the problems? There are 26C5 = 65,780 ways the students can be chosen because the order they are chosen matters. There are 26P5 = 7,893,600 ways the students can be chosen because the order they are chosen matters. There are 26C5 = 65,780 ways the students can be chosen because the order they are chosen does not matter. There are 26P5 = 7,893,600 ways the students can be chosen because the order they are chosen does not matter.
"There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen does not matter." is correct statement. Therefore, the answer is option C.
The problem asks us to choose 5 students out of a class of 26 to present homework problems. Since the order in which the students present the problems does not matter, we need to use the combination formula. The combination formula is used to calculate the number of ways to choose a subset of k elements from a set of n elements without regard to order, and it is denoted by nCk.
Option A, "There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen matters," is incorrect because the order in which the students are chosen does not matter.
Option B, "There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen matters," is incorrect because we are choosing 5 students out of 26, and the order in which they are chosen does not matter.
Option D, "There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen does not matter," is also incorrect because the order in which the students are chosen does not matter.
Therefore, the answer is option C.
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Complete question is:
In a class of 26 students, a teacher chooses a different student to each present five different homework problems. Which statement describes the number of ways the students can be chosen to present the problems?
A) There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen matters.
B) There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen matters.
C) There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen does not matter.
D) There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen does not matter.
Write the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) in slope intercept form.
Answer: y = (9/5)x + 5.
Step-by-step explanation:
The slope of the given line is -5/9. The slope of a line perpendicular to it would be the negative reciprocal of -5/9, which is 9/5. Using the point-slope form of a line, we can write the equation of the line as y - (-4) = (9/5)(x - (-5)). Simplifying this equation gives y + 4 = (9/5)x + 9. Solving for y, we get y = (9/5)x + 5. This is the equation of the line in slope-intercept form.
In summary, the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) is y = (9/5)x + 5.
A local maximum of the function f(x) occurs for which x-value? A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 16, negative 2, 0, 6, 0, negative 2. Group of answer choices –4 –3 –2 –1
There is a local maximum at the point (-1,6), therefore, for x = -1
option D is correct
What do we mean by local maximum point?A local maximum point on a function is described as a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).
We see that the function adopts values smaller than 6 to the left of x = -1, and to the right of it:
(-3, -2), (-2, 0) to the left of x = -1 where the function's value is 6
and (0, 0), and (1, -2) to the right of x = -1
Therefore, we can say that the pints (-1, 6) is a maximum, that is for x = -1, where the function renders a value of 6.
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Ocarolyn and Abby
went camping and
caught a total of a fish.
How many fish
weighed 8 1/4 pounds
or less?
XX
XX
X X
x+
XX-
X
8 8
8
8 9
Weight of Fish in Pounds
1
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
The solution for x in the equation (x – 7)^2 = 36 are x = 13 and x = 1
Solving for x in the equationWe can solve for x by taking the square root of both sides of the equation:
(x – 7)^2 = 36
Taking the square root of both sides:
x - 7 = ±6
Adding 7 to both sides:
x = 7 ± 6
Therefore, the values of x are:
x = 7 + 6 = 13
x = 7 - 6 = 1
So the correct answers are x = 13 and x = 1. The values x = -29 and x = 42 are not solutions to the equation.
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A swimming pool holds 450, 000 L
of water and has two drainage
pipes.
Pipe A, by itself, can drain the pool
in 150 minutes. Pipe B, by itself, can
drain the pool in 225 minutes.
If you turned on both pipes at the
same time, how many minutes
would it take to drain the pool?
Using a linear equation, the minutes it would take both pipes to drain the swimming pool that holds 450,000 liters is 90 minutes.
What is a linear equation?A linear equation is an equation of a straight line written in the form of y = mx +b, where m is the slope.
The quantity of water the swimming pool holds = 450,000 liters
The drainage time of Pipe A working alone = 150 minutes
Drainage rate of Pipe A = 3,000 liters per minute (450,000 ÷ 150)
The drainage time of Pipe B working alone = 225 minutes
Drainage rate of Pipe B = 2,000 liters per minute (450,000 ÷ 225)
The drainage rate of the combined pipes = 5,000 liters per minute (3,000 + 2,000)
Let the number of minutes for both pipes to drain the pool = x
Therefore, the linear equation is 5,000x = 450,000
x = 90 minutes (450,000 ÷ 5,000)
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Find the slope of the line that passes through A (3, 7) and B (7, 10).
Answer:
[tex]m = \frac{10 - 7}{7 - 3} = \frac{3}{4} [/tex]
find the probability that a randomly selected point within the large square falls in the red shaded square 6 6 15 15 p= enter as a decimal rounded to the nearest hundredth
The probability that a randomly selected point within the red-shaded square is 0.16
Finding the probability of a pointFrom the question, we have the following parameters that can be used in our computation:
Red square of 6 by 6White square of length 15The areas of the above shapes are
Red square = 6 * 6 = 36
White square = 15^2 = 225
The probability is then calculated as
P = Red square /White square
So, we have
P = 36/225
Evaluate
P = 0.16
Hence, the calculated value of the probability that the point falls in the red square is 0.16
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For the right triangle shown below, find the exact values of:
sinB b)tanA c)cosA
Answer:
17
Step-by-step explanation:
11+6=17
(a) The exact value of sin B is 6 / 12.53
(b) The exact value of tan A is 11 / 6
(c) The exact value of cos A is 6 / 11
What is the value of sin (B) , tan (A) and cos (A)?The value of sin (B), cos (A) and tan (A) is calculated by applying trigonometry ratio as follows;
The trigonometry ratio is simplified as;
SOH CAH TOA;
SOH ----> sin θ = opposite side / hypothenuse side
CAH -----> cos θ = adjacent side / hypothenuse side
TOA ------> tan θ = opposite side / adjacent side
The value of the hypotenuse side of the right triangle is;
L = √ (6² + 11²)
L = 12.53
(a) The exact value of sin B is;
sin B = 6 / 12.53
(b) The exact value of tan A is;
tan A = 11 / 6
(c) The exact value of cos A is;
cos A = 6 / 11
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If the terminal point of 0 is (0, -1), what is tan 0?
A. Undefined
B. 1
C. -1
D. 0
If the terminal point of θ is (0, -1) then tanθ is undefined.
The point (0, -1) lies on the negative y-axis.
Since the tangent function is defined as the ratio of the opposite side to the adjacent side of a right triangle, and the adjacent side is zero for any point on the y-axis, the tangent of θ is undefined.
Therefore, if the terminal point of θ is (0, -1) then tanθ is undefined.
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There are 6 bottles of water.
Each bottle is 1/2 full. If you
were to combine all the
water, how many full bottles
of water would there be?
Answer:3
Step-by-step explanation: 1/2 X 6 = 3
Answer:
6 x 1/2 = 3 full bottles
Step-by-step explanation:
Solve the equation without using a calculator
[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex]
Answer:
x = 5 ± √26-------------------------
Convert the given equation as below:
[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+10x^9(9x)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+90x^{10}[/tex][tex](x^2-9x-1)^{10}+9x^{10}=10x^9(x^2-9x-1)[/tex][tex](x^2-9x-1)^{10}-9x^9(x^2-9x-1)=x^9(x^2-9x-1)-9x^9x[/tex]Let's substitute x² - 9x - 1 = t, then the equation is:
[tex]t^9t-9x^9t=x^9t-9x^9x[/tex]Comparing both sides, we see that x = t, so:
x² - 9x - 1 = xx² - 10x - 1 = 0Solving this quadratic equation we get:
x = 5 ± √26The National Academy of Science reported in a 1997 study that 40% of research in mathematics is published by U.S. authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 40%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 130 recent articles published by reputable mathematics research journals and finds that 62 of these articles have U.S. authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 40%? Use a 0.05 level of significance.
There is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.
How to test for the evidenceTo test the claim that the percentage of research in mathematics published by U.S. authors is no longer 40%, we can use a hypothesis test with a 0.05 level of significance.
Let p be the true proportion of mathematics research published by U.S. authors.
The null hypothesis is that p = 0.4, and the alternative hypothesis is that p ≠ 0.4 (two-tailed test).
sample proportion, x/n = 62/130 = 0.477
The test statistic for a two-tailed test is given by:
z = (0.477 - 0.4) / √(0.4 * 0.6 / 130)
= 2.41
Using a z-table, we find that the p-value for a two-tailed test with z = 2.41 is approximately 0.016.
Since 0.016 < 0.05
, we reject the null hypothesis and conclude that there is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.
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Select the correct answer from each drop-down men
menu.
What is the distance and midpoint between points D and E on the number line?
D
E
-4 -3 -2 -1 0 1 2 3 4 5
distance =
midpoint =
Reset
Next
The midpoint is M = 0.6 and the distance is D = 4.2
Given data ,
The distance between points D and E on the number line
D = 4.2
Now , the first point D = -1.8
And , the point E = 2.4
And , the distance D = 2.4 - 1.8 = 4.2 units
Thus, the midpoint between points D and E on the number line = 0.6
Hence, the distance and midpoint between points D and E on the number line 4.2 and 0.6
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The complete question is attached below :
What is the distance and midpoint between points D and E on the number line?