Answer:
30, 50, and 120
Step-by-step explanation:
3/20 × 200 = 30
5/20 × 200 = 50
12/20 × 200 = 120
The measures of three angles that are in ratio 3:5:12 are 30 degrees,50 degrees and 120 degrees.
Given that:
The sum of the measures of three angles = 200.
Let the ratios be x.
The ratio of first angle be 3x
The ratio of second angle be 5x
The ratio of third angle be 12x
According to the question,
3x+ 5x+ 12x = 200
20x = 200
Divide both sides by x
x = 200/20
x = 10
The ratio of first angle be 3x = 3(10) = 30 degrees
The ratio of second angle be 5x = 5(10) = 50 degrees
The ratio of third angle be 12x = 12(10) = 120 degrees
The measures of three angles that are in ratio 3:5:12 are 30 degrees,50 degrees and 120 degrees.
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Michelle asks her husband to build a pen for her chickens. Three of the sides will be built with mesh fencing, while the fourth side will back up to the east side of her house. She wants the enclosed area to be 400 square feet. The cost of the fence meshing will be $4.18 per foot and the pen will also need 4 corner posts costing $9.50 each. a. [6 pts] Let x be the length of the side of the chicken coop that backs up to the east side of the house. Write a function P(x), for the price of the materials for the pen in terms of x. Simplify your answer. b. [3 pts] Use your calculator to find the dimensions of the pen that costs the least. Set your window with: 0≤x≤80 and 10≤ y ≤400, and round your answer to 2 decimal places. (Insert your graph here. You may hand draw the graph or insert an image of the graph from Desmos) c. [1 pt] What is the total cost of the pen? Round to dollars and cents.
The function P(x), for the price of the materials for the pen is 4.18(800/x + x) + 38.
How to illustrate the function?Based on the information, the function P(x), for the price of the materials for the pen will be:
P(x) = 4.18 (2 × 400/x + x) + 38
= 4.18(800/x + x) + 38.
The dimensions will be:
We'll differentiate the function which will give 20✓2. Therefore, the value for x will be 20✓2 which is 28.28 feet and that of y will be 10✓2 which is 14.14 feet.
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Would this expression:
[tex](x^{2} -16)^{2}[/tex]
be classified as a difference of squares? Or a perfect square trinomial?
Why?
The given expression is a perfect square trinomial.
How to classify the given expression?
Here we have the expression:
[tex](x^2 - 16)^2[/tex]
Notice that we can rewrite it as:
[tex](x^2 - 4^2)^2[/tex]
Then we can see that inside the parenthesis we have a difference of squares, but it is squared, so if we define:
[tex]x^2 = a\\4^2 = b[/tex]
We will have:
[tex](a - b)^2 = a^2 + -2ab + b^2 = (x^2)^2 - 2*(4^2)*(x^2) + (4^2)^2[/tex]
Which is in fact, a perfect square trinomial.
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The area of a square quilt is 35 ft 2. How will it look stretched across a queen sized bed measuring 60 inches wide and 80 inches long?
The quilt will be 10.99 inches wider and 9.01 inches shorter than the bed.
What is the relationship between the quilt and the bed?The first step is to determine the dimensions of the quilt.
Dimensions = √35 = 5.92 feet
Now convert the dimensions of the quilt to inches
1 feet = 12 inches
5.92 x 12 = 70.99 inches
Difference in the width of the bed and the quilt = 70.99 - 60 = 10.99
Difference in the length of the bed and the quilt = 80 - 70.99 = 9.01
Here are the options:
A. The quilt will cover half of the surface of the bed.
O B. The quilt will match up with the length of the bed, but 20 inches will hang over the length. °
C. The quit will be 14.6 inches wider and 15.4 inches shorter than the bed. O D. The quilt will be 10.99 inches wider and 9.01 inches shorter than the bed.
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Can you please help me identify the property that justifies the work between step 3 and step 4
Answer:
Division property of inequality
Step-by-step explanation:
24<4x
24/4<4x/4
6<x
(1/4)×24 < (1/4) ×4x
6 < x
Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.
What is the value of y?
3 StartRoot 3 EndRoot units
6 StartRoot 3 EndRoot units
9 StartRoot 3 EndRoot units
12 StartRoot 3 EndRoot units
The value of y in the triangle is B. 6✓3.
How to calculate the value?From the information given,
NU = 9
UM = 3
MN = 3 + 9 = 12
NT² = 9 × 12 = 108
NT = ✓108
NT = 6✓3
Therefore, y is 6✓3.
The value of y in the triangle is 6✓3.
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Answer:
B
Step-by-step explanation:
If the greatest value the variable m can be is less than 9, which of the following inequalities best shows all the possible values of m?
m < 9
m > 9
m ≤ 9
m ≥ 9
The inequality which shows all possible values of m is; m < 9.
Which inequality best shows all possible values of m?It follows from the task content that the variable in discuss, m is described as less than 9.
On this note, the most appropriate inequality to represent the set of all possible values of m is; m < 9.
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Using the drawing what is the vertex of angle 4?
Answer: A
Step-by-step explanation:
You are buying a house and you are financing the purchase with a mortgage of $130,000. The mortgage has a 30 year term and requires monthly payments. The mortgage charges an interest rate of 0.3% every month. What is the total interest payment over the life of the mortgage?
Answer:
130,000 -:- by 30 x 0.3 x 12 = 15,600.
Step-by-step explanation:
(I hope its right, Im not good at math)
A room has a floor dimension of 30 feet by 50 feet. The height of the basement is 6 feet. What is the total area of all four walls?
Answer:
960 feet
Step-by-step explanation:
30×6=180
180×2=360
50×6=300
300×2=600
360+600=960
9) Find the median of the data set.
O a.) 8
Ob.) 5
Oc.) 10
O d.) 13
Data:
5, 8, 12, 6, 7, 10, 14, 6, 13
Answer:
a
Step-by-step explanation:
the median is the middle value of the data arranged in ascending order
5 , 6 , 6 , 7 , 8 , 10 , 12 , 13 , 14 ← ascending order
↑ middle value
median = 8
Answer:
8
Step-by-step explanation:
To find the median, we must put all of the data in order and select the middle number. Since there are 9 terms, the median will be the 5th term.
5, 6, 6, 7, 8, 10, 12, 13, 14
Brainliest, please :)
Select the graph that best represents the inequality above.
Answer: B
Step-by-step explanation: Since x is less than 7, the graph would be all real numbers that are less than 7, so the arrow would be on the left.
Also, since x is not 7 itself (not less than or equal to), the dot cannot be a full dot. Thus, the dot must be open (or curved in some textbooks) to indicate x is not apart of 7 but less than 7.
Hope this helped!
Split [tex](4ax-a^2)/(x^2+ax-2a^2)[/tex] into partial fractions.
The decomposition of the partial fraction is [tex]\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}[/tex]
How to split the fraction?The expression is given as:
[tex]\frac{4ax-a^2}{x^2+ax-2a^2}[/tex]
Expand the denominator
[tex]\frac{4ax-a^2}{x^2- ax+2ax-2a^2}[/tex]
Factorize
[tex]\frac{4ax-a^2}{x(x- a)+2a(x-a)}[/tex]
Factor out x - a
[tex]\frac{4ax-a^2}{(x+ 2a)(x-a)}[/tex]
The denominator of the partial fraction is a product of two linear factors.
So, the decomposition can be represented as:
[tex]\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}[/tex]
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imes A
20) A clinical trial was conducted using a new method designed to increase
the probability of conceiving a girl. As of this writing, 914 babies were
born to parents using the new method, and 877 of them were girls. Use a
(b).01 significance level to test the claim that the new method is effective in
increasing the likelihood that a baby will be a girl. Use the P-value method
and the normal distribution as an approximation to the binomial
distribution.
(10)
a. Identify the null and alternative hypothesis.
b. Compute the test statistic z.ollowenien e to jaata ni(8)
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c. What is the P-value?
d. What is the conclusion about the null hypothesis?
e. What is the final conclusion?
The test statistic is 27.8484, the p-value is 0, and the final conclusion is that the null hypothesis H is rejected.
Given that 914 babies were born to parents who used the new method, and 877 of them were girls, the significance level to test the claim that the new method is effective in increasing the likelihood of a baby being a girl, is 0.01.
The following information is provided: the sample size is N = 914, the number of favorable cases is X = 877, and the sampling ratio is
pˉ = X / N
Pˉ = 877/914
pˉ = 0.9595 and the significance level is α = 0.01
(a) Hypothesis Zero and Alternative
The following null and alternative hypotheses should be tested:
null: p = 0.5
Alternative: p> 0.5
This is equivalent to a right-tailed test, which requires a z-test for a proportion of the population.
(b) Critical Value
Based on the information provided, the significance level is α = 0.01, so the critical value for this right-tailed test is Zc = 2.3263. This can be found using Excel or the Z distribution table. Region of rejection
The rejection area for this test on the right side is Z> 2.3263
Test statistics
The z-statistic is calculated as follows:
[tex]\begin{aligned}Z&=\frac{\bar{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\ &=\frac{0.9595-0.50}{\sqrt{\frac{0.5(1-0.5)}{914}}}\\ &=\frac{0.4595}{0.0165}\\ &=27.8484\end[/tex]
(c) The p-value
The p-value is the probability that the sample results are extreme or more extreme than the sample results obtained, assuming the null hypothesis is true. In this case,
the p-value is p = P (Z> 27.8484) = 0
(d) The decision on the null hypothesis
Using the traditional method
Since we observe that Z = 27.8484> Zc = 2.3263, we conclude that the null hypothesis is rejected.
Using the p-value method
Using the approximation of the P-value: the p-value is p = 0, and since p = 0≤0.01 we conclude that the null hypothesis is rejected.
(e) Conclusion
It is concluded that the null hypothesis H is rejected. Therefore, there is sufficient evidence to state that the population proportion p is greater than 0.5, at the significance level of 0.01.
Hence, for 914 babies born to parents using the new method, of which 877 were girls, the test statistic is 27.8484, the p-value is 0, and the final conclusion is that the null hypothesis is rejected.
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A city mayor in Michigan is planning the number of new snow plows he must purchase to remove the snow next winter. The
average snowfall in the past 10 years has been normally distributed with a mean of 112 inches and a standard deviation of
14 inches. What amount, in inches, separates the lowest 20% of the means of yearly snowfall in the past 10 years from the
highest 80%?
The amount that separates the lowest 20% of the means of yearly snowfall in the past 10 years from the highest 80% is 23.57 inches.
Given mean of 112 inches, standard deviation of 14 inches.
We are required to find the amount that separates the lowest 20% ofthe means of yearly snowfall in the past 10 years from the highest 80%.
a) Bottom 20% would have a z score of -0.8416.
b) Top 80% would have a z score of 0.842.
Use the z formula to find the raw score.
z=(X-m)/sd
X=the raw score
m= mean
sd=standard deviation
Putting the value of low score.
-0.8416=(X-112)/14
X=-11.7824+112
=100.2176
Putting the values of high score.
0.842=(X-112)/14
X=123.788
The amount that seprates the lowest from highest is 123.788-100.2176
=23.57 inches.
Hence the amount that separates the lowest 20% of the means of yearly snowfall in the past 10 years from the highest 80% is 23.57 inches.
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write a piecewise function defined by three equations that has a domain of all real numbers and a range of "-3
A piece-wise function that has domain of all real numbers and range of [tex][-3, \infty)[/tex] is f(x) = |x| - 3, as:
[tex]|x| - 3 = x - 3, x \geq 0[/tex]
[tex]|x| - 3 = -x - 3, x < 0[/tex]
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input.
One example is the absolute value function, defined as follows:
[tex]|x| = x, x \geq 0[/tex]
[tex]|x| = -x, x < 0[/tex]
The function is defined for all real values, with a range of [tex][0, \infty)[/tex]. Shifting it down 3 units, it will have the desired range, as follows:
[tex]|x| - 3 = x - 3, x \geq 0[/tex]
[tex]|x| - 3 = -x - 3, x < 0[/tex]
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Determine whether the relationship is linear, quadratic, or neither by completing each table. Be sure to give
a reason for your choice.
The 1st table represents a linear as well as the quadratic relationship, the 2nd table represents neither and the 3rd table also represents neither relationship.
Why do the given tables have the above relationship?The first table is having linear as well as quadratic because the 1st table has its first difference equal as well as the second difference is also equal i.e., why it is linear and quadratic respectively.The second table is having neither because 1st difference is not equal to each other as well as 2nd the difference is also not equal.The third table is having neither because 1st difference is not equal to each other as well as 2nd the difference is also not equal to each other. Therefore, the 3rd table is neither.Hence, the 1st table represents a linear as well as a quadratic relationship, the 2nd table represents neither and the 3rd table also represents neither relationship.
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Solve log (3x + 4) = log (x – 2) + 3 log 2
Answer:
x + 4
Step-by-step explanation:
Sine the bases are all the same, I can write the equation:
3x+4 = (x-2) 2^3 When we are adding with logs, that means to multiple. Also, when we have 3 log 2, that can be written as 2^3 or 8 (2x2x2)
3x+4=(x-2)8
3x+4 = 8x-16
4=5x-16
20 = 5x
4=x
A ribbon is 4 m long. How many pieces each 30 cm long can be cut from the ribbon?
Answer:
13 pieces
Step-by-step explanation:
First we convert 4m into cm :
1m = 100cm
4m = 400cm
Now we need to figure out how many 30s go into 400 :
400 ÷ 30 = 13 remainder 10
So 13 pieces can be cut from the ribbon
Hope this helped and have a good day
Answer:
13
Step-by-step explanation:
4 meters is equal to 400 centimeters.
400/30 = 13 1/3
You don't want partial pieces, so your answer is 13
The graph below represents which of the following functions?
-12
-10
OA.
OB.
O C.
D.
4
F(x) =
[[|-*|× <1}
(x+4×21}
F(x) =
F(x) =
F(x) =
{/4-x²|x<2}
x2 2f
X
14-x²|x> 21
x x≤ 2}
2}
XS
{|-*² |× > 3)
(x+4× ≤3)
10
12
C
Answer: B
Step-by-step explanation:
The parabola has an open hole at x=2, and the line has a closed hole at x=2.
This means the top part of the function should have domain [tex]x < 2[/tex], and the second part of the function should have domain [tex]x \geq 2[/tex].
This eliminates everything except for B.
what percent of 74.39 is 8 %
Answer:
5.9512
Step-by-step explanation:
1. Convert the percentage to decimal
8% = 8/100 = 0.08
2. Multiply the decimal by the quantity to be extracted
(0.08)(74.39) = 5.9512
Hope this helps
Emma has money in two savings accounts. One rate is 6% and the other is 14%. If she has $950 more in the 14% account and the total interest is $342, how much is invested in each savings account?
$1045 was invested at the interest rate 6% whereas $1,995 was invested at 14%
How is interest computed?
Interest is determined as the amount invested multiplied by the interest rate.
Let Y be the amount invested at 6%
Interest=Y*6%
Interest=0.06Y
The amount invested at 14%, which is $950 more , is Y+950
Interest=(Y+950)*14%
Interest=0.14Y+133
Total interest =0.06Y+0.14Y+133
Note that total interest is 342
342=0.06Y+0.14Y+133
342=0.20Y+133
342-133=0.20Y
209=0.20Y
Y=209/0.20
Y=$1,045(amount invested at 6%)
Amount invested at 14%=$1,045+$950
Amount invested at 14%=$1,995
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1. There are 50 contestants signed up for a TV show. There are 36 more female contestants than male contestants. How many female contestants have signed up to compete? Show your solution and explain how you plan to explain this to your students.
Answer:
males = 7
females = 43
Step-by-step explanation:
whilst it may seem intuitive to simply subtract 36 from 50, it is not saying "there are 36 males, how many females?" but instead, "the difference between the number of males and females is 36".
You can solve this equation most easily algebraically. For example:
Number of males = x
number of females = y
the question states that the total number of people = 50
therefore we can say that the total number of males (x) + the total number of females (y) = 50 people
therefore: x + y = 50
similarly, the question says that the number of males (x) + 36 = the total number of females (y)
therefore: x + 36 = y
we now have two equations:
x + y = 50
x + 36 = y
whilst both equations have two unknowns (x and y), therefore we can't simple solve for x or y, with the combination, we can see a pattern.
focusing on the second equation: x + 36 = y
we can add x to both sides, because you can pretty much do anything to the equation as long as you do it to both sides.
x + 36 + x = y + x
now this may seem very random, but you now see that one side of the equation equals y + x, and remember from the other equation, x + y = 50. Therefore we can substitute x + y in the second equation for 50.
our two equations:
x + 36 + x = y + x
x + y = 50
therefore:
x + 36 + x = 50
for the sake of clarity, we can combine like terms...
x + x = 2x
therefore:
x + 36 + x = 50
2x + 36 = 50
solve for x by subtracting 36 from both sides, then dividing both sides by 2
2x + 36 - 36 = 50 - 36
2x = 14
2x / 2 = 14 / 2
x = 7
now remember:
Number of males = 7 (we now know x = 7)
now that we've solved for x, we can go back to our original equation:
x + 36 = y
and substitute x...
7 + 36 = y
43 = y
Now remember:
Number of females = 43 (we now know y = 43)
therefore there are 7 males and 43 females. we can proof this by adding 7 and 43, and you'll see you reach 50, which is the correct total number of people.
hope this helps :)
A group of yeast cells grows by 75% every 3hrs. At 9am, there are 200 yeast cells [9 marks].
a) write an equation that models the number of cells, given the number of hours after 9am
b) Determine the number of yeast cells after 10 hours.
a) The exponential function that models the number of cells is: [tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]
b) There will be 1292 cells after 10 hours.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^{\frac{t}{n}}[/tex]
In which:
A(t) is the amount after t hours.A(0) is the initial amount.r is the rate of change, as a decimal.n is the time it takes to change.For this problem, the parameters are:
A(0) = 200, r = 0.75, n = 3.
Hence the equation is:
[tex]A(t) = A(0)(1 + r)^{\frac{t}{n}}[/tex]
[tex]A(t) = 200(1 + 0.75)^{\frac{t}{3}}[/tex]
[tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]
The number of cells after 10 hours is:
[tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]
[tex]A(10) = 200(1.75)^{\frac{10}{3}}[/tex]
A(10) = 1292.
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;
Use the expression in the accompanying discussion of sample size to find the size of each sample if you want to estimate the
difference between proportions of men and women who own smartphones. Assume that you want 99% confidence that your
error is no more than 0.035.
Click the icon to view the discussion of sample size.
The sample should include men and
(Type whole numbers.)
women.
The sample should include 2702 men and 2702 women.
Given that you want to be 99% sure your error doesn't exceed 0.035.
A sample is a group of people selected from a larger population to provide data to researchers. The number of members of the population included in the sample is called the sample size.
The significance level is the probability that the test statistic is in the critical range if the null hypothesis is actually true. The confidence interval is 99% or 0.99.
The level of significance α = 1-0.99 = 0.01
the margin of error, ME = 0.035
The Z-critical value at the 99% confidence level or at the significance level of 0.01 is 2.575 (from standard normal tables).
We will now use the formula:[tex]n=\frac{Z^2_{critical}}{2(ME)^2}[/tex].
Substitute the values in the above formula, we get
n = (2.575) ² / (2 × (0.035) ²)
n = 6.630625 / (2 × 0.001225)
n = 6.630625 / 0.00245
n = 2701.966
Therefore, the sample should include 2702 males and 2702 females with a 99% certainty that the error does not exceed 0.035
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Evaluate ( 75 − 3/17 + 1 ) 2
Answer:
2=1289/17
Step-by-step explanation:
use the given functions to set up and simplify 2
Initially, Ernie does not like a book that he is reading, so he reads very few pages. Then, the story becomes interesting, and he reads more pages. The more Ernie reads, the more he enjoys, so he reads faster and faster until he finishes the book. Choose the graph that best corresponds to the situation.
The graph that best corresponds to the situation is graph 4; option C
Time graphAssume, the first hour, Ernie read just 2 pagesSecond hour, 5 pagesThird hour, 7 pagesFourth hour, 10 pagesNumber of pages read is on the y - axis
Time taken is on the x - axis
Therefore, graph 4 represent the situation
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paulette spent 45.50 on concert tickets before fees. there was a service fee of 6% added on to her purchase.
The original price of concert tickets before the addition of service fee is 42.93
PercentageAmount spent on tickets including service fee = 45.50Percentage if service fee = 6%Original cost before service fee = x45.50 = x + (6% of x)
45.50 = x + (0.06 × x)
45.50 = x + 0.06x
45.50 = 1.06x
x = 45.50/1.06
x = 42.9245283018867
Approximately,
x = 42.93
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Use two formulas for volume to find the volume of the figure. Express the volume in terms of 3.14 and than round to the nearest whole number. Note that the figure may not be drawn to scale
The volume of the figure to the nearest whole number = 756π m³.
How to estimate the volume of the given figure?The figure shown exists composed of a cone and a cylinder.
The volume of the figure = volume of cone + volume of the cylinder
Height of cone = 12 - 8 = 4
Radius (r) of cone = 18/2 = 9 m
The volume of the cone V = 1/3hπr²
= 1/3 [tex]*[/tex] 4π [tex]*[/tex] 9² = 108π
The volume of the Cylinder = πr²h
radius (r) = 18/2 = 9 m
height (h) = 8 m
Volume of cylinder = π [tex]*[/tex] 9² [tex]*[/tex] 8 = 648π m³
Volume of the figure = 108π + 648π = 756π
The volume of the figure to the nearest whole number = 756π m³.
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Select the two values of x that are roots of this equation x^2-5x+2=0
The roots of the equation is x = 4.56 OR x = 0.44
Quadratic equationFrom the question, we are to determine the roots of the given equation
The given equation is
x² -5x +2 = 0
Using the formula method,
[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]
In the given equation,
a = 1, b = -5, c = 2
Putting the values into the formula,
[tex]x =\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(2) } }{2(1)}[/tex]
[tex]x =\frac{5 \pm \sqrt{25-8} }{2}[/tex]
[tex]x =\frac{5 \pm \sqrt{17} }{2}[/tex]
[tex]x =\frac{5 + \sqrt{17} }{2}[/tex] OR [tex]x =\frac{5 - \sqrt{17} }{2}[/tex]
[tex]x =\frac{5 + 4.12}{2}[/tex] OR [tex]x =\frac{5 - 4.12}{2}[/tex]
[tex]x =\frac{9.12}{2}[/tex] OR [tex]x =\frac{0.88}{2}[/tex]
x = 4.56 OR x = 0.44
Hence, the roots of the equation is x = 4.56 OR x = 0.44
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3
Seven students cut 5 inches of thread from a spool for a school project. What number represents the change in the
amount of the thread on the spool?
O-40 inches
3
O-35 inches
-29 inches
-26 inches
Answer:
35 inches
Step-by-step explanation:
7 x 5 = 35 lol
The number which represents a change in the amount of thread on the spool exists 35 inches.
What are mathematical operations?In mathematics, an operation exists as a process that takes zero or more input values to a well-defined output value.
Given: Length of thread a student cuts = 5 inches
Total number of students that cut thread = 7
Length of thread a student cuts = 5 inches
Length of thread 7 student cuts = 5 [tex]*[/tex] 7 = 35 inches
The negative length that 7 students cut from the spool exists the number that represents a change in the amount of thread.
The number which represents a change in the amount of thread on the spool exists 35 inches.
Therefore, the correct is option b) 35 inches.
To learn more about mathematical operations, refer to:
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