c² + 9 + 6c is the solution by distributive property .
What in mathematics is a distributive property?
This characteristic states that multiplying the total of two or more addends by a number will produce the same result as multiplying each addend separately by the number and then combining the products collectively.
When you multiply one value by another, you are using the distributive property of multiplication over addition. When multiplying 5 by the sum of 10 plus 3, for instance, add 3. We typically add the numbers first, then multiply the result by 5, since the terms are similar. However, in accordance with the property, you can first multiply each addend by 5.
= (c+3)^2
= c² + 9 + 2 * c * 3
= c² + 9 + 6c
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Gun ownership. A friend read online that 37% or less Americans have a gun in their household. I claim that the percent of Americans that have a gun in their household is actually greater than 37%. To test this claim, I survey 200 random Americans and find that 86 of them have a gun in their household. At the .05 alpha level, what should I conclude about my claim?
b) Find the p-value (round to four decimal places).
At 0.05 alpha level, your claim is not significant.
What is p - value?In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct.
Given is that a friend read online that 37% or less Americans have a gun in their household. I claim that the percent of Americans that have a gun in their household is actually greater than 37%. To test this claim, I survey 200 random Americans and find that 86 of them have a gun in their household. The alpha level is at .05.
We can write -
P{E} % = 86/200 x 100
P{E} % = 86/2
P{E} % = 43%
We can find the p - value using the formula -
[tex]$Z = \frac{\hat{p}-p 0}{\sqrt{\frac{p 0(1-p 0)}{n}}}[/tex]
where -
[tex]$\hat{p}=[/tex] Sample Proportion
[tex]$p_{o}[/tex] = Assumed population proportion in the null hypothesis.
It can be calculate to find that the p value is less than 0.05. So, we can conclude that the null hypothesis is rejected.
Therefore, at 0.05 alpha level, your claim is not significant.
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Your interest rate is compounded semi annually. If you have a annual interest rate of 7.5%, how much is the semi annual interest rate
Answer:
3.75%
Step-by-step explanation:
You want to know the semiannual interest rate if the annual rate is 7.5%.
Periodic rateThe rate of interest for a period is the annual rate divided by the number of periods in a year.
Interest compounded semiannually is compounded 2 times per year. The semiannual rate is ...
7.5%/2 = 3.75% . . . . semiannual rate
Which function describes this graph?
-61
-5
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
O A. y = (x+5)(x-3)
OB. y-(x-2)(x - 5)
OC. y = x² +5x+12
OD. y=x+7x+10
5
if is found that out of 53 cars,41 had clocks,30 had radios and 6 had neither. how many had a clock but no radio?
The number of 17 cars have clocks but no radios.
What is subtraction?Subtraction is a mathematic operation. Which is used to remove terms or objects in the expression.
Given:
Out of 53 cars,41 had clocks,30 had radios and 6 had neither.
That means,
53-6 = 47 cars have either clocks or radios or both.
47 - 30 = 17 cars have no radio.
47 - 41 = 6 cars have no clocks.
Hence, 17 cars have clocks but no radios.
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The side lengths of AABC are 27, 9x, and 63. The side lengths of ADEF are
18, 36, and 7x. Is it possible that the triangles are similar? If so, find the value
of x that makes the triangles similar.
Yes, it's possible that the triangles are similar. With value of x is 6. Therefore, the side length Triangle ABC are 27,54 and 63. While Triangle DEF are 18,36 and 42.
Triangle congruenceA flat shape that has 3 angles is what we usually call a triangle. If there are 2 similar triangles, and an equation is made that will be able to express the ratio of the sides, then we will get a ratio of similar triangles. In simple terms, congruence is two shapes that have the same angles and side lengths. Congruence also has a special notation, namely ≈. To find this, a certain formula will be needed.
Based on the question above, we could find value of x:
with comparison
27/18= 9x/36
27 × 36 = 9x × 18
972=162x
x= 6
X is 6 so we can multiply the length that contain x with the value 6.
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In a particular game of dice, you roll a single fair 6-sided die. You win 50 points for rolling a 1 or a 6, but you lose 5 points anytime you roll any other number. If you rolled the die 100 times, how many points would you expect to gain
or lose?
A. a gain of about 1,333 points
B. a gain of about 4,500 points
C. a loss of about 500 points
D. a gain of about 2,000 points
Answer: The expected value for rolling a 1 or 6 is 50 points, and the expected value for rolling any other number is -5 points. The chance of rolling a 1 or 6 is 2/6, or 1/3. The chance of rolling any other number is 4/6, or 2/3. The expected value for rolling the die once is:
(1/3 * 50) + (2/3 * -5) = 16.67
So, if you rolled the die 100 times, you would expect to gain or lose:
100 * 16.67 = 1667 points
The answer is: a gain of about 1,667 points.
Step-by-step explanation:
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If a = 3 meters and b = 6 meters, what is c? If necessary, round to the nearest tenth.
Here's how I will do it:
1. Recite the Pythagorean theorem, which is [tex]a^{2} +b^{2} =c^{2}[/tex]
2. Substitute the variables of a and b, so the equation will look like this [tex]3^{2} +6^{2} =c^{2}[/tex] now.
3. Simplify the equation which gives you, [tex]9+36=c^{2}[/tex]. Simplifying more would give you [tex]45=c^{2}[/tex].
4. Solve for the c value :
[tex]c=\sqrt{45}[/tex]
Plug this into a calculator and it will give you 6.70820....
Rounding to the nearest tenth will give you, about 6.7.
The length of the hypotenuse of a right triangle can be calculated using the Pythagorean theorem: c^2 = a^2 + b^2.
Given that a = 3 meters and b = 6 meters, we can substitute those values into the equation:
c^2 = 3^2 + 6^2
c^2 = 9 + 36
c^2 = 45
c = sqrt(45)
c = 6.7 meters
Rounding to the nearest tenth, c = 6.7 meters becomes c = 6.7 meters.
50x+ 20 - 60(1/5y+60x) simplify the expression.
Answer:
-3550x - 12y + 20
Step-by-step explanation:
50x+ 20 - 60(1/5y+60x)
50x + 20 - 12y - 3600x
-3550x - 12y + 20
There are 7 roses and 9 daisies in a vase. What is the ratio of all flowers in the vase to daisies? and What is the ratio of roses to all flowers in the vase? Thanks
For what value(s) of h is b in the plane spanned by a1 and a2?a1 = [1, 4, -2] a2 = [-2, -3, 7] b = [4, 1, h]
For b to be in the plane spanned by a1 and a2, h= -17 .
What is plane?
In two dimensions, a plane can continue on forever. The lack of breadth. A plane is an example of coordinate geometry. A point's location in a plane is determined by its coordinates.
A plane is a two-dimensional, flat surface that never ends in mathematics. A plane is a two-dimensional equivalent of a three-dimensional equivalent that contains three spatial dimensions, a line, and a point. Planes can resemble subspaces in some higher-dimensional situations, as if the room's walls had been substantially stretched. These walls have their own existence, exactly as in the context of Euclidean geometry.
A flat surface in three dimensions can be represented using the plane equation. There are several approaches for determining the equation for a given function.. The equation for the plane can be expressed in either cartesian form or vector form.
Hence, the general form of the equation is A(x−x1)+B(y−y1)+C(z−z1)=0
Now,
y is a linear combination of a1 and a2 if it is in the plane, For the plane spanned by a1 and a2,
y = a a1 + b a2, a and b are constants here
[4,1,h] = a[1,4,-2] + b[-2,-3,7]
[4,1,h] = [a - 2b,4a -3b,-2a+ 7b] Vectors are equal if their components are equal by the rules of vector addition and multiplication.
4 = a - 2b
1 = 4a - 3b
h = -2a + 7b
solve for a and b from the two equations for h:
a = -2
b = -3
h = -17
We see that -2[1,4,-2] - 3[-2,-3,7] = [4,1,-17].
Hence,
For b to be in the plane spanned by a1 and a2, h= -17 .
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in an experiment to study the dependence of hypertension on smoking habits, the following data were collected on 180 individuals:
Smoking Status
Nonsmoker Moderate Smoker Heavy Smoker
Hypertension Status Hypertension 21 36 30
No Hypertension 48 26 19
What is the probability that a randomly selected individual is experiencing hypertension? Given that a heavy smoker is selected at random from this group, what is the probability that the person is experiencing hypertension? Are the events "hypertension" and "heavy smoker" independent? Give supporting calculations.
Answer: The probability that a randomly selected individual is experiencing hypertension can be calculated by taking the ratio of the number of individuals with hypertension to the total number of individuals:
P(hypertension) = (21 + 36 + 30) / 180 = 87 / 180 = 0.4833
Given that a heavy smoker is selected at random, the probability that the person is experiencing hypertension can be calculated by taking the ratio of the number of heavy smokers with hypertension to the total number of heavy smokers:
P(hypertension | heavy smoker) = 30 / (30 + 19) = 30 / 49 = 0.6122
To determine if the events "hypertension" and "heavy smoker" are independent, we can compare the joint probability of both events happening to the product of their individual probabilities:
P(hypertension and heavy smoker) = 30 / 180 = 0.1667
P(hypertension) * P(heavy smoker) = 0.4833 * (30 / 180) = 0.1083
Since P(hypertension and heavy smoker) ≠ P(hypertension) * P(heavy smoker), we can conclude that the events "hypertension" and "heavy smoker" are not independent.
Step-by-step explanation:
please solve this, What is the product of the binomials below?
(d−1)(d+2)(d+3)
Answer:
d^3-2d^2-5d+6
Step-by-step explanation:
Step 1: (d-1)(d+2)=d^2+d-2
Step 2: (d-3)(d^2+d-2) = d^3+d^2-2d-3d^2-3d+6 = d^3-2d^2-5d+6
Answer: The product of the binomials (d-1)(d+2)(d+3) is [tex]d^3 + 4d^2 +d - 6[/tex].
Step-by-step explanation:
When multiplying the binomials, you can break it down and multiply two expressions first then multiply that last expression:
(d−1)(d+2)(d+3)
first: (d−1)(d+2)
when multiplying expressions you can multiply using the 'box method' where you would draw a box and put each part of the expression on the top and the left side of the box, multiplying each on into the box and adding like terms.
You can also multiply it by first taking the expression, (d−1)(d+2) and multiplying the variable 'd' to the (d + 2) and then multiplying the '-1' to the (d+2) and then adding like terms:
(d−1)(d+2)
[tex]d^{2} + 2d - d - 2[/tex]
'd' is the only like term in this expression so lets add 2d and -d together
[tex]d^{2} + d - 2[/tex]
finally, we need to multiply the (d + 3) to expression, [tex]d^{2} + d - 2[/tex]
We will treat this multiplying process the same as before.
[tex](d + 3)(d^{2} + d - 2)[/tex]
[tex]d^3 + d^2 -2d + 3d^2 + 3d - 6[/tex]
now lets add like terms
[tex]d^3 + 4d^2 +d - 6[/tex]
So the product of the binomials (d-1)(d+2)(d+3) is [tex]d^3 + 4d^2 +d - 6[/tex].
a set of 8 numbers has a mean of -2. what additional number must be included in this set to create a new set with a mean that is 4 more than the mean of the original set
The new set that follows has a mean that is 4 more than the mean of the previous set: (-2, -2, -2, -2, -2, -34).
what is set ?A set is a graphical function of many object classes. One of the terms or elements that compose a set could include any kind of mathematical object. Symbols, digits, lines, other geometrical features, space-based points, variables, and even other quantities. In mathematics, a proposition is a structured set of components that can be written as a list or a hypothesis builder. To designate sets, curly brackets are usually applied. A = 1, 2, 3, and 4 is an illustration of a set. Basically, a set is an assortment of objects that are displayed together. A set's components or elements are the components that make up the set. Any object might make up a set's components, but for the purposes of the discussion,
given
Mean is the sum of all numbers divided by the amount of numbers. That means the sum of the first set would be 8*-2=-16.
With that in mind, you can simply have the first set be eight -2s (-2, -2, -2, -2, -2, -2, -2, -2).
Now we need to calculate the sum of the second set. This set has 9numbers, and the mean is 2. 9*2=18. To find the number to add to your set, take 48–63. Your set becomes (-2, -2, -2, -2, -2, -2, -2, -34).
The new set that follows has a mean that is 4 more than the mean of the previous set: (-2, -2, -2, -2, -2, -34).
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100 POINTS HELP IM ALMOST DONE If a business uses a monthly accounting period, how often would it prepare a post closing trial balance?
A. yearly
B. weekly
C. monthly
D. daily
Answer:
C. Monthly
Step-by-step explanation:
If a business uses a monthly accounting period, it would prepare a post-closing trial balance once a month, at the end of the accounting period. Therefore, the correct answer is option C, monthly.
A post-closing trial balance is a list of all the accounts and their balances after adjusting entries have been made and closing entries have been posted to the general ledger. It is used to verify that the debits and credits are equal and that all temporary accounts have been closed out. The post-closing trial balance is prepared after the closing entries have been made at the end of the accounting period. For a business that uses a monthly accounting period, this would typically be done once a month, at the end of each month.
The volume of a right cone is 2325
�
π units
3
3
. If its radius measures 15 units, find its height.
The height of the right cone will be 9.86 units.
What is the volume of a cone?The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.
Given that the volume of the cone is 2325 cubic units and the radius of the cone is 15 units.
The height of the cone will be calculated as:-
Volume = 2325
(1/3)πr²h = 2325
( 1/3 ) x π x 15)² x h = 2325
h = ( 2325 x 3 ) / ( 15 x 15 x π )
h = 9.86 units
Therefore, the height of the right cone will be 9.86 units.
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Solve with a = 5.
20÷8
Answer:I.65
Step-by-step explanation:
15. ABC is
a. Congruent
b. Similar
c. Neither
to A'B'C'.
Answer:
Step-by-step explanation: 3
7
9
0
7
5
The business manager of an agricultural company reviews information on trends in the cattle industry to support financial decisions for the coming year.
In what year did cattle prices remain relatively stable, total expenses increase slightly, and cattle income increase significantly?
2011
2012
2013
2014
In 2011 cattle prices remain relatively stable, total expenses increase slightly, and cattle income increase significantly. Therefore, option A is the correct answer.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
In the graph we can see in 2011 total expenses increase slightly, and cattle income increase significantly.
Therefore, option A is the correct answer.
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The top of a silo is a hemisphere with a radius of 12ft. The bottom of the silo is a cylinder with a height of 40 ft. How many cubic feet of grain can the silo hold?
Use 3.14 for pi.
The total number of cubic feet of grain or volume of the grain that the silo can hold is 28947.41 [tex]ft^3[/tex].
What is the volume of an object?
The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Given that the top of a silo is a hemisphere
radius(r) = 12 ft.
Then,
the volume of a hemisphere = [tex]\frac{2}{3} \pi r^3[/tex] = [tex]\frac{2}{3} * 3.14* 12^3 = 10851.84[/tex] [tex]ft^3[/tex]
And, the bottom of the silo is a cylinder with
height (h) = 40ft.
the volume of a cylinder =[tex]\pi r^{2} h = 3.14*12^2*40=18095.57 ft^3[/tex]
So, the total volume is
V = 10851.84 + 18095.57 = 28947.41 [tex]ft^3[/tex]
Then, total volume = total number of cubic feet of grain
Hence, the required answer is 28947.41 [tex]ft^3[/tex].
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LA and L B are vertical angles. If m/ A = (« + 15)° and m/B = (5x - 17)°, then find the measure of ZB.
Answer:
∠ B = 23°
Step-by-step explanation:
vertical angles are congruent , then
∠ B = ∠ A , that is
5x - 17 = x + 15 ( subtract x from both sides )
4x - 17 = 15 ( add 17 to both sides )
4x = 32 ( divide both sides by 4 )
x = 8
Then
∠ B = 5x - 17 = 5(8) - 17 = 40 - 17 = 23°
Trayvon enters a competition to guess how many balls are in a barrel. Trayvon’s guess is 63 balls. The actual number of balls is 60 . What is the percent error of Trayvon’s guess?
Travon's guess was off by?
what was his percent error
Answer:
1.8
3 percent of 60 is 1.8
In 3 to 5 sentences how can I describe weather or not files should be deleted from your computer. “quick I’m being timed”
For a variety of reasons, files on your computer shouldn't be destroyed. One, you might have to keep them since your work is crucial. Two, I should have them just in case.
Describe a computer.A computers is a piece of electrical equipment used to manipulate data or information. It has the ability to store, retrieve, and process data.You may already be aware of the fact you are able to use a computers to surf the Internet, send emails, type documents, and play games.
What makes it a computer?Modern computers are given their names after the jobs that they replaced. The term "computer" was first used in the English language in the 17th century to refer to a person who performed mathematical computations. It made its first mention of a calculator in 1897. The "human" computer is now outdated in the age of the "machine."
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What is 2(n+17)/8=3/8
Please help I will give brainly quickly
Answer:
2(n+17)/8 = 3/8
2(n+17)/8 × 8 = 3/8 ×8
2(n+17) = 3
2n +34 = 3
2n = -31
n = -15.5
Use the law of sines to find the value of y. Round to the nearest tenth.Law of sines: StartFraction sine (uppercase A) Over a End Fraction = StartFraction sine (uppercase B) Over b End Fraction = StartFraction sine (uppercase C) Over c End Fraction1.4 units1.6 units2.5 units2.6 units
Using the law of Sine, the value of y becomes 1.6 units.
Correct option: B
What is Sine rule?Rule of Sines The sine law, sine formula, sine rule, or law of sines is an equation in trigonometry that connects the lengths of any triangle's sides to the sines of its angles. The ratio of a triangle's sides and angles may be calculated using the sine rule.
The formula: a/sinA = b/sinB = c/sinC
It may be used to describe the sine rule. Here, the triangle's angles are A, B, and C, while its sides' lengths are denoted by the letters a, b, and c.
The sine rule:
a/Sin A = b/Sin B = c / Sin C = 2R
Given, a = 2 and b = y
∠A = 75° and ∠B = 50°
by sine rule:
⇒ 2/ Sin 75° = y/ Sin 50°
⇒ 2 × Sin 50° = y × Sin 75°
⇒ y = 1.586 ≈ 1.6 units
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Simplify fully:
Please help!!
Answer:
-8/-4
Step-by-step explanation:
-8/-4
The x cancel each other
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{3x^2 - 8x - 3}{2x^2 - 6x}}[/tex]
[tex]\large\text{We cannot do too much to this equation because we do not have any}\\\\\large\text{like terms. So we will solve it this way to make it easier to get to the}\\\\\large\text{answer.}[/tex]
[tex]\mathsf{= \dfrac{(3x + 1)(x - 3)}{2x(x - 3)}}[/tex]
[tex]\mathsf{= \dfrac{3x + 1 \ * \ x - 3}{2x \ * \ x - 3}}[/tex]
[tex]\large\text{Simplify it}[/tex]
[tex]\mathsf{= \dfrac{3x + 1}{2x}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{3x + 1}{2x}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
geometric series $b 1 b 2 b 3 \cdots b {10}$ has a sum of $180$. assuming that the common ratio of that series is $\dfrac{7}{4}$, find the sum of the series $b 2 b 4 b 6 b 8 b {10}.$
The sum of the series b 2 b 4 b 6 b 8 b {10} is [tex]$\dfrac{180}{3}$[/tex] since it is a geometric series with a common ratio of [tex]$\dfrac{7}{4}$[/tex].
Since the given series [tex]$b 1 b 2 b 3 \cdots b {10}$[/tex] has a sum of 180, it can be deduced that the series is a geometric series with a common ratio of[tex]$\dfrac{7}{4}$[/tex]. This means that the ratio of any two consecutive terms in the series is a constant, [tex]$\dfrac{7}{4}$[/tex]. Therefore, the sum of the series b 2 b 4 b 6 b 8 b {10} can be calculated as follows:
[tex]$S = b2 + b4 + b6 + b8 + b_{10}$[/tex]
[tex]$= b2\left(\dfrac{7}{4}\right)^0 + b2\left(\dfrac{7}{4}\right)^2 + b2\left(\dfrac{7}{4}\right)^4 + b2\left(\dfrac{7}{4}\right)^6 + b2\left(\dfrac{7}{4}\right)^8$[/tex]
[tex]$= b2 \left[1 + \left(\dfrac{7}{4}\right)^2 + \left(\dfrac{7}{4}\right)^4 + \left(\dfrac{7}{4}\right)^6 + \left(\dfrac{7}{4}\right)^8\right]$[/tex]
[tex]$= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{1-\left(\dfrac{7}{4}\right)^2}\right]$[/tex]
[tex]$= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{\dfrac{3}{4}}\right]$[/tex]
[tex]$= \dfrac{4b2}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]
Since the sum of the series[tex]$b 1 b 2 b 3 \cdots b {10}$[/tex] is 180, we can substitute $b2$ with [tex]$\dfrac{180}{3}$[/tex]nd calculate the sum of the series $b 2 b 4 b 6 b 8 b {10}$:
[tex]$S = \dfrac{4\left(\dfrac{180}{3}\right)}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]
[tex]$= \dfrac{180}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]
Therefore, the sum of the series [tex]$b 2 b 4 b 6 b 8 b {10}$ is $\dfrac{180}{3}$[/tex].
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Kaia says the graph does not represent a function. Is Kaia correct? Explain your reasoning.
Answer: Kaia is not correct
Step-by-step explanation: A function works as long as there is only one 'output' for every 'input', or for every x value, only one y value works. (There can be multiple x values for any y value). If you do the verticle line test on this graph, the line won't pass through two points at the same time anywhere. Therefore, Kaia is incorrect.
use unit rates to determine the better buy and provide the unit price for your answer round your answer to the nearest hundredth if necessary
$17.52 for 20 packs of gum
$26.09 for 30 packs of gum
On solving the provided question, we cans ay that By unitary method 1 packs of gum = 17.52 /20 = $0.876 and = 26.09/30 = $0.866
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
We have,
$17.52 for 20 packs of gum
$26.09 for 30 packs of gum
By unitary method
$17.52 for = 20 packs of gum
1 packs of gum = 17.52 /20 = $0.876
$26.09 for 30 packs of gum
1 pack = 26.09/30 = $0.866
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Which table shows a proportional relationship between x and y?
A. x 2.5 3 5 6
y 5 6 10 15
B. x 7 14 28 35
y 1 2 4 5
C. x 1 3 4 7
y 2 5 8 14
D. x 1 2 3 4
y 4 10 12 16
Answer:
D
Step-by-step explanation:The proportional relationship between x and y is;
x 7 14 28 35
y 1 2 4 5
The correct option is D.
Proportional relationships;
Proportional relationships between x and y satisfy the following equation;
Where k is some constant.
Rearranging the equation;
Then,
The proportional relationship between x and y is;
Hence, the proportional relationship between x and y is the correct option is D.
Find the distance between the points on a number line. -8,9
Answer:
Below
Step-by-step explanation:
Start at -8... you have to go 8 units to reach 0
then you have to go another 9 to reach 9 total = 8 + 9 = 17