Trace metals in drinking water affect the flavor and an unusually high concentration can pose a health hazard. Ten pairs ...
Answers
a) The hypothesis are given as follows:
Null: [tex]H_0: \mu_d \leq 0[/tex]Alternative: [tex]H_1: \mu_d > 0[/tex]b) The significance level is of α = 0.1.
c) The test statistic is of: t = 4.86.
d) The p-value is of: 0.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the mean level is greater at the bottom of the surface, that is, if the mean is not positive, hence:
[tex]H_0: \mu_d \leq 0[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the mean level is greater at the bottom of the surface, that is, if the mean is positive, hence:
[tex]H_1: \mu_d > 0[/tex]
As stated in the problem, the significance level is of:
α = 0.1.
How to calculate the test statistic?
The test statistic is calculated by the formula presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The variables of this formula are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null and at the alternative hypothesis.s is the standard deviation of the sample.n is the sample size.From the table, the sample is composed by the differences and given as follows:
0.015, 0.028, 0.177, 0.121, 0.102, 0.107, 0.019, 0.066, 0.058, 0.121.
The above sample is inserted into a calculator, to obtain the parameter values given as follows:
[tex]\overline{x} = 0.0814, \mu = 0, s = 0.053, n = 10[/tex]
Hence the numeric value of the test statistic is given as follows:
t = (0.0814 - 0)/(0.053/sqrt(10))
t = 4.86.
What is the p-value?Using a t-distribution calculator, considering a right-tailed test, as we are testing if the mean is greater than a value, with 10 - 1 = 9 df and t = 4.86, the p-value is of 0.
More can be learned about the t-distribution at https://brainly.com/question/13873630
#SPJ1
Related Questions
How do I put 8x=26+14y in standard form
Answers
The given equation written in standard form is 8x - 14y = 26
Writing a linear equation in standard formFrom the question, we are to write the given linear equation is standard form.
From the given information, the given linear equation is
8x = 26 + 14y
The standard form of linear equation is given as
Ax + By = C
Where x and y are the variables
A, B, and C are the constants
Now, we will write the given equation in standard form
8x = 26 + 14y
Subtract 14y from both sides of the equation
8x - 14y = 26 + 14y - 14y
8x - 14y = 26
Hence, the equation is 8x - 14y = 26
Learn more on Writing an equation in standard form here: https://brainly.com/question/28981240
#SPJ1
Find the least common denominator for this pair of algebraic fractions:
p/4 and p/16
Answers
The least common denominator for this pair of algebraic fractions: p/4 and p/16 is 16.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In the case, the fraction is illustrated as p/4 and p/16.
It should be noted that the lowest common multiple for 4 and 16 is 16. This is the denominator.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
1. The difference of a number and 46 is at most 153. What is the largest integer that could be used for the number?
2. Vanessa must earn at least 360 points to make an A in her Pre-Algebra class. If she currently scores of 81, 91, and 89 points from her first three test, how many more points does she need to make an A?
3. The band has been selected to march and play in the holiday parade. The 105 members must raise at least $49,500 for the trip. What is the least amount that each one needs to raise (to the next whole dollar)?
4. All the cars a company sells require a down payment of $2,000 and 48 monthly payments. The contract amount for any of the cars is at least $19,940. What is the least amount of the monthly payment (to the next whole dollar)?
5. A particular type of TV is being sold for $1,200 cash for $500 down with 48 monthly payments. Find the amount of the monthly payment if the plan resusts in charges of at least $1,484 over the life of the contract. Find the amount of interest paid if the monthly payment plan is chosen.
please help, its due tomorrow. thank you.
Answers
The basic calculation values are;
1. The largest number is 199
2. The score Vanessa needs is 99 points
3. Each person should raise approximately $471
4. The approximate minimum monthly payment is $374
5. The approximate monthly payment is $55.9
The interest is 123.[tex]\overline {6}[/tex]
What are basic mathematical operations?Basic mathematical operations includes addition, subtraction, multiplication, division, and combinations of the above operations.
1. Let x represent the number, we have;
x - 46 ≤ 153
x ≤ 153 + 46 = 199
x ≤ 199
The largest integer that could be used for the number is 199
2. Vannesa's current scores are;
81 points, 91 points, 89 points
The score Vannesa requires so as to get an A is 360 points
The score Vannesa needs = 360 - (81+91+89) = 99
Vannesa needs 99 points to get an A
3. The number of members in the band = 105
The amount the band needs to raise = $49,500
The amount each one should raise therefore is 49500 ÷ 105 ≈ 471
Each one needs to raise $471
4. The down payment is $2,000
Number of monthly payment = 48
Least contract amount = $19,940
The monthly payment = (19,940 - 2,000)/48 ≈374
The least monthly payment ≈ $374
5. The cash price for the TV = $1,200
The down payment = $500
The charges = $1,484
Number of monthly payment = 48
Total payment = $1,200 + $1,484 = $2,684
The monthly payment = 2,684 ÷ 48 ≈ 55.9
The monthly payment is approximately $55.9
The interest is therefore;
[tex] \dfrac{1484}{1200}\times 100 = 123.\overline 6 \%[/tex]
Learn more about basic calculations in mathematics here:
https://brainly.com/question/13338580
#SPJ1
Write a mathematical sentence that expresses the information given below.
Use p as your variable name. If necessary:
type <= to mean <
or > = to mean 2.
A football team had 52 players at the start of the season, but then some
players left the team. After that, the team had 43 players.
Answers
The mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season or p = 52-43.
According to the question,
We have the following information:
A football team had 52 players at the start of the season, but then some players left the team. After that, the team had 43 players.
Now, let's take the number of players who left the team to be p.
So, we have the following expression:
p = 52-43
p = 9
Hence, the mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season.
To know more about mathematical sentence here
https://brainly.com/question/22248350
#SPJ1
2(x-3)^2-12=116 help
Answers
Step-by-step explanation:
[tex]2(x - 3) {}^{2} - 12 = 116 \\ [/tex]
[tex]2 \times ( {x}^{2} - 6x + 9) - 12 = 116[/tex]
[tex] {2x}^{2} - 12x + 18 - 12 = 116[/tex]
[tex] {2x}^{2} - 12x - 110 = 0[/tex]
[tex] {x}^{2} - 6x - 55 = 0[/tex]
[tex] {x}^{2} - 11x + 5x - 55 = 0[/tex]
[tex]x(x - 11) + 5(x - 11) = 0[/tex]
[tex](x +5 )(x - 11) = 0[/tex]
Sum and Product of Two Numbers Find two numbers whose sum is 20 and whose product is the maximum possible value. (Hint: Let x be one number. Then 20 - x is the other number. Form a quadratic function by multiplying them, and then find the maximum value of the function.)
Answers
Answer:
The numbers are 10 and 10Step-by-step explanation:
As described in the hint:
the numbers are x and 20 - x, their product is maximum possible value.The product is:
x(20 - x) = - x² + 20xThis is a quadratic expression ax² + bx + c with the leading coefficient of a = - 1, b = 20 and c = 0.
It has a maximum and no minimum value since a < 0.
The x-coordinate of the maximum is the vertex which is x = - b/2a.
The x- coordinate of the vertex is:
x = - 20/-2 = 10The maximum value itself is:
- 10² + 20*10 = - 100 + 200 =100Answer:
10 and 10.
[tex]f(x)=-x^2+20x[/tex]
Maximum value of the function is 100.
Step-by-step explanation:
Two numbers whose sum is a positive integer, and whose product is the maximum possible value have to be two positive integers.
Pairs of positive integers whose sum is 20:
1 and 192 and 183 and 174 and 165 and 156 and 147 and 138 and 129 and 1110 and 10The pair of numbers whose product is the maximum possible value is the pair of numbers that are closest to each other.
Therefore the pair of numbers is 10 and 10:
[tex]\implies x = 10[/tex]
[tex]\implies 20 - x = 10[/tex]
Form a quadratic function by multiplying:
[tex]\implies f(x)=x(20-x)[/tex]
[tex]\implies f(x)=20x-x^2[/tex]
[tex]\implies f(x)=-x^2+20x[/tex]
The maximum value of the function is the y-value of its vertex.
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
To convert the function to vertex form, complete the square.
Factor out negative 1:
[tex]\implies f(x)=-(x^2-20x)[/tex]
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies f(x)=-\left(x^2-20x+\left(\dfrac{-20}{2}\right)^2-\left(\dfrac{-20}{2}\right)^2\right)[/tex]
[tex]\implies f(x)=-(x^2-20x+100-100)[/tex]
[tex]\implies f(x)=-(x^2-20x+100)+100[/tex]
Factor the perfect square trinomial:
[tex]\implies f(x)=-(x-10)^2+100[/tex]
Therefore, the vertex of the function is (10, 100), and so the maximum value of the function is 100.
A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomrua in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 min and a standard deviation of 42.3 min (based on data from "Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomrua in Older Adults," by Sivertsen et al., Journal of the American Medical Association, Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population, and test the claim that after treatment with zopiclone, subjects have a mean wake time of less than 102.8 min. Does zopiclone appear to be effective?
Answers
A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.
What is a confidence interval?
A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.
Here,
From the standard normal table, the z-critical value at 98% confidence interval is 2.33 so,
98%C.I. = µ ± z * σ / n = 98.90 ± 2.33 * 42.30 / sqrt of 16 = 98.90 ± 24.64 = 74.26 to 125.54
The mean wake time of 102.80 minutes before the treatment due to the mean wake time of 102.80 minutes included in the 98% confidence interval which is between 74.26 and 125.54. Zopiclone does not appear effective.
Hence, A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.
To learn more about the confidence interval from the given link
https://brainly.com/question/26658887
#SPJ4
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
2, 8, 14, ...
Find the 42nd term.
Answers
The 42nd term of the sequence is 248
What is Arithmetic Progression?
Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.
The furmula is [tex]a_{n}[/tex]=a + (n - 1 )d
where a = The first form of A.P
n = Number of terms given to find
d = Common difference between each terms
Given,
a = 2
n = 42
d = 6
Now,
[tex]a_{42\\[/tex] = 2 + (42 - 1)6
[tex]a_{42}[/tex] = 2 + (41)6
[tex]a_{42}[/tex] = 2+ 246
Therefore, for 42nd term
[tex]a_{42}[/tex] = 248
Read more about Arithmetic Progression
https://brainly.com/question/29394721
#SPJ1
Select all of the roots of x3 + 2x2 – 16x– 32.
–1
–2
–4
1
4
5
Answers
Answer:
-4, -2, 4
Step-by-step explanation:
You want the roots of the polynomial x³ +2x² -16x -32.
FactorsThe polynomial can be factored by grouping:
x³ +2x² -16x -32
= (x³ +2x²) -(16x +32) . . . . . . group pairs of terms
= x²(x +2) -16(x +2) . . . . . . . . factor each group
= (x² -16)(x +2) . . . . . . . . . . . . factor out the common factor
Now, the difference of squares can be factored:
= (x -4)(x +4)(x +2)
RootsThe zero product rule tells us the roots are the values of x that make the factors zero:
x -4 = 0 ⇒ x = 4
x +4 = 0 ⇒ x = -4
x +2 = 0 ⇒ x = -2
The roots of the polynomial are {-4, -2, 4}.
__
Additional comment
The factorization of the difference of squares is a special form:
a² -b² = (a +b)(a -b)
Answer:
-2, -4, and 4 are the correct answers on edge
Step-by-step explanation:
What is the area of a quadrilateral with vertices at (1, 1), (5, -1),
(1,5), and (5,5)?
Answers
The area of the quadrilateral is = 15 square units.
What is area of the quadrilateral ?The quantity of territory contained within a quadrilateral determines its area. Let's review the definition of a quadrilateral. A closed shape with four line segments enclosing it is referred to as a quadrilateral. Both regular and irregular quadrilaterals exist. A quadrilateral with regular sides is one with equal-length sides. An irregular quadrilateral is a quadrilateral that is not regular. There are six different kinds of quadrilaterals.square \srectangle \sparallelogram \strapezoid \srhombus \skite.The area of a quadrilateral is nothing but the region enclosed by the sides of the quadrilateral. It is measured in square units such as m2, in2, cm2, etc.acc to our quesstion-
There are two sets of Y values identical ( 0 and 5 ).There are two sets of identical X values ( -1 and 2)This makes a rectangle.The length is 5-0 = 5The width is 2 - -1 = 3Area = Length x width = 5 x 3 = 15 square units.hence,The area of the quadrilateral is = 15 square units.
learn more about area of quadrilateral click here:
https://brainly.com/question/22297305
#SPJ1
Josh has to walk 9/10 of a kilometre to school.He is 1/3 of the way there. How much further will he have to walk?
Answers
Triangle w z y is cut by bisector z x. the lengths of sides z w and z y are congruent. zx bisects ∠wzy. if the measure of ∠yxz is (6m â€" 12)°, what is the value of m? 6 17 90 102
Answers
The value of m in the angle (6m - 12)° is m = 17 , the correct option is (b) .
In the question ,
it is given that ,
the triangle WZY is cut by the bisector ZX ,
and also given that ZW and ZY are congruent ,
that means ZW = ZY
Based on the characteristics of the triangle given ,
we can conclude that triangle WYZ is an isosceles triangle ,
that means , triangle WXZ = triangle YXZ
So , ∠YXZ = ∠WXZ = 90°
given that ∠YXZ = (6m - 12)°
So , (6m - 12)° = 90°
6m - 12 = 90
6m = 90 + 12
6m = 102
m = 102/6
m = 17
Therefore , the value of m in the angle (6m - 12)° is m = 17 .
The given question is incomplete , the complete question is
Triangle W Z Y is cut by bisector Z X. The lengths of sides Z W and Z Y are congruent. ZX bisects ∠WZY. If the measure of ∠YXZ is (6m – 12)°, what is the value of m?
(a) 6
(b) 17
(c) 90
(d) 102
Learn more about Triangles here
https://brainly.com/question/12347204
#SPJ4
Answer:
17
Step-by-step explanation:
i got it right on edge 2022
a 14-ounce can of green beans contains two teaspoons of salt. how much sodium is present in 2 teaspoons (11.5 grams) of salt?
Answers
The percentage of salt in green beans can is 2.89%.
It is important to know about the percentage first, the percentage is a part of the sample in the population. It can be determined by this formula
A% = x / N . 100%
where A% is the percentage, x is the sample and N is the total population
From the question above, we know that :
x = 11.5 grams
N = 14 ounce = 396.89 grams
By substituting the parameter to the equation, we get
A% = x / N . 100%
A% = 11.5 / 396.89 . 100%
A% = 2.89%
Hence, the total salt in the can is 2.89%
Find more percentages at: brainly.com/question/24304697
#SPJ4
suppose that five microchips in a production run of fifty are defective. a sample of seven is to be selected to be checked for defects. (a) how many different samples of seven can be chosen from the production run of fifty? (b) how many samples will contain at least one defective chip? the set of samples that do not contain any defective chips and the set of samples that contain at least one defective chip are ---select--- sets. so, the number of samples with at least one defective chip is . (c) what is the probability (as a percent) that a randomly chosen sample of seven contains at least one defective chip? (round your answer to one decimal place.) %
Answers
The answer to following parts are and this can be solved by using probability.
a) 15,890,700 different samples can be chosen
b) 6,523,881 will contain at least one defective chip
c) 41.1%
What is probability?
A probability is the number of desired outcomes divided by the number of total outcomes.
Main body:
The order in which the microchips are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
Cₙ,ₓ is the number of different combinations of x objects from a set of n elements, given by the following formula.
Cₙ,ₓ =[tex]\frac{ n!}{x!(n-x)!}[/tex]
(a) How many different samples can be chosen?
Samples of 6 from a set of 50.
Then
C₅₀,₆ = [tex]\frac{50!}{6!(50-6)!}[/tex] =15,890,700
15,890,700 different samples can be chosen
(b) How many samples will contain at least one defective chip?
Either a sample contains no defective chip, or it contains at least one. From a), the sum of them is 15890700.
Then
No defective chips:
Four are defective.
So 50-4 = 46 are not.
This is samples of 6 from a set of 46.
C₄₆,₆ = 46!/6!*40!
9,366,819 samples contain no defective chips.
At least one:
9366819 + n = 15890700
n = 6523881
6,523,881 will contain at least one defective chip
(c) What is the probability (as a percent) that a randomly chosen sample of six contains at least one defective chip
6,523,881 out of 15,890,700
6,523,881/15,890,700 = 0.411
As a percent
41.1%
Hence the answer are as follows.
To learn more about probability click on the link below
https://brainly.com/question/24756209
#SPJ4
Leticia is selling raffle tickets for her class fundraiser. Her class receives four-fifths of the money raised from selling the raffle tickets. Prior to the selling of raffle tickets, her class fund had a balance of $200.00.
Which function can be used to find m, the amount of money in Leticia's class fund, based on t, the amount of money Leticia has made from selling raffle tickets?
Answers
The function for the given situation is m=200+0.8t.
Given that, Leticia is selling raffle tickets for her class fundraiser. Her class receives four-fifths of the money raised from selling the raffle tickets.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, the amount of money in Leticia's class fund=m and the amount of money Leticia has made from selling raffle tickets is t
Now, the function is
m=200+4/5 t
⇒m=200+0.8t
Therefore, the function for the given situation is m=200+0.8t.
To learn more about the function visit:
https://brainly.com/question/28303908.
#SPJ1
Select each exact root. If the exact roots cannot be found, select the consecutive integers between which the roots are located. If there are no roots, select no real solution.
x2+6x+6=0
Multiple select question.
A) no real solution
B) between −2 and −1
C) between −5 and −4
D) −5
E) −1
F) between 4 and 5
G) between 1 and 2
Answers
Answer:
C, B
Step-by-step explanation:
[tex]x^2+6x+6=0 \\ \\ x=\frac{-6 \pm \sqrt{6^2-4(6)}}{2(1)} \\ \\ x=-3 \pm \sqrt{3} \\ \\ \sqrt{3} \approx 1.7 \implies -5<-3-\sqrt{3}<-4, -2<-3+\sqrt{3}<-1[/tex]
BobbyLou's cell company charges $27 a month for voice service plus $0.43 for each text message. Write the equation that would give you the amount each month, given a certain number of text messages.
Answers
The equation that would give the amount each month, given a certain number of text messages is 27 + 0.43t.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of text messages be represented as t.
Since BobbyLou's cell company charges $27 a month for voice service plus $0.43 for each text message. The amount will be:
= 27 + (0.43 × t)
= 27 + 0.43t
Learn more about equations on
brainly.com/question/2972832
#SPJ1
what is an equivelent fraction of 8x^4 * 5x ^3
Answers
The equivalent fraction is 40x⁷ of the given expression 8x⁴ × 5x³.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The expression is given in the question as:
8x⁴ × 5x³
We have to determine the equivalent fraction of the given expression.
⇒ 8x⁴ × 5x³
⇒ 8 × 5 × x⁴× x³
Multiply the coefficients in the above expression,
⇒ 40 × x⁴× x³
Add the exponents in the above expression,
⇒ 40 × x⁴⁺³
⇒ 40x⁷
Thus, the equivalent fraction is 40x⁷ of the given expression 8x⁴ × 5x³.
Learn more about Expressions here :
brainly.com/question/21751419
#SPJ1
How do you factor g³ - 343?
Answers
Answer:
(g-7)^3
Step-by-step explanation:
(x-y)^3 = x^3 - y^3
In this case you are solving for y, or 343
The cube root of 343 is 7
g^3 - 7^3 = (g-7)^3
(g-7)^3
Step-by-step explanation:
g³-343=0
g³=343
g=³√343
g=7
g³-7³=0
(g-7)^3=0
please i need it quick
Answers
The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.
How to solve a trigonometric equation
In this problem we need to find the solutions of a trigonometric equation, which can be done by means of algebra properties and trigonometric formulas. Now we proceed to present the entire procedure:
Step 1 - Introduce the trigonometric equation:
cos 2x - cos x = - 1
Step 2 - Use the trigonometric formula cos 2x = cos² x - sin ² x:
cos² x - sin ² x - cos x = - 1
Step 3 - Use fundamental trigonometric formula:
cos² x - 1 + cos² x - cos x = - 1
2 · cos² x - cos x = 0
Step 4 - Use algebra properties to factor the expression:
cos x · (2 · cos x - 1) = 0
Step 5 - Find the solutions of the expression:
cos x = 0 → x = {π / 2, 3π / 2}
2 · cos x - 1 = 0
2 · cos x = 1
cos x = 1 / 2 → x = {π / 3, 5π / 3}
The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.
To learn more on trigonometric equations: https://brainly.com/question/22624805
#SPJ1
Find the area of the triangle.
A=?in^2
Answers
Answer:
A = 7.5 in^2
Step-by-step explanation:
the formula for a triangles area is [(h)(b)]/2
2.5 is the h (height) and 6 is the b (base)
first multiply h and b
2.5 * 6 = 15
now divide by 2
15 / 2 = 7.5
that is your answer
Help please <3 end of quarter is soon!
Answers
Answer:
x = 2
Step-by-step explanation:
8x - 21 - 5x = - 15 ( collect like terms on left side )
3x - 21 = - 15 ( add 21 to both sides so numeric values on right side )
3x = 6 ( isolate x by dividing both sides by 3 )
x = 2
The equation that has the solution 8x – 21 – 5x = -15 is x = 2.
Solving steps :
A. Collect like term.
8x – 21 – 5x = -15
Collect term that have the same variables raised to the same power by subtracting their coefficients.
(8 – 5)x
Subtract the numbers.
We'll start by rewriting this subtraction as an addition problem. To do that, let's copy over the 8.
8 – 5 = 8
We're rewriting as addition, so change the minus sign to a plus.
8 – 5 = 8 +
Now we'll write the opposite of 5 after the plus sign.
8 – 5 = 8 + (-5)
We did it! The result is 3.
8 – 5 = 3
We did it!
(8 – 5)x
3x
We did it!
8x – 21 – 5x = -15
3x – 21 = -15
B. Move the constant to the right.
3x – 21 = -15
Move the constant to the right-hand side by adding it’s opposite to both sides.
3x – 21 + 21 = - 15 + 21
Since two opposites add up to 0, remove them from the expression.
3x = -15 + 21
C. Calculate the sum.
3x = -15 + 21
Keep the sign of the number with the large absolute value and substract the smaller absolute value from the larger.
- 15 + 21
+ (21 - 15)
Substract the numbers.
We did it! The result is 6.
3x = 6
D. Divide both sides.
3x = 6
Divide both sides of the equation by 3.
3x ÷ 3 = 6 ÷ 3
Any expression divided by itself equals 1.
x = 6 ÷ 3
Calculate the quotient.
x = 2
Learn more: brainly.com/question/24169758
#SPJ1
Convert meters to centimeters. 9.2 m = afers x 1. cm m) cm)
Answers
Here i a ample data et, 19 39 9 33 15 16 2 33 16 Find the mallet number (Minimum) from the data et Find the firt quartile Q1 Find the median Find the third quartile Q3 Find the larget number (Maximum) from the data et
Answers
a) The smallest number is 2
b) The first quartile Q1 is 12
c) The median is 16
d) Third quartile Q3 is 33
e)The largest number is 39
What Is Quartile Formula?
To divide a set of observations into four equal pieces, use the quartile formula. The median and the first term are where the first quartile is located. The median represents the middle quartile. The third quartile represents the midway value that falls between the median and the last term.
Given data set:
19, 39, 9, 33, 15, 16, 2, 33, 16
Arrange the data in ascending order:
2, 9 ,15 ,16 ,16 ,19 ,33 ,33 ,39
a) Smallest number: 2
b) The first quartile Q1 :
number of terms=n=9
Q1= (n+1)/4 th term
Q1= (9+1)/4 = 2.5th terms
This means, Q1=mean of 2nd and 3rd terms= (9+15)/2 = 12
c) Median:
M=(n+1)/2 th term = (9+1)/2 =5th term = 16
d) Third quartile Q3:
Q3= 3[(n+1)/4] th term
Q3= 3[(9+1)/4] = 7.5th terms
This means, Q3=mean of 7th and 8th terms= (33+33)/2 = 33
e) largest number : 39
To learn more about the quartile from the given link
https://brainly.com/question/28168026
#SPJ4
HELP ASPPP PLEASE THANK SHOW UR WORK PLEASE
Answers
Step-by-step explanation:
y + 4 = 8 ( x - 6 )
Multiple 8 by -6 and x
y+4 = 8x -48
Subtract 4 from both sides
y = 8x -52
Take two points from this equation, I took (7,4) and (8,12)
Find the slope with these points, which should give you 8
Step-by-step explanation:
when we have the equation in the form of
y = ax + b
then "a" is the slope.
in our equation
y + 4 = 8(x - 6)
the only thing that contributed to the factor of x is
8(x ...)
so, in the end the equation is (we sit need to bother about the rest)
y = 8x ...
so, the slope is 8.
question 9
this is trickier.
again, we want the form
y = ax + b
we have
6y - 3x = 12
6y = 3x + 12
y = 3/6 x + 2 = 1/2 x + 2
so, the slope is 1/2.
A sheet of metal 10 inches by 8 inches is to be used to make a open box. Squares of equal sides x are cut out of each corner then the sides are folded to make the box. Find the value of x (correct to 2 decimal places) that makes the volume a maximum.
Answers
Answer:
1.81 inches
Step-by-step explanation:
What is one possible dividend, greater than 1,000, if the quotient is 37 R4
Answers
The equation y=4–x is graphed on the coordinate plane. Which point(s) will NOT be on the line? Select all that apply.
Answers
Answer: (6,1), (2,-1) etc
Step-by-step explanation:
Just pick any points on the graph and see if they aren't on the line and if they aren't, then you can pick that one.
Given: If a triangle is equilateral, then the triangle is isosceles.
Identify the following statements as the inverse, the converse and the contrapositive.
Answers
To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.
So, inverse of the given statement is "If △ABC is not equilateral , then it is not isosceles"
We have to find the inverse of the given statement:
" If ∆ABC is equilateral, then it is isosceles."
A triangle is said to be equilateral if all of the three sides are equal in measure and a triangle is said to be isosceles if two sides of a triangle are equal in measure.
To learn more about equilateral visit:https://brainly.com/question/9872652
#SPJ1
Dilate the figure by the scale factor. Then enter the new coordinates
K=10
A'(0,20)
B'([?],[])
C'([ ][ ])
Answers
The will be A'(0, 20), B'(20, 10) and '(-10, 0). Transformation is the of a point from its to a. Types of transformation are reflection, translation, rotation and dilation.
What is transformation?
When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply moving the graph of the function g(x) = x2 up by 3 units, the graph of the function f(x) = x2 + 3 is obtained. Function transformations are very useful for graphing functions without having to start from scratch because they allow you to move, expand, compress, or reflect the curve. In this article, we will examine the guidelines for function transformations as well as examples of how to transform various function types.
Let ABC be a with coordinates A(0, 2), B(2, 1), C(-1, 0).
The coordinate of points A, B, C will change by below rule
(x, y)↔(10x, 10y)
where 10 is the scale factor.
∴A(0, 2) ↔A'(0, 20)
B(2, 1) ↔B'(20, 10)
C(-1,0) ↔C'(-10, 0)
Hence, will be A'(0, 20) ,B'(20, 10) and C'(-10, 0)
To learn more about transformation
https://brainly.com/question/27895117
#SPJ9