Answer:
0.5867 (or 58.7%)
Step-by-step explanation:
The probability that a randomly selected student has a score between 350 and 550 is 59%.
What is z score?Standard score or z score in statistics is defined as the number of standard deviations by which that the value of a score is above or below the mean value.
Given that,
The scores of the students on a standardized test are normally distributed.
Mean, μ = 500
Standard deviation, σ = 110
z score = (x - μ) / σ
For x = 350,
z = (350 - 500) / 110 = -1.36
Probability = 1 - 0.9131 = 0.0869
For x = 550,
z = (550 - 500) / 110 = 0.45
Probability = 0.6736
Probability that a randomly selected student has a score between 350 and 550 is,
P = 0.6736 - 0.0869 = 0.5867 ≈ 59%
Hence the required probability is 0.5867 or 58.67%.
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18. A random sample of n = 16 scores is obtained from a
population with a mean of μ = 45. After a treatment
is administered to the individuals in the sample, the
sample mean is found to be M = 49.2.
a. Assuming that the sample standard deviation is
s = 8, computer and the estimated Cohen's d to
measure the size of the treatment effect.
b. Assuming that the sample standard deviation is
s = 20, computer and the estimated Cohen's d to
measure the size of the treatment effect.
c. Comparing your answers from parts a and b, how
does the variability of the scores in the sample
influence the measures of effect size?
Through reporting statistical results, we found that [tex]r^{2}[/tex] is 0.22 and Cohen's [tex]d[/tex] is 0.52 when s = 8, and [tex]r^{2}[/tex] is 0.04 and Cohen's [tex]d[/tex] is 0.21 when s = 20. It is also observed that when the variability of the scores in the sample, [tex]r^{2}[/tex] decreases, there is simultaneous decrease in the measures of effect size, Cohen's [tex]d[/tex] as well.
It is given to us that -
A random sample of n = 16 scores
Population with a mean of μ = 45
Sample mean is found to be M = 49.2
In Reporting Statistical results, there are two different effect sizes, namely eta-squared [tex]r^{2}[/tex] and Cohen's [tex]d[/tex].
Eta-square, [tex]r^{2} = \frac{t^{2} }{t^{2}+df }[/tex]
where, [tex]df = n-1[/tex]
[tex]SEM = \frac{s}{\sqrt{n} }[/tex]
and, [tex]t=\frac{x_{2} -x_{1} }{SEM}[/tex]
Cohen's [tex]d=\frac{x_{2} -x_{1} }{s}[/tex]
a) Given that the sample standard deviation is s=8
We have n = 16
So, [tex]df = n-1 = 16-1 = 15[/tex]
[tex]SEM = \frac{s}{\sqrt{n} } = \frac{8}{\sqrt{16} } = \frac{8}{4} = 2[/tex]
We also have μ = 45 and M = 49.2. This implies
[tex]t=\frac{x_{2} -x_{1} }{SEM} = \frac{49.2-45}{2} = \frac{4.2}{2} =2.1[/tex]
Now,
[tex]r^{2} = \frac{t^{2} }{t^{2}+df } = \frac{(2.1)^{2} }{(2.1)^{2}+ 15 }= \frac{4.41}{4.41+15} \\= \frac{4.41}{19.41} = 0.22[/tex]
Cohen's [tex]d=\frac{x_{2} -x_{1} }{s} = \frac{49.2-45}{8} = \frac{4.2}{8} = 0.52[/tex]
b) Given that the sample standard deviation is s=20
We have n = 16
So, [tex]df = n-1 = 16-1 = 15[/tex]
[tex]SEM = \frac{s}{\sqrt{n} } = \frac{20}{\sqrt{16} } = \frac{20}{4} = 5[/tex]
We also have μ = 45 and M = 49.2. This implies
[tex]t=\frac{x_{2} -x_{1} }{SEM} = \frac{49.2-45}{5} = \frac{4.2}{5} =0.84[/tex]
Now,
[tex]r^{2} = \frac{t^{2} }{t^{2}+df } = \frac{(0.84)^{2} }{(0.84)^{2}+ 15 }= \frac{0.706}{0.706+15} \\= \frac{0.706}{15.706} = 0.04[/tex]
Cohen's [tex]d=\frac{x_{2} -x_{1} }{s} = \frac{49.2-45}{20} = \frac{4.2}{20} = 0.21[/tex]
c) Comparing a and b, we see that the variability of the scores in the sample, [tex]r^{2}[/tex] is 0.22 when s = 8 and [tex]r^{2}[/tex] is 0.04 when s = 20. Similarly, Cohen's [tex]d[/tex] is 0.52 when s = 8 and [tex]d[/tex] is 0.21 when s = 20.
Thus, we can see that when the variability of the scores in the sample, [tex]r^{2}[/tex] decreases, there is simultaneous decrease in the measures of effect size, Cohen's [tex]d[/tex] as well.
Therefore, through reporting statistical results, we found that [tex]r^{2}[/tex] is 0.22 and Cohen's [tex]d[/tex] is 0.52 when s = 8, and [tex]r^{2}[/tex] is 0.04 and Cohen's [tex]d[/tex] is 0.21 when s = 20. It is also observed that when the variability of the scores in the sample, [tex]r^{2}[/tex] decreases, there is simultaneous decrease in the measures of effect size, Cohen's [tex]d[/tex] as well.
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NO LINKS!! Please assist me with this problem Part 3m
If a and h are real numbers, find the following values for the given function
[ 9(a + h) - 3 - 9a + 3]/h =
9h /h = 9
Answer:
[tex]\textsf{(d)} \quad \boxed{9a+9h-3}[/tex]
[tex]\textsf{(e)} \quad \boxed{9a+9h-6}[/tex]
[tex]\textsf{(f)} \quad \boxed{9}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x) = 9x - 3[/tex]
Part (d)
To find f(a + h), substitute x = a + h into the function:
[tex]\begin{aligned}\implies f(a+h)&=9(a+h)-3\\&=9a+9h-3\end{aligned}[/tex]
Part (e)
Find f(a) by substituting x = a into the function:
[tex]\implies f(a)=9a-3[/tex]
Find f(h) by substituting x = h into the function:
[tex]\implies f(h)=9h-3[/tex]
Therefore:
[tex]\begin{aligned}\implies f(a)+f(h)&=(9a-3)+(9h-3)\\&=9a-3+9h-3\\&=9a+9h-6\end{aligned}[/tex]
Part (f)
[tex]\begin{aligned}\implies \dfrac{f(a+h)-f(a)}{h}&=\dfrac{(9(a+h)-3)-(9a-3)}{h}\\\\&=\dfrac{9a+9h-3-9a+3}{h}\\\\&=\dfrac{9h}{h}\\\\&=9\end{aligned}[/tex]
ahmad bought 2 books for 120 at a book fair. Another time he bought 4 books for 280 .wwrite an equation in standard form that represents. Ahmad spending with respect to the number of books purchased.
An equation in standard form is written as y = 80x - 40
How to write equation for books ahmad boughtLet the cost of books Ahmad bought be represented by m
let the flat cost by c (c reduction at the fair)
Information given in the question is interperted as
ahmad bought 2 books for 120 at a book fair
2m + c = 120
Another time he bought 4 books for 280
4m + c = 480
The required equation leads to 2 simultaneous equation with 2 unknown
2m + c = 120
4x + c = 480
solving the 2 equations gives
m = 80 and y = -40
representing the equation as 1 we have
y = mx + c
Definition of variables to suit the problem to be solved
y = Total cost
m = cost per book
x = number of books
c = flat cost
writing the equation
y = 80x - 40
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Find sin x/2, cos x/2, tan x/2. from the given information. tan x = [tex]\sqrt{2}[/tex]. 0° < x < 90°
The trigonometric measures for the given angle are as follows:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{6}}[/tex][tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 + \sqrt{3}}{6}}[/tex][tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]How to obtain the trigonometric measures?We are given the measure of the sine for the angle and we need to find the three measures, sine, cosine and tangent for half the angle.
These measures are dependent on the cosine of the function, hence we apply the definition of the tangent as follows:
[tex]\tan{x} = \frac{\sin{x}}{\cos{x}}[/tex]
Hence:
[tex]\sqrt{2} = \frac{\sin{x}}{\cos{x}}[/tex]
[tex]\sin{x} = \sqrt{2}\cos{x}[/tex]
The exact value of the cosine can be found applying the identity as follows:
sin²(x) + cos²(x) = 1.
Then, from the equation of the sine as a function of the cosine from the tangent relation, we have that:
[tex](\sqrt{2}\cos{x})^2 + \cos^2{x} = 1[/tex]
[tex]2^\cos^2{x} + \cos^2{x} = 1[/tex]
[tex]\cos^2{x} = \frac{1}{3}[/tex]
[tex]\cos{x} = \pm \sqrt{\frac{1}{3}}[/tex]
The angle is of the first quadrant, as 0° < x < 90°, hence the cosine is positive, thus:
[tex]\cos{x} = \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}[/tex]
The identity that gives the sine for half the angle is:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \cos{x}}{2}}[/tex]
Hence:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \frac{\sqrt{3}}{3}}{2}}[/tex]
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{6}}[/tex]
The identity for the cosine is almost the same, just there is a plus instead of a minus, hence:
[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 + \cos{x}}{2}}[/tex]
[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 + \frac{\sqrt{3}}{3}}{2}}[/tex]
[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 + \sqrt{3}}{6}}[/tex]
The tangent is the sine divided by the cosine, hence the inserting the entire division and the same square root and simplify the common denominator, thus:
[tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]
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A pole that is 2.5 m tall casts a shadow that is 1.65 m long. At the same time, a nearby building casts a shadow that is 50.25 m long. How tall is the building?
Round your answer to the nearest meter.
The building is 76.545 m tall.
Given:
A pole that is 2.5 m tall casts a shadow that is 1.65 m long. At the same time, a nearby building casts a shadow that is 50.25 m long.
Let x be the height of the building.
2.5/1.65 = x/50.25
2.5*50.25 = x * 1.65
25/10*5025/100 = x*165/100
25*5025/10 = 165x
25*5025 = 1650x
126300 = 1650x
x = 126300/1650
x = 76.545 m.
Therefore the building is 76.545 m tall.
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Customer: "If I purchase this product for $79.99 and two accessories for $9.99 and $7.00, how much would I owe after the 8.75% tax is applied?"
Employee: "Your total would be __________."
Which represents Newton's second law?
Ov=d/t
a = F/m
OF=0
OF = m/v
a = F/m
because F = ma
please help this is due tomorrow
Write an equation that represents the difference in seed yield between beans without treatment and beans with treatment.
The equation that represents the difference in seed yield between beans without treatment and beans with treatment is (seed yield with treatments-seed yield without treatment) whose value will be 340.
According to the question,
We have the following information:
We have a diagram where seed yield is given.
Now, the required equation represents the difference in seed yield between beans without treatment and beans with treatment will be:
(seed yield with treatments-seed yield without treatment)
(300+310-270)
(610-270)
340
Hence, the equation that represents the difference in seed yield between beans without treatment and beans with treatment is (seed yield with treatments-seed yield without treatment) whose value will be 340.
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Michelle is selling blueberries and raspberries at a farmers' market. She makes $1.75 for each pint (pt) of blueberries she sells and $2.40 for each pint of raspberries. At the end of the day, she has made exactly $116.65 by selling a total of 57 pt of fruit.
How many pints of blueberries did she sell?
The number of the blueberries is 31.
How many pints of blueberries did she sell?In this case, the only way that we can be able to obtain the number of the pints of the blueberries that she sold is by the use of a simultaneous equation.
Let the number of the blueberries be x and the number of the raspberries be y.
We have
x + y = 57 ------ (1)
1.75x + 2.40y = 116.65 ------- (2)
x = 57 - y ------ (3)
Then we have;
1.75(57 - y) + 2.40y = 116.65
99.75 - 1.75y + 2.40y = 116.65
Collecting like terms;
- 1.75y + 2.40y = 116.65 - 99.75
0.65y = 16.9
y = 16.9/0.65
y = 26
To obtain the number of blueberries
x + 26 = 57
x = 57 - 26
x = 31
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The value of a car is $34535, in 20 years the value will decrease to $500. What is the average amount of depreciation per year?
Answer:
$1701.75
Step-by-step explanation:
34535-500=34035
34035/20=$1701.75 per year
Question 2(Multiple Choice Worth 2 points)
(Scientific Notation LC)
Write 2,850,000,000 in scientific notation.
A. 2.85 x 109
B. 285 x 107
C.285 x 10-7
D. 2.85 x 10-9
The value of 2,850,000,000 in scientific notation is 2.85*[tex]10^{9}[/tex], so option A is correct.
Given:
= 2,850,000,000
= 2850,000 * [tex]10^{3}[/tex]
= 2850 * [tex]10^{3}[/tex] * [tex]10^{3}[/tex]
= 2850 * [tex]10^{6}[/tex]
= 285*[tex]10^{7}[/tex]
= 28.5*[tex]10^{8}[/tex]
= 2.85*[tex]10^{9}[/tex]
Therefore the value of 2,850,000,000 in scientific notation is 2.85*[tex]10^{9}[/tex], so option A is correct.
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If a=-5xa=−5x and b=3x-4ib=3x−4i, then find the value of the a^{3}ba
3
b in fully simplified form.
The value of expression a³b will be;
⇒ - 75x⁴ + 100x³i
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The expression is,
⇒ a³b
The values are;
a = - 5x
b = 3x - 4i
Now,
Substitute the value of a and b, we get;
The expression is,
⇒ a³b
⇒ (-5x)³ × (3x - 4i)
⇒ - 25x³ (3x - 4i)
⇒ - 75x⁴ + 100x³i
Thus, The value of expression a³b will be;
⇒ - 75x⁴ + 100x³i
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Consider the equation equation v + 4 + v = 8. What is the resulting equation after the first step in the solution? Age Erde Sade IME 5 -y+4= 8 1 V 10-1950 LEIL DIE 35 Las 12 he will 1913DF0 HIS AG pale au vopse FINE E
The resulting equation after the first step in the solution is: 2v + 4 = 8.
What is an equation?In Mathematics, an equation is sometimes referred to as an expression and it can be defined as a mathematical expression which shows that two (2) or more thing are equal.
In this exercise, you're required to describe the steps that should be taken to find a solution to the given equation by solving for v. Therefore, the appropriate and required steps that should be used include the following:
Step 1: Rearrange the equation by collecting like terms.
(v + v) + 4 = 8
Step 2: Add the like terms together.
2v + 4 = 8
Step 3: Subtract 4 from both sides of the equation.
2v + 4 - 4 = 8 - 4
2v = 4
Step 4: Divide both sides of the equation by 2.
v = 4/2
v = 2.
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Complete Question:
Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?
v +4 = 8 – v
v +4 = 8
4 + v = 8 – v
2v + 4 = 8
Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y=ax^2+Bx+C and how they can be identified from the equation. How can this
form be used to find the other features of the graph?
Please help
When a quadratic equation is given in the form y = ax^2 + Bx + C the easily seen features are
the opening of the curve in the axis - open upwardthe x - coordinate of the vertex, v(h, k) h = -b/2a the axis of the parabola - y axisthe discriminant given by (b² - 4ac)How this form can be used to find other featuresEquation of a parabola is the equation used to trace the path of a parabola. this equation is a quadratic equation
The formula for the roots of the quadratic equation is derived from the equation of the form y = ax^2 + Bx + C to be
-b ± √{(b² - 4ac)2a)
the y intercepts is gotten by equating x = 0
The axis of symmetry refers to the axis where the parabolic curve can be bisected. this is in the y axis
"a" shows if the curve opens upwards or downwards.
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A small town has two local high schools. High School A currently has 900 students and is projected to grow by 30 students each year. High School B currently has 750 students and is projected to grow by 45 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Write an equation for each situation, in terms of t,t, and determine how many students would be in each high school in the year they are projected to have the same number of students.
After 10 years students in both schools are same.
Algebra is a branch of mathematics that uses mathematical expressions to represent problems. To form a meaningful mathematical expression, variables such as x, y, and z are combined with mathematical operations such as addition, subtraction, multiplication, and division. It teaches you how to solve a problem by following a logical path. As a result, you will have a better understanding of how numbers function and interact in an equation. You will be able to do any type of math better if you have a better understanding of numbers.
There are two high schools in a small town.
High school A has currently 900 students and is projects to grow by 30 students each year
Similarly
High school B has currently 750 students and is projected to grow by 45 students each year.
To find the equation for each situation in terms of t years.
also in how many years t' the number of students in both high schools would be same?
Given
The initial strength of school A = 900
the increasing rate of students = 30 students per year
i.e students in 1 year = 30
students in t years = 30t
Total students of school A after 't' years = 900+ 30t
⇒ A = 600+ 65t
The initial strength of school B = 750
increasing rate of students = 45 per year
i.e. student in 1 year = 45
⇒ student in 't' years = 45t
Total students of school B in 't' years = 950 + 30t
=> B=950+30t
Now to find no. of years 't' when students in both schools are the same i.e. A =B
⇒ 900+ 30t = 750 + 45t
⇒ 45t-30t = 900-750
⇒ 15t = 150
⇒t= 150 /15
⇒t=10
Therefore after 10 years, students in both schools are the same.
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Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 26.35°. What is the measure of ∠P?
The required measure of ∠P would be 76.825° in the given triangle PQR.
Given that two angles in triangle PQR are congruent, ∠P and ∠Q;
∠R measures 26.35°.
Let the measure of ∠P would be x
∠P = x = ∠Q
We know that the sum of interior angles is always 180 degrees in the triangle.
⇒ ∠P + ∠Q + ∠R = 180°
⇒ x + x + 26.35° = 180°
⇒ 2x + 26.35° = 180°
⇒ 2x = 180° - 26.35°
⇒ 2x = 153.65
⇒ x = 153.65/2
⇒ x = 76.825°.
Therefore, the required measure of ∠P would be 76.825° in the given triangle PQR.
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A chef uses ⅔ cup of flour for every ⅛ cup of water in a dough recipe. If the chef follows the recipe proportions, which statement is true?
If the chef follows the recipe proportions, then the true statement is;
A: The chef uses 3/16 cup of flour for every cup of water because 1/8 ÷ 2/3 = 3/16
How to solve fraction word problems?
Fractions can be presented in the form of word problems just like algebraic word problems.
Now, we are told that the chef uses 2/3 cup of flour for every 1/8 cup of water in a dough recipe.
This means that;
2/3 cup of flour = 1/8 cup of water
Thus;
1 cup of flour = (1 * 1/8)/(2/3) = 3/16 cups of flour for every cup of water
Looking at the given options, we can conclude that the only correct one based on our answer is Option A.
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Please help me I am a poor person and I’m not able for a reason but please
Answer:
d /c
Step-by-step explanation:
if its rotated at an 270 angle then its d or c cause they are the same
it takes Barry 634 hours to detail a car. If he worked 81 hours during the week, how many cars did he detail?
Answer:
He would have detailed 16 cars.
Step-by-step explanation:
912/57=16
" I hoped I helped you matey : - ) "
15 milliliters of pure drug are in 500 mL of solution. What is the percent strength of the solution?
When 15 milliliters of pure drug are in 500 mL of solution, the percent strength of the solution is
How to find the percent strength of the solution'information from the problem
15 milliliters of pure drug are in 500 mL of solution
the percent strength of the solution = ?
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
= volume of pure drug / volume of solution * 100
= 15 milliliters / 500 milliliters * 100
= 0.03
= 3%
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if Jonny had 674
appes he gave away 379 how much does he have now?
Answer:
295
Step-by-step explanation:
he has 379 less apples now so you have to subtract 379 from 674
674 - 379 = 295
when he shoots a free throw he makes a basket 20% of the time Jai shoots 120 free throws in Use benchmarkercents of 1% and 10% to help you determine the answer
Benchmark percentage of 1% = 9.6 & 10% = 24.
What is Free Throw Percentage?
Free throw percentage (FT%) puts a player’s successful free throws in perspective to their total attempts.
In basketball, a free throw (or foul shot) is awarded to a player who has been fouled by the other team. The number of free throws depends on where on the court the player was while being fouled.
To find 1% of a number, we can move the decimal point of the number two places to the left.
Therefore, 1% of 120 is 1.2
To find 10% of a number, we can move the decimal point of the number one place to the left.
Therefore, 10% of 120 is 12
Since 10% of 120 is 12 and
20% = 2 x 10%
then 20% of 120 = 2 x 10% of 120
= 2 x 12 = 24
Since 1% of 120 is 1.2 and
8% = 8 x 1%
then 8% of 120 = 8 x 1% of 120
= 8 x 1.2 = 9.6
Hence the answer is, Benchmark percentage of 1% = 9.6 & 10% = 24.
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What is the equation of the line?
y=-3x
y=3x
y=3x+1
y=4x
The equation of the given straight line is y = 3x.
We are given a graph. The graph shows a straight line. Several points are marked on the line in the graph. The coordinates of two such points are (1, 3) and (2, 6). We need to find the equation of the straight line.
The equation of the straight line can be found using the two-point form of a line. The equation is solved below.
(y - y1) = [(y2 - y1)/(x2 - x1)]×(x - x1)
(y - 3) = [(6 - 3)/(2 - 1)]×(x - 1)
y - 3 = 3(x - 1)
y = 3x - 3 + 3
y = 3x
Hence, the equation of the line shown in the graph is y = 3x.
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Which equation defines the distance, d, between points (-3,3) and
(a,b)? Select all that apply.
d=√(a-3)² + (b+3)²
d √(-3-a)² + (3 — b)²
d=√(a+b)² + (−3 − 3)²
d=√(a+3)² + (b − 3)²
-
The distance is d = √(-3 - a)² + (3 - b)²
What is Distance between two points ?
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula is d =√(x₁ - x₂)² + (y₁ - y₂)²
Points are (-3, 3) and (a, b)
We know, the distance formula is
d =√(x₁ - x₂)² + (y₁ - y₂)²
Let, (x₁, y₁) = (-3, 3)
(x₂, y₂) = (a, b)
Now, plug in the values in given formula
d = √(-3 - a)² + (3 - b)²
Hence, the distance is d = √(-3 - a)² + (3 - b)²
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select all coordinate pairs that could represent a solution to 3x - 2y = 12
The coordinate pairs that could represent the equation 3x - 2y = 12 are
( x₁ , y₁ ) = ( 2 , -3 )
( x₂ , y₂ ) = ( 4 , 0 )
( x₃ , y₃ ) = ( 0 , -6 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be A
3x - 2y = 12
Now , Substituting the values of x and y in the above equation , we get
a)
The coordinate pair ( 2 , -3 )
So , the equation becomes
3 ( 2 ) - 2 ( -3 ) = 12
6 + 6 = 12
12 = 12
Therefore , the coordinate pair satisfies the given equation
b)
The coordinate pair ( 4 , 0 )
So , the equation becomes
3 ( 4 ) - 2 ( 0 ) = 12
12 = 12
Therefore , the coordinate pair satisfies the given equation
c)
The coordinate pair ( 0 , -6 )
So , the equation becomes
3 ( 0 ) - 2 ( -6 ) = 12
12 = 12
Therefore , the coordinate pair satisfies the given equation
Hence , the coordinate pairs that satisfies the the equation 3x - 2y = 12 are
( 2 , -3 ) , ( 4 , 0 ) and ( 0 , -6 )
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Determine the vertex of the graph of the following parabola. f(x)=−(x−2)2−3
The vertex of the Parabola is (2, -3)
What is a vertex?The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape. If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.
From the function f(x) =[tex]-(x-2)^{2}[/tex] - 3
The equation of parabola in vertex form is
y=[tex]a(x-h)^{2}[/tex]+k
where h and k are the coordinates of the vertex
comparing the two equations
h = 2, k = -3
The coordinates of the vertex is (2, -3)
In conclusion, the vertex is (2, -3).
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f(x)= 0.6x5-2x4+8x Describe the end behaviour of the polynomial function
Step-by-step explanation:
if I understand your typing correctly, and there is nothing missing, we have
f(x) = 0.6x⁵ - 2x⁴ + 8x
the "end behavior" means the general tendency of the result values for very large or very low values of x (going to +infinity and -infinity).
the higher (or lower in the negative direction) x gets, the more the highest exponent will dominate the result values.
it does not matter, that it has a diminishing factor (or coefficient) like 0.6.
the much stronger progression of x⁵ vs. smaller exponents like x⁴ or x will easily compensate for that with sufficiently large x.
so, ultimately, the term with the highest exponent (in our case 0.6x⁵) defines the end behavior.
with x going to +infinity, so does the function result (+infinity).
with x going to -infinity, so does the function result (-infinity, because an odd exponent number like 5 will maintain the sign of the argument).
14. Four friends decide to share
equally 7 packs of baseball cards.
There are 8 cards in each pack.
Part A
How many cards does each
friend get?
Part B
Explain your strategy.
Answer:
Each gets 14 cards.
Step-by-step explanation:
7*8=56
56 Is the total amount of cards
56/4 equals 14
We divide 56 by 4 since 4 is the total number of friends.
A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 170 gallons of a mixture that contains 80% pure antifreeze, how many gallons of each brand of antifreeze must be used?
first brand: ?
Second brand ?
please dont answer if you dont know it.
The quantity of first brand is 102 gallons and quantity of second brand is 68 gallons
Given,
The first brand of antifreeze = 70% pure antifreeze
The second brand of antifreeze = 95% pure antifreeze
The quantity of mixture = 170 gallons contains 80% pure antifreeze
We have to find the quantity of each brand of antifreeze must be used;
Now,
The quantity of first brand = x gallons
The quantity of second brand = y gallons
Then,
x + y = 170
x = 170 - y ....(1)
70x / 100 + 95y / 100 = (80 × 170) / 100
70x + 95y = 13600
Now, putting the value of x from equation 1:
70 (170 - y) + 95y = 13600
11900 - 70y + 95y = 13600
11900 + 25y = 13600
25y = 13600 - 11900
25y = 1700
y = 1700/25
y = 68
Now, putting this value of y in equation 1:
x = 170 - 68
x = 102
Therefore,
The quantity of first brand is 102 gallons and quantity of second brand is 68 gallons
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A scientist invents a car that can travel for many hours without stopping for fuel. The
car travels around a track at 54 miles an hour for 24 hours. At the end of the 24
hours, how far has the car traveled?
o 1,286 miles
o 1, 296 miles
• 78 miles
• 1, 080 miles
Answer:
1,296 miles
Step-by-step explanation:
to answer this question, we have to apply the next formula:
Distance = Speed rate x time
speed rate = 54 miles per hour
time = 24 hours
Replacing with the values given and solving for D (distance)
D = 54 mph x 24 h = 1,296 m
The car traveled 1,296 miles
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