Using the t-distribution, it is found that the desired measures are given as follows:
The test statistic is t = -4.29.The p-value is of 0.What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 63.5, that is:
[tex]H_0: \mu = 63.5[/tex]
At the alternative hypotheses, it is tested if the mean is less than 63.5, that is:
[tex]H_1: \mu < 63.5[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given as follows:
[tex]\overline{x} = 56.3, \mu = 63.5, s = 13.2, n = 62[/tex]
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{56.3 - 63.5}{\frac{13.2}{\sqrt{62}}}[/tex]
t = -4.29.
What is the p-value?We have a left-tailed test, as we are testing if the mean is less than a value, with 62 - 1 = 61 df and t = -4.29. Hence, using a t-distribution calculator, the p-value is of 0.
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Wyatt bought $40 worth of materials to make braided keychains. If Wyatt Sells his keychains for $2.50
each, how many keychains must he sell to earn a profit?
Inequalities help us to compare two unequal expressions. Wyatt needs to sell at least 17 keychains.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Given Wyatt bought $40 worth of materials to make braided keychains. Also, it is given that Wyatt Sells his keychains for $2.50 each. Therefore, the minimum number of keychains he should sell to make a profit are,
Number of keychains>(40/2.50)
Number of keychains > 16
Thus, Wyatt needs to sell at least 17 keychains.
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Answer:
Step-by-step explanation:
17
please answer this question
Answer:
[tex]a_n=3n-2[/tex]
Step-by-step explanation:
General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth term[tex]a[/tex] is the first term[tex]d[/tex] is the common difference between termsCreate expressions for the 4th and 6th terms:
[tex]\implies a_4=a+(4-1)d=a+3d[/tex]
[tex]\implies a_6=a+(6-1)d=a+5d[/tex]
The ratio of the 4th term to the 6th term is 5:8, therefore:
[tex]\implies \dfrac{a_4}{a_6}=\dfrac{5}{8}[/tex]
[tex]\implies \dfrac{a+3d}{a+5d}=\dfrac{5}{8}[/tex]
[tex]\implies 8(a+3d)=5(a+5d)[/tex]
[tex]\implies 8a+24d=5a+25d[/tex]
[tex]\implies 8a-5a=25d-24d[/tex]
[tex]\implies 3a=d \quad \leftarrow \textsf{Equation 1}[/tex]
Sum of the first n terms of an arithmetic series:
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
The sum of the first 7 terms of an arithmetic progression is 70:
[tex]\implies S_7=70[/tex]
[tex]\implies \dfrac{7}{2}[2a+(7-1)d]=70[/tex]
[tex]\implies 2a+6d=20[/tex]
[tex]\implies a+3d=10 \quad \leftarrow \textsf{Equation 2}[/tex]
Substitute Equation 1 into Equation 2 and solve for [tex]a[/tex]:
[tex]\implies a+3(3a)=10[/tex]
[tex]\implies a+9a=10[/tex]
[tex]\implies 10a=10[/tex]
[tex]\implies a=1[/tex]
Substitute found value of [tex]a[/tex] into Equation 1 and solve for [tex]d[/tex]:
[tex]\implies 3(1)=d[/tex]
[tex]\implies d=3[/tex]
Finally, substitute found values of [tex]a[/tex] and [tex]d[/tex] into the general form of the arithmetic sequence:
[tex]\implies a_n=1+(n-1)3[/tex]
[tex]\implies a_n=1+3n-3[/tex]
[tex]\implies a_n=3n-2[/tex]
What are the coordinates of the focus of the parabola?
y=−0.25x2+6
Translate to an equation and solve the following. The quotient of k and 22 is -66. What is k
Answer:
Below.
Step-by-step explanation:
k / 22 = -66
k = 22*-66
= -1452.
1. What is the volume of this composite figure?
i6m
16 m
10 m
4 m
5 m
Answer:
560
Step-by-step explanation:
16 times 5 times 4=320
6 times 16 divide 2 then multiple 5
If h(x)=(0,-9),(5,2)(8,-3),(10,11) which set of ordered pairs represents the inverse of h(x)
Set of ordered pairs is {(-9,0),(2,5)(-3,8),(11,10)
What is ordered pair?
An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.
Given:
h(x)=(0,-9),(5,2)(8,-3),(10,11)
The inverse of anything interchange the position of variables or numbers or etc.
In ordered set the inverse will be x- coordinate become y- coordinate and y- coordinate become x- axis.
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Can someone please just check my answers over to make sure I got them right. Thank you so much!
Let me know if you need a close up on any of the pictures!
Answer: they are all correct congrats!
Step-by-step explanation:
What is the median of the data represented by the box plot?
Answer: 20
Step-by-step explanation:
Box plots give us the median just by looking at them. See attached.
Linda asked the students of her class their hockey scores and recorded the scores in the table shown below:
Hockey Scores
Score Number of Students
0 2
1 1
2 3
3 6
4 2
5 3
6 2
Based on the table, what is the mean hockey score?
2.7
2.9
3.2
5.2
Answer:
C) 3.2
Step-by-step explanation:
[tex]\text{Mean}=\frac{2(0)+1(1)+3(2)+6(3)+2(4)+3(5)+2(6)}{19}\approx3.2[/tex]
Answer:
2.7
Step-by-step explanation:
the hockey score is 2.7
Which of the following statements is true?
A. The experimental probability of an outcome is always the same as the theoretical probability of the outcome
B. The experimental probability of an outcome is never the same as the theoretical probability of the outcome.
C. As the number of trials of a random process decreases, the experimental probability of an outcome approaches the theoretical probability of the outcome
D. As the number of trials of a random process increases, the experimental probability of an outcome approaches the theoretical probability of the outcome
Answer:
B
Step-by-step explanation:
first of all articles are perfect and there is . sign at the last of the sentence
A triangle has a base of 4 m and a height of 3 m.
What is the area of the triangle?
Enter your answer in the box.
m²
Answer:
Area of the triangle is 6
Step-by-step explanation:
The formula for the area of a triangle is the base x height / 2. This means we can just plug in the variables and solve
A = b x h/2
A= 4 x 3/2
A= 12/2
A= 6
Answer: 6
Step-by-step explanation:
PLEASE HELP ME
Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level a.
n=11, a = 0.01
A r=+0.735
B r=+0.602
C r= 0.765
D r= 0.735
simplify. 5ab/15a+10a²
Please help me. I don’t understand at all.
Answer:
Option 2
Step-by-step explanation:
Evaluating the options :
Option 1
2 |x - 5| - 4 < -82 |x - 5| < -4|x - 5| < -2Empty set as modulus cannot be less than 0Option 2
|2x - 1| - 7 < -6|2x - 1| < 1x < 1There is a solution set other than empty setOption 2 is the right answer.
On his third math quiz of the semester, Cooper answered 28 questions correctly and got 7 wrong. What is the ratio of the number of questions he got right on the quiz to the total number of questions?
Step-by-step explanation:
Given that Cooper answered 28 questions correctly and 7 incorrect answers, If the total number of questions is x,
let total number of questions be X,therefore X = 28+7
= 35
ratio of right answered questions to the total questions, R isR =
[tex] \frac{28}{35} [/tex]
=
[tex] \frac{4}{5} [/tex]
therefore, the ratio is 4:5
Find the HEIGHT of a cylinder if the volume is 160 and the radius is 4
Step-by-step explanation:
this is the answer
hope it help
Answer this volume based Question. I will make uh brainliest + 50 points
Answer:
[tex]\huge{\purple {r= 2\times\sqrt[3]3}}[/tex]
[tex]\huge 2\times \sqrt [3]3 = 2.88[/tex]
Step-by-step explanation:
For solid iron sphere:radius (r) = 2 cm (Given)Formula for [tex]V_{sphere} [/tex] is given as:[tex]V_{sphere} =\frac{4}{3}\pi r^3[/tex][tex]\implies V_{sphere} =\frac{4}{3}\pi (2)^3[/tex][tex]\implies V_{sphere} =\frac{32}{3}\pi \:cm^3[/tex]For cone:r : h = 3 : 4 (Given)Let r = 3x & h = 4xFormula for [tex]V_{cone} [/tex] is given as:[tex]V_{cone} =\frac{1}{3}\pi r^2h[/tex][tex]\implies V_{cone} =\frac{1}{3}\pi (3x)^2(4x)[/tex][tex]\implies V_{cone} =\frac{1}{3}\pi (36x^3)[/tex][tex]\implies V_{cone} =12\pi x^3\: cm^3[/tex]It is given that: iron sphere is melted and recasted in a solid right circular cone of same volume[tex]\implies V_{cone} = V_{sphere}[/tex][tex]\implies 12\cancel{\pi} x^3= \frac{32}{3}\cancel{\pi}[/tex][tex]\implies 12x^3= \frac{32}{3}[/tex][tex]\implies x^3= \frac{32}{36}[/tex][tex]\implies x^3= \frac{8}{9}[/tex][tex]\implies x= \sqrt[3]{\frac{8}{3^2}}[/tex][tex]\implies x={\frac{2}{ \sqrt[3]{3^2}}}[/tex][tex]\because r = 3x [/tex][tex]\implies r=3\times {\frac{2}{ \sqrt[3]{3^2}}}[/tex][tex]\implies r=3\times 2(3)^{-\frac{2}{3}}[/tex][tex]\implies r= 2\times (3)^{1-\frac{2}{3}}[/tex][tex]\implies r= 2\times (3)^{\frac{1}{3}}[/tex][tex]\implies \huge{\purple {r= 2\times\sqrt[3]3}}[/tex]Assuming log on both sides, we find:[tex]log r = log (2\times \sqrt [3]3)[/tex][tex]log r = log (2\times 3^{\frac{1}{3}})[/tex][tex]log r = log 2+ log 3^{\frac{1}{3}}[/tex][tex]log r = log 2+ \frac{1}{3}log 3[/tex][tex]log r = 0.4600704139[/tex]Taking antilog on both sides, we find:[tex]antilog(log r )= antilog(0.4600704139)[/tex][tex]\implies r = 2.8844991406[/tex][tex]\implies \huge \red{r = 2.88\: cm}[/tex][tex]\implies 2\times \sqrt [3]3 = 2.88[/tex]Stan pays a 10% deposit to put a pool table on lay-by.
If the pool table costs $1590, how much does he have left to pay?
Answer:
$1431
Step-by-step explanation:
If Stan pays a 10% deposit, he pays $159. 10% of $1590 is simply 0.1 * 1590 = 159. Assuming this is the only amount he pays, he then simply needs to pay the full price minus $159. We can find this by simply subtracting 159 from 1590 to get 1431. Stan still needs to pay $1431.
Triangle ABC is congruent to triangle DEF. Angle B is a right angle, and m∠C = 34°. What is m∠D?
56°
34°
64°
46°
Answer: 56°
Step-by-step explanation:
4x+3y=6
-4x+2y=14
Solve the system of equations.
A. x= 1/2, y=3
B. x=3, y =1/2
C. x=4, y = -3/2
D. x=-3/2, y = 4
Answer:
D
Step-by-step explanation:
4x + 3y = 6
-4x + 2y = 14
0 + 5y / 5 = 20/ 5 = 4 = y
4x + 3(4) = 6
4x + 12 - 12 = 6 - 12
4x / 4 = -6 / 4 = -3 / 2 =x
The area of a triangle is 7.5 . The base of the triangle is 5 cm .what is the height of this triangle.
Answer:
3 cm
Step-by-step explanation:
Formula :
Area = 1/2 x Base x HeightGiven :
Area = 7.5 cmBase = 5 cmSolving :
Height = 7.5/5 x 2Height = 3 cmSix people want to share five boxes of raisins. How many boxes of raisins will each person get?
5/6 or 0.83 boxes of raisins
Find X
A = 49
B = 27
C = 98
D = 76
Answer:
C=98°
Step-by-step explanation:
125°- 27°
=98°
Use the graph to determine the function’s DOMAIN and RANGE
Answer:
Domain = x ≥ 0
Range = f( x ) ≥ 1
Step-by-step explanation:
The graph starts from 0 in the x - axis and 1 in the y hence the given domain and range.
A plumber fixed a leaky sink and charged $55 for parts and $45 per hour for labor. If the total bill was $190, how many hours did the plumber spend fixing the sink?
The plumber spend 3 hours to fixing the sink if the plumber fixed a leaky sink and charged $55 for parts and $45 per hour for labour.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the plumber spend x hours to fixing the sink.
Then we can frame a linear equation in one variable:
55 + 45x = 190
45x = 135
x = 3 hours
Thus, the plumber spend 3 hours to fixing the sink if the plumber fixed a leaky sink and charged $55 for parts and $45 per hour for labour.
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I really need a help, help help helppp Helpppppp please
Answer:
I am clueless. Take care though.
Step-by-step explanation:
use a formula to find the surface area of the cylinder use 3.14 for pi
Answer:
376.8 cm²
Step-by-step explanation:
Given:
Radius of circular base: 4 cmHeight of cylinder: 11 cmSurface area = 2πrh + 2πr²
[Where "r" and "h" represents the radius and the height respectively]
Let's substitute the height and the radius in the formula and simplify it.
[tex]\implies 2\pi rh + 2\pi ^{2}[/tex]
[tex]\implies 2\pi (4)(11) + 2\pi (4)^{2}[/tex]
[tex]\implies 2\pi (44) + 2\pi (16)[/tex]
[tex]\implies 88\pi + 32\pi[/tex]
We can factor π out of the expression. Therefore, we get:
[tex]\implies 88\pi + 32\pi[/tex]
[tex]\implies \pi (88 + 32)[/tex]
Now, simplify the expression inside the parentheses.
[tex]\implies \pi (88 + 32)[/tex]
[tex]\implies \pi (120)[/tex]
The value of π, we are given, is 3.14. When substituted, we get:
[tex]\implies \pi (120)[/tex]
[tex]\implies 3.14(120) = 31.4(12) = \boxed{376.8 \ \text{cm}^{2} }[/tex]
Therefore, the surface area of the cylinder is 376.8 cm².
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A quarterback is standing on the football field preparing to throw a pass. His receiver is standing 20 yards down the field and 15 yards to the quarterback’s left. The quarterback throws the ball at a velocity of 60 mph towards the receiver at an upward angle of 30° (see the following figure). Write the initial velocity vector of the ball ⃑ , in component form.
Answer:
I did the work and uploaded the answer as a picture for you
I hope it was helpful!!
Step-by-step explanation:
solve the equation 1/x+3/x=16
[tex] \frac{1}{x} + \frac{3}{x} = 16 \\ [/tex]
[tex] \frac{4}{x} = 16 \\ [/tex]
[tex]16x = 4[/tex]
[tex]x = \frac{4}{16} \\ [/tex]
[tex]x = \frac{1}{4} \\ [/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ \frac{1}{x} + \frac{3}{x} = 16} \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ \frac{4}{x } = 16 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ x = 16 \times 4 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \implies \orange{\underline{\boxed{\large\frak \pink{x = 64 }}}} \\ \end{gathered}[/tex]
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1: solve the following pair of equations simultaneously using the method stated.
a) 2x-3y = 5 and 3x+4y = 6 (elimination method)
b) 4x-y = 9 and 3xy = -6 (substitution method)
c) y=x^2 - 2x and y = 2x -3 (substitution method)
Answer:
Your answers are below ↓
Step-by-step explanation:
Given ↓
A) 2x-3y = 5 and 3x+4y = 6 ( The method this has to be solved in is the elimination method. )
Now using these,
(1)×3 - (2)×2 = 6x + 9y - 6x - 8y = 15 - 12
therefore,
y = 3
putting the value of y in eqn. (1)
2x + 6 = 5
therefore,
x = -1/2
B) y=x^2 - 2x and y = 2x -3 ( The method this has to be solved in is the substitution method. )
Reduce the greatest common factor on both sides of the equation:
[tex]\left \{ {{4x-y=9} \atop {xy=-2}} \right.[/tex]
Rearrange like terms to the same side of the equation:
[tex]\left \{ {{-y=9-4x} \atop {xy=-2}} \right.[/tex]
Divide both sides of the equation by the coefficient of the variable:
[tex]\left \{ {{y=-9+4x} \atop {xy=-2}} \right.[/tex]
Substitute the unknown quantity into the elimination:
[tex]x(-9+4x)=-2[/tex]
Apply Multiplication Distribution Law:
[tex]-9x+4x^2=-2[/tex]
Reorder the equation:
[tex]4x^2-9x=-2[/tex]
Divide the equation by the coefficient of the quadratic term:
[tex]\frac{1}{4}(4x^2)+\frac{1}{4}(-9x)=\frac{1}{4}*(-2)\\[/tex]
Calculate:
[tex]x^2-\frac{9x}{4}=-\frac{1}{2}[/tex]
Add one term in order to complete the square:
[tex]x^2-\frac{9x}{4}+(\frac{9}{4}*\frac{1}{2})^2=-\frac{1}{2}+(\frac{9}{4}*\frac{1}{2})^2[/tex]
Calculate:
[tex]x^2-\frac{9x}{4}+(\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]
Factor the expression using [tex]a^2$\pm$2ab+b^2=(a$\pm$b)^2[/tex]:
[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]
Simplify using exponent rule with the same exponent rule: [tex](ab)^n=a^n*b^n[/tex]
[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +\frac{9^2}{8^2}[/tex]
Calculate the power:
[tex](x-\frac{9}{8} )^2=-\frac{1}{2}+\frac{81}{64}[/tex]
Find common denominator and write the numerators above the denominator:
[tex](x-\frac{9}{8} )^2=\frac{-32+81}{64}[/tex]
Calculate the first two terms:
[tex](x-\frac{9}{8} )^2=\frac{49}{64}[/tex]
Rewrite as a system of equations:
[tex]x-\frac{9}{8} =\sqrt{\frac{49}{64} }[/tex] or [tex]x-\frac{9}{8} =-\sqrt{\frac{49}{64} }[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]x=\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]
Rewrite the expression using [tex]\sqrt[n]{ab} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:
[tex]x=\frac{\sqrt{49} }{\sqrt{64} } +\frac{9}{8}[/tex]
Factor and rewrite the radicand in exponential form:
[tex]x=\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]
Simplify the radical expression:
[tex]x=\frac{7}{8} +\frac{9}{8}[/tex]
Write the numerators over the common denominator:
[tex]x=\frac{7+9}{8}[/tex]
Calculate the first two terms:
[tex]x=\frac{16}{8}[/tex]
Reduce fraction to the lowest term by canceling the greatest common factor:
[tex]x=2[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]x=-\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]
Rewrite the expression using [tex]\sqrt[n]{a} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:
[tex]x=-\frac{\sqrt{49} }{\sqrt{64} }+\frac{9}{8}[/tex]
Factor and rewrite the radicand in exponential form:
[tex]x=-\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]
Simplify the radical expression:
[tex]x=-\frac{7}{8} +\frac{9}{8}[/tex]
Write the numerators over common denominator:
[tex]x=\frac{-7+9}{8}[/tex]
Calculate the first two terms:
[tex]x=\frac{2}{8}[/tex]
Reduce fraction to the lowest term by canceling the greatest common factor:
[tex]x=\frac{1}{4}[/tex]
Find the union of solutions:
[tex]x=2[/tex] or [tex]x=\frac{1}{4}[/tex]
Substitute the unknown quantity into the elimination:
[tex]y=-9+4*2[/tex]
Calculate the first two terms:
[tex]y=-9+8[/tex]
Calculate the first two terms:
[tex]y=-1[/tex]
Substitute the unknown quantity into the elimination:
[tex]y=-9+4*\frac{1}{4 }[/tex]
Reduce the expression to the lowest term:
[tex]y=-9+1[/tex]
Calculate the first two terms:
[tex]y=-8[/tex]
Write the solution set of equations:
[tex]\left \{ {{x=2} \atop {y=-1}} \right.[/tex] or [tex]\left \{ {{x=\frac{1}{4} } \atop {y=-8}} \right.[/tex] -------> Answer
C) y=x^2 - 2x and y = 2x -3 ( This method this has to be solved in is the substitution method. )
Step 1: We start off by Isolating y in y = 2x - 3
y=2x-3 ----------> ( Simplify )
y+(-y)=2x-3+(-y) ---- > ( Add (-y)on both sides)
0=-3+2x-y
y/1 = 2x-3/1 --------> (Divide through by 1)
y = 2x - 3
We substitute the resulting values of y = 2x - 3 and y = x^2 - 2x
(2 * x - 3) = x^2 - 2x ⇒ 2x -3 = x^2 - 2x ----> ↓
(Substituting 2x - 3 for y in y = x^2 -2x )
Next: Solve (2x - 3 = x^2 - 2x) for x using the quadratic formular method
2x - 3 = x^2 - 2x
x = -b±b^2-4ac/2a Step 1: We use the quadratic formula with ↓
a = -1,b=4,c= - 3
x = -4±(4)^2-4(-1)(-3)/2(-1) Step 2: Substitute the values into the Quadratic Formular
x = -4± 4/ - 2 x = 1 or x = 3 Step 3: Simplify the Expression & Separate Roots
x = 1 or x = 3 ------- ANSWER
Substitute 1 in for x in y = 2x - 3 then solve for y
y = 2x - 3
y = 2 · (1) - 3 (Substituting)
y = -1 (Simplify)
Substitute 3 for in y = 2x - 3 then solve for y
y = 2x - 3
y = 2 · (3) - 3 (Substituting)
y = 3 (Simplify)
Therefore, the final solutions for y = x^2 -2x; y = 2x - 3 are
x₁ = 1, y₁ = -1
x₂ = 3, y₂ = 3