There is sufficient evidence to conclude that, the percentage of the families who own a pet is different than 60%.
What are null hypotheses and alternative hypotheses?In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
It Is said That 60% of families own a pet.
Of a sample of 95 families, 70 owned pets.
Whether the percent of families who own pets is different than 60%.
Let P be a proportion of the family who owns pets
Then by the test, we have
H₀: P = 0.60
Hₐ: P ≠ 60
Then by the test statistic, we have
[tex]z_o = \dfrac{\bar{P} - P_o}{\sqrt{\dfrac{P_o(1 - P_o)}{n}}}[/tex]
Where
[tex]\bar P[/tex] = sample proportion
P₀ = hypothesis proporion
n = sample size
Then we have
[tex]\bar P[/tex] = x/n
[tex]\bar P[/tex] = 70/95
[tex]\bar P[/tex] = 0.74
Then the test statistic will be
[tex]z_o = \dfrac{0.74-0.60}{\sqrt{\dfrac{0.60(1-0.60)}{95}}}[/tex]
z₀ = 2.785
Then the critical region will be
Critical value = ± [tex]z_{\alpha /2}[/tex]
α = 0.05
α/2 = 0.025
Then we have
z₀.₀₂₅ = 1.96
Then the critical value will be
Critical value = ± 1.96
We reject if [tex]|z_o| > |z_{\alpha /2}|[/tex]
We have
[tex]|z_o| > |z_{\alpha /2}|\\[/tex]
2.79 > 1.96
We reject the null hypothesis at a 5% significance level.
There is sufficient evidence to conclude that, the percentage of the families who own a pet is different than 60%.
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A triangular brace has an angle measure of 30 degrees, with a side opposite
this angle measuring 8 inches. The base of the triangular brace, which is
adjacent to the given angle measure, is 11 inches in length. Which of the
following statements is correct?
A. There is not a solution for the angle opposite the side measuring
11 inches.
B. The angle opposite the side measuring 11 inches has one solution
of approximately 43 degrees.
C. The angle opposite the side measuring 11 inches has one solution
of approximately 62 degrees.
D. The angle opposite the side measuring 11 inches, has two
solutions of approximately 43 degrees and 137 degrees.
The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Using the sine rule, the measurement of the angle of opposite the side measuring 11 inches can be done. Therefore, the measure can be written as,
8/ Sin(30°) = 11/ Sin(θ)
Sin(θ) = [11 × Sin(30°)]/8
Sin(θ) = 0.6875
θ = Sin⁻¹ (0.6875)
θ = 43.4325° ≈ 43°
Hence, The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.
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Maddie's backyard is 25 meters by 25 meters. She wants to put a square cement patio in her backyard. She does not want the patio to be as
large as the yard. Let A be the area of the patio, in square meters.
Which inequality represents the possible length of the patio?
A. √A> 25
B. √A < 25
C. √A> 625
D. √A < 625
The inequality that represents the possible length of the patio is √A < 625.
How to represent an inequality?Maddie's backyard is 25 meters by 25 meters.
Therefore,
area of the backyard = 25 × 25 = 625 m²
Hence,
She wants to put a square cement patio in her backyard.
A = area of the patio, in square meters.
Hence,
area of the backyard = 625 m²
Therefore, the inequality that represents the possible length of the patio is √A < 625.
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Leg = 11 meters, Hypotenuse = 15 meters
Answer:
10.19
Step-by-step explanation:
Use the Pythagorean Theorem:
[tex]a^{2}+b^{2}=c^{2}[/tex]
Substitute the numbers given:
[tex]11^{2}+b^{2}=15^{2}[/tex]
[tex]121+b^{2}=225\\ b^{2}=225-121\\ b^{2}=104\\ \sqrt b^{2}= \sqrt{104} \\ b=10.19[/tex]
What is the surface area in square inches of a basketball that has a diameter of 9 inches
if its diameter is 9, that means its radius is half that, or 4.5.
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4.5 \end{cases}\implies \begin{array}{llll} SA=4\pi (4.5)^2\implies SA=81\pi \\\\\\ SA\approx 254.47~in^2 \end{array}[/tex]
The surface area of the basketball with diameter of 9 in will be 254.34 in².
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given that, a basketball has a diameter of 9 inches we need to find its surface area,
Since, the basketball is in the shape of the sphere and the surface area of the sphere = 4π×radius²
Therefore, the surface area of the basketball =
= 4×3.14×(9/2)²
= 4×3.14×4.5×4.5
= 254.34 in²
Hence the surface area of the basketball with diameter of 9 in will be 254.34 in².
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A number, increased by four times the number, is 35. Find the number.
How do I simplify this (w²+6)-(3w² + 4w)
Answer:
6-2w(w+2)
Step-by-step explanation:
6-2w²+4w
6-2w(w+2)
The area of the garden was 2 2/5yd2. if the lrngth is 1 1/2 yd, find the width
Help!! I don’t understand how to answer this
Answer:
The answer is option A
Step-by-step explanation:
The solution is in the image
Answer all of these for brainliest?
Answer:
always, always, never, always, always
Step-by-step explanation: brainliest?
Roll of the Dice Are the chances of rolling a 3 with one die the same as the chances of rolling a total of 6 with two dice? If not, which has the higher probability ?
Answer:
The probability is the same.
Step-by-step explanation:
The chances of rolling a 3 with one die is 1/6. The chances of rolling a 6 with 2 dice is 2/12.
1. The area of a rectangular carpet is X² + X - 2. HINT: Area = length X breadth
a). if X is a whole number, use factorization to find the length and the breadth of the carpet in terms of X.
b). if X = 2 m, find the actual dimensions of the carpet.
c). it costs R50 per square metre to make such this carpet. how much will it cost to manufacture 5 carpets?
Answer:
a) Length= (x+2) and breadth=(x-1) b) 4 m^2 c) R1000
Answer:
answers in photo / +explanation
Step-by-step explanation:
a)
length: x+2
width/breadth: x-1
b)
length: 4m
width/breadth: 1m
area: 4m²
c)
R1000
I need help ASAP pleaseee!!
Answer:
Vertex(1,7)
Vertex form: [tex]f(x)=-2\left(x-1\right)^2+7[/tex]
Step-by-step explanation:
Vertex form equations for x is [tex]v=-\frac{b}{2a}[/tex]
which the vertex here is
[tex]-\frac{4}{2\left(-2\right)}[/tex]
->
x = 1, plugin to find y, y = 7
On Monday the temperature was -7 degrees Fahrenheit in Akron Ohio on Tuesday the temperature was colder than Monday what is a possible temperature in degrees Fahrenheit for Tuesday
the degrees Fahrenheit is -9
It costs $363 to make 90 bags of cotton candy and $440 to make 200 bags of cotton candy.
a) find the cost equation.
Answer:
363=90bags
then you look into it and say
440=200bags
What is the product of 3x(x²+4)?
Ox²+3x+4
O 3x³ +4
O 3x³ + 12x
O 3x² + 12x
Answer:
3x³ + 12x
Step-by-step explanation:
3x(x² + 4)
3x³ + 12x
Which of the following is the solution set of 6x + 5 = -29?
O {-4}
O {-17/3)
O (17/3)
Answer:
-[tex]\frac{17}{3}[/tex]
Step-by-step explanation:
please help, 30 points, will give brainly
Answer:
∠ABC = 39°
Step-by-step explanation:
Since ED bisects ∠CBD :
∠EBD = ∠CBE = 30°
Now, ∠ABD = ∠ABC + ∠CBE + ∠EBD = 99°
Solving :
99° = ∠ABC + 30° + 30°∠ABC = 99° - 60°∠ABC = 39°What is the value of x in the equation shown Below?2(x+4)-4x=10x-4
Answer: 1
Step-by-step explanation:
During a game of golf, Kayley hits her ball out of a sand trap. The equation h = t? + 4t -
21 models the height of the golf ball in feet in relation to the number of t seconds since it was hit. Kayley solved the quadratic by factoring: .
a. How many seconds does it take for her ball to reach the green?
b. How do we know the 2nd value isn't also a solution?
A quadratic equation is in the form of ax²+bx+c. It took 3seconds for the golf ball to reach the green.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
A.) The time that the ball takes to reach the green can be found by equation the equation against zero. As the ball will have 0 height when it will be on the green,
t²+4t-21=0
t²+7t-3t-21=0
t(t+7)-3(t+7)=0
(t+7)(t-3)=0
t = -7, 3
Hence, it took 3seconds for the golf ball to reach the green.
B.) Since the time can not be negative the second value is wrong.
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25% of 80 help nowww
80 * 25 /100 = 20 .........
Answer:
20
Step-by-step explanation:
25% of 80
to turn 25% into a decimal, 25 / 100 = 0.25
multiply 80 by 0.25, 80 x 0.25 = 20
The equation y= -3x7 describes a parabola. Which way does the parabola
open?
Answer:
See below
Step-by-step explanation:
y = -3 x^7 is NOT a parabola.... y = -3x^2 IS a parabola that opens downward due to the negative coefficient (-3)
Can someone please help? This is sooooooooo hard!!! :(
Answer:
BD = BE
Step-by-step explanation:
If BD = BE , angle BED = angle BDE.
Because they are in a same triangle.
And also they are congruent.
factor completely 4a^3b^5-18a^2b^3+8a^3b^3
The factored expression of the expression 4a^3b^5 - 18a^2b^3 + 8a^3b^3 is 2a^2b^3(2ab^3 - 9 + 4a)
How to factor the expression?The expression is give as:
4a^3b^5 - 18a^2b^3 + 8a^3b^3
Factor out 2
2(2a^3b^5 - 9a^2b^3 + 4a^3b^3)
Factor out a^2b^3
2a^2b^3(2ab^3 - 9 + 4a)
Hence, the factored expression of the expression 4a^3b^5 - 18a^2b^3 + 8a^3b^3 is 2a^2b^3(2ab^3 - 9 + 4a)
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The Perimeter of the triangle is 141cm work out value of p
By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.
How to determine the lengths of the side of a triangle
The three sides of a triangle are consecutive if and only if they are represented by three consecutive natural numbers. The perimeter is the sum of the three side lengths, whose formula is presented below:
x + (x + 1) + (x + 2) = 141
3 · x + 3 = 141
3 · (x + 1) = 141
x + 1 = 47
x = 46
By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.
Remark
The statement is complete, the correct statement is the following:
The triangle has three consecutive sides and its perimeter is 141 centimeters. Work out the value of each side.
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HELP ASAP
Find the volume of the sphere. Round your answer to the nearest tenth.
Answer:
V = 3053.63 mm^3
Step-by-step explanation:
radius : 9mm
V = 4/3 * pi * r^3
V = 4/3 * (3.1415926535898...) * 9^3
V = 3053.63 mm^3
Pls help I will give brainliest!!
Answer:
A. (-8, 0)
Step-by-step explanation:
The side of the line that is shaded contains the solutions to the inequality. (-8, 0) is in the shaded part of both graphs.
Also, 0 > -15 and 0 [tex]\geq[/tex] -9
I hope this helps :)
Define a quadrilateral.
please explain and help me pls
Answer:
A Quadrilateral is a 4 sided figure. In other words any shape that has 4 sides is a quadrilateral for example square, rectangle, trapezium etc
Step-by-step explanation:
The value of x is 50% more than the value of t.
the value of y is 10% less than the value of w.
x = y
work out t/w
Answer:
To hard sorry
Step-by-step explanation:
What is the volume of a cylinder of radius 3.5m and height 12m ?
Answer:
462
Step-by-step explanation:
Base=π × r²
=> π × 3.5²
=>38.48
Volume:
Base times height
=>38.48 x 12
=>461.81
Answer:
426m²Step-by-step explanation:
Given ;
radius = 3.5m , hieght = 12mVolume of cylinder = π2²h
22/7 × ( 3.5 )² × 1222/7 × ( 7/2 )² × 12 22/7 × 7/2 × 7/2 × 12462m²Volume of the cylinder is 426m².
Write the slope intercept form of each equation of the line. Use a fraction for slope if needed.
Parallel to y=−x+5, through (2, 4)
Answer:
y=-x+6
Step-by-step explanation:
Start by graphing y=-x+5. Then mark the point (2,4) for easier reference. A parallel line just has the same slope, so if you make another line with the same slope, and change the y-intercept until the line goes through (2,4), you will have the answer.