Answer:
The possible number of goats is 6 and the possible number of chicken is 24
Step-by-step explanation:
Let
chicken=c
Goat=g
the number of chickens could be four times the number of goats
c=4g
Total number of animals=30
c+g=30
Recall, c=4g
So,
c+g=30
4g+g=30
5g=30
Divide both sides by 5
5g/5=30/5
g=6
Recall,
c+g=30
c+6=30
c=30-6
=24
c=24
The possible number of goats is 6 and the possible number of chicken is 24 making a total of 30 animals
You are testing the claim that the mean GPA of night students is greater than the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.36 with a standard deviation of 0.96 You sample 60 day students, and the sample mean GPA is 2.19 with a standard deviation of 0.66 Calculate the test statistic, rounded to 2 decimal places
Answer:
Z = 0.87
Explanation:
Given the following data;
Sample 1:
n1 = 30
Mean, X = 2.36
Standard deviation, Ox = 0.96
Sample 2:
n2 = 60
Mean, Y = 2.19
Standard deviation, Oy = 0.66
The formula for test statistics for two population is;
[tex]Z = \frac{X-Y}{\sqrt{(\frac{Ox^2} {n_1} } +\frac{Oy^2}{n_2} )}}[/tex]
Substituting the values, we have;
[tex]Z = \frac{2.36-2.19}{\sqrt{(\frac{0.96^2} {30} +\frac{0.66^2}{60} )}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{(\frac{0.9216} {30} +\frac{0.4356}{60} )}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{(0.03072 +0.00726)}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{0.03798}}[/tex]
[tex]Z = \frac{0.17}{0.19488}[/tex]
Z = 0.8723
The test statistics to 2 d.p is 0.87
Therefore, Z = 0.87
Sadie simplified the expression √54a^7b^3, where a>=0, as shown: √54a^7b^3= √3^2•6•a^2•a^5•b^2•b=3ab √6a^5b
Answer:
We are to find the error made by Sadie and then find the correct simplification.
The error Sadie made is that she wrote [tex]a^7[/tex] as [tex]a^2 * a^5[/tex] instead of [tex]a^6 * a[/tex].
The square root of [tex]a^6[/tex] is [tex]a^3[/tex] and so she could have further simplified.
The correct simplification is shown below:
[tex]\sqrt{54a^7b^3} = \sqrt{2 * 3 * 3 * 3 * a^6 * a * b^2 * b} \\ \\= \sqrt{3^2 * a^6 * b^2 * 6 * a * b} \\\\= 3a^3b\sqrt{6ab}[/tex]
Answer:
We are to find the error made by Sadie and then find the correct simplification.
The error Sadie made is that she wrote as instead of .
The square root of is and so she could have further simplified.
Step-by-step explanation:
On edge2021
Helen has three lessons in the morning.
Lesson 1 starts at 0910.
Each lesson is 60 minutes long.
There is a 15-minute break between lessons 2 and 3.
At what time does lesson 3 end?
Answer:
1225
Step-by-step explanation:
Please see attached picture for full solution.
determine (a) the volume and (b) the surface area of the three-dimensional figure. when appropriate, use the pi key on your calculator.
Step-by-step explanation:
The figure above is a cube since all it's sides are equal
Volume of a cube = l³
where l is the length of one side
From the question
l = 5
So the volume of the cube is
Volume = 5³
Volume = 125 cm³Surface area of a cube = l²
= 5²
Surface area = 25cm²Hope this helps you
Ahmed earns $1.50 for every video game he sells. When he sells one carton of 30 video game, he earns an additional $10. What is the minimum number of video games he has to sell in order to earn $450?
Answer:
Step-by-step explanation:
1.50x + 10[x/30] >= 450
x >= 246.3
check:
1.50*246 + 10*8 = 449
$450
Which equation correctly represents the line in slope-intercept form? A. y = -1/4x-6 B.y=1/4x-6 C.y=-4x+6 D.y=4x+6
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 6) and (x₂, y₂ ) = (8, - 4) ← 2 points on the line
m = [tex]\frac{-4+6}{8-0}[/tex] = [tex]\frac{2}{8}[/tex] = [tex]\frac{1}{4}[/tex]
The line crosses the y- axis at (0, - 6 ) ⇒ c = - 6
y = [tex]\frac{1}{4}[/tex] x - 6 → B
Jason was surveying students about their use of the new software lab in a school. Which question in the survey is a statistical question? a. How many hours do you spend developing software in the software lab? b. What is the number of learning stations at the software lab? c. Where is the software lab located in the school? d. What are the times the software lab is open? helpppp pls i will give u 20 points
Answer:
I think it's a
Step-by-step explanation:
Because this would ddetermine if the software lab is successfull working.
On average, the post office processes 45.6 letters every hour. How many letters can the office process during the 9 hours it is open? 410.4 4104 405 None of the above During Christmas, the post office opens 12 hours a day. Compared to usual days (9 hours), how many more letters can the post office process? 410.4 136.8 547.2 None of the above
Answer:
410.4
136.8
Step-by-step explanation:
Because the post office processes 45.6 letters every hour and is open 9 days an hour, it processes 45.6*9, or 410.4 letters per day. Because it is open on Christmas for 3 hours more than normal days(12-9), it produces 45.6*3, or 136.8 more letters on Christmas.
Hope it helps <3
Answer:
A. 410.4 letters
B. 136.8 more letters
Step-by-step explanation:
1.
We know that the post office processes 45.6 letters per hour. If we want to know how many letters they process in 9 hours, we can multiply 45.6 and 9.
45.6 * 9
Multiply
410.4
The post office can process 410.4 letters in 9 hours, therefore A is correct.
2.
The post office still process 45.6 letters per hour, but they are open for 12 hours. First, multiply 12 and 45.6.
12 * 45.6
547.2
We are asked to find how many more letters they can process. We need to find the difference between the letters they normally process and the letters they process on Christmas.
Christmas - normal
They process 547.2 on Christmas and 410.4 normally.
547.2 - 410.4
136.8
They process 136.8 more letters on Christmas. Therefore, choice B is correct. Thank
I missed the class on rationalising denominators.
Can anyone please help me with these three maths along with explanations.
Answer:
[tex] 4\sqrt{3} [/tex]
[tex] \dfrac{5 - \sqrt{3}}{11} [/tex]
[tex] \dfrac{11(3 + \sqrt{5})}{8} [/tex]
Step-by-step explanation:
If you have a simple square root in the denominator, multiply the fraction by a fraction that is the root over the root.
[tex] \dfrac{12}{\sqrt{3}} = [/tex]
[tex] = \dfrac{12}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}} [/tex]
[tex]= \dfrac{12\sqrt{3}}{\sqrt{3}\sqrt{3}}[/tex]
[tex] = \dfrac{12\sqrt{3}}{3} [/tex]
[tex] = 4\sqrt{3} [/tex]
If you have a denominator consisting of a rational number plus a root, multiply the fraction by a fraction that is the denominator over the denominator in which you change only the sign outside the root.
[tex] \dfrac{2}{5 + \sqrt{3}} = [/tex]
[tex] = \dfrac{2}{5 + \sqrt{3}} \times \dfrac{5 - \sqrt{3}}{5 - \sqrt{3}} [/tex]
[tex] = \dfrac{2(5 - \sqrt{3})}{(5 + \sqrt{3})(5 - \sqrt{3})} [/tex]
[tex] = \dfrac{2(5 - \sqrt{3})}{25 - 3} [/tex]
[tex] = \dfrac{2(5 - \sqrt{3})}{22} [/tex]
[tex] = \dfrac{5 - \sqrt{3}}{11} [/tex]
[tex] \dfrac{11}{6 - 2\sqrt{5}} = [/tex]
[tex] = \dfrac{11}{6 - 2\sqrt{5}} \times \dfrac{6 + 2\sqrt{5}}{6 + 2\sqrt{5}} [/tex]
[tex] = \dfrac{11(6 + 2\sqrt{5})}{(6 - 2\sqrt{5})(6 + 2\sqrt{5})} [/tex]
[tex]= \dfrac{22(3 + \sqrt{5})}{36 - 4 \times 5}[/tex]
[tex] = \dfrac{22(3 + \sqrt{5})}{36 - 20} [/tex]
[tex] = \dfrac{22(3 + \sqrt{5})}{16} [/tex]
[tex] = \dfrac{11(3 + \sqrt{5})}{8} [/tex]
Answer:
see attached
Step-by-step explanation:
A right triangle has legs of 5 ft and 6 ft. What is the length of the hypotenuse? _____ ft. A. 7.8 B. 3.3 C. 11.0 D. 1.0
Answer:
7.8Option A is the correct option.
Step-by-step explanation:
Base (b) = 5 ft
Perpendicular (P) = 6 ft
Hypotenuse (h) = ?
Now,
Using Pythagoras theorem,
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {h}^{2} = {(6)}^{2} + {(5)}^{2} [/tex]
[tex] {h}^{2} = 36 + 25[/tex]
[tex] {h}^{2} = 61[/tex]
[tex]h = \sqrt{61} [/tex]
[tex]h = 7.8 \: ft[/tex]
Hope this helps...
Good luck on your assignment
Answer:
a. 7.8
Step-by-step explanation:
I need the answer to this question please! :)
Answer: .28
Step-by-step explanation:
.3+.42= .72
1-.72=.28
Answer:
0.28
Step-by-step explanation:
The sum of a list of probabilities = 1
Sum of given probabilities = 0.72
So, probability of getting pasta = 1-0.72 = 0.28
Hope this helps
On an uphill hike Ted climbs at 3mph. Going back down, he runs at 5mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike? if possible, I would like a clear equation.
Answer:
He hiked 10 miles.
Step-by-step explanation:
rate x time = distance
The distance up and the distance down are equal
3 mi/1 hr x (h hours + 2/3 hr) = 5 mi/1 hr x h hours
3h + 2 = 5h
2 = 2h
h = 1 hour
3mi/hr x 1 2/3 hr = 5 miles
5 mi/hr x 1 hr = 5 miles
Write an equation that represents your total earnings based on the price of your item and how many you sell. my price of my item is 25 and spending limit was 200. PLEASE SOMEONE HELP ME OUT
Answer:
The data that we have is:
Price per item = $25
spending limit = $200
Now, if you sell x items, then your earnings will be:
E = $25*x
So if you sell two items, we have x = 2
E(2) = $25*2 = $50
But the maximum spending possible will be such that:
$25*x = $200
x = $200/$25 = 8
Then the equation is:
E(x) = $25*x
such that 0 ≤ x ≤ 8
Which means that you can sell any number of units between 0 and 8.
Given f(x) = log x and g(x) = -x + 1,
which is the graph of
(fog)(x)?
Answer:
the third graph is correct
Step-by-step explanation:
edge
the second part is x<1
Answer:
the third graph and the send part it is x<1
Step-by-step explanation:
a coat was marked down by 60 percent from its original price of $99 . including an 8% sale tax , what is the final cost of the coat?
Answer:
i think its 42.77... might be wrong tho
Step-by-step explanation:
being marked down by 60 percent means to multiply original number by 0.4
so we get 39.6
the multiply it by 1.08 to get 42.768
Answer:
See below.
Step-by-step explanation:
To find the marked down price, multiply the total by the percentage.
[tex]99*.6=59.4[/tex]
Next, subtract the amount from the total.
[tex]99-59.4=39.6[/tex]
Then, multiply to find the sales tax.
[tex]39.6*0.08=3.168[/tex]
[tex]39.6+3.168=42.768[/tex]
Answer: $42.77
Find the measure of one exterior angle for the following regular polygon.
Answer:
72º
Step-by-step explanation:
Hey there!
Well the interior of a pentagon's angle is 108º,
so we do,
180 - 108 = 72º
Hope this helps :)
Answer:
72°
Step-by-step explanation:
→ First find the measure of all interior angle, utilise the formula (n-2) × 180° where n is the number of sides
(n-2) × 180° ⇔ (5-2) × 180° ⇔ 3 × 180° ⇔ 540°
→ 540° is the total sum of the angles in the pentagon, divide this by 5 to get one of the interior angles
540° ÷ 5 = 108°
→ Now, remember the fact that 1 interior + 1 exterior angle = 180°
180 - ( 1 interior angle ) → 180 - (108) = 72°
1.
solve the
following
simultaneous equations graphically.
y = 8-x
y=x-2
Answer:
(5,3)
Step-by-step explanation:
Well to solve the following,
y = 8 - x
y = x - 2
Graphically.
We need to graph both equations,
Look at the image below ↓
By looking at the graph we can tell the intercept point is at (5,3).
Thus,
the solution is (5,3).
Hope this helps :)
is 4,8,10 pithogoreon triplet
Answer: No
Step-by-step explanation:
No, because 4^2 is 16, 8^2 is 64, 10^2 is 100 and 16+64 = 80 and 80≠100
Need help on these ASAP!!
Answer:
surface area of sphere = 615.44mm²
volume of sphere = 523.33mm³
Step-by-step explanation:
S.A = 4πr²
4 × 3.14 × 7 × 7 = 615.44.
volume = 4πr³/3
4 × 3.14 ×5 × 5 × 5 ÷ 3 = 523.33
Point P' is the image of P(3, 5) under a reflection across the y-axis. What are the coordinates of P'?
Answer:
hope this helps :)
Step-by-step explanation:
.......
This is used for the next few questions: The rating for the new scary movie has a scale of 0 to 10. The average response was that the regular movie attendant enjoyed the movie with 8.3 points and a standard deviation of 0.5 points. What is the percent of people who gave the movie a rating between 6.8 and 8.8? (Write the number as a percent only without a percent sign.)
Answer:
The percentage that of people who gave the movie a rating between 6.8 and 8.8
P(6.8≤X≤8.8) = 83.9≅ 84 percentage
Step-by-step explanation:
Step(i):-
Mean of the Population = 8.3 points
Standard deviation of the Population = 0.5 points
Let 'X' be the random variable in normal distribution
Let X = 6.8
[tex]Z = \frac{x-mean}{S.D} = \frac{6.8-8.3}{0.5} = -3[/tex]
Let X = 8.8
[tex]Z = \frac{x-mean}{S.D} = \frac{8.8-8.3}{0.5} = 1[/tex]
The probability that of people who gave the movie a rating between 6.8 and 8.8
P(6.8≤X≤8.8) = P(-3≤Z≤1)
= P(Z≤1)- P(Z≤-3)
= 0.5 + A(1) - ( 0.5 -A(-3))
= A(1) + A(3) (∵A(-3)=A(3)
= 0.3413 +0.4986 (∵ From Normal table)
= 0.8399
Conclusion:-
The percentage that of people who gave the movie a rating between 6.8 and 8.8
P(6.8≤X≤8.8) = 83.9≅ 84 percentage
a fish tank is : 16 in
Height : 10 in
Width : 8 in how many gallons is it ? NEED HELP ASAP
Answer:
5.541 gallons
Step-by-step explanation:
The fish tank is 1280 cubic inches, which equates to 5.541 US liquid gallons.
Answer:
5.54 gallons (aprox.)
Step-by-step explanation:
volume = 16in * 10in * 8in
volume = 1280in³
Convert cubic inch to gallons is:
1 inch³ = 0.004329 gallon
then:
1280in³ = 1280*0.004329 = 5.54 gallons (aprox.)
PLEASE ANSWER FAST.What is the probability that only girls bought lunches? 25% 41.6% 75% 50%
Answer:
The correct answer is 50.6195
Step-by-step explanation:
The probability that only girls bought lunches is given as D. 50%
How to solve
To find the probability that only girls bought lunches, we solve:
We can see that the total number of girls is 30 and the total number of both boys and girls is 60
So, to solve, it becomes:
30/60= 50%
Probability is a mathematical concept used to measure the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain), and is calculated using ratios, frequencies, or subjective judgments.
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A cylinder with a base diameter of x units has a volume of πx3 cubic units. A cylinder with a base diameter of x units has a volume of pi x cubed cubic units. Which statements about the cylinder are true? Select two options. The radius of the cylinder is 2x units. The area of the cylinder’s base is One-fourthπx2 square units. The area of the cylinder’s base is One-halfπx2 square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.
Answer:
The height of the cylinder is 4 x units.
The area of the cylinder’s base is One-fourthπx2 square units
Step-by-step explanation:
Formula for volume of the cylinder:
V = r² π h
Volume of the cylinder=
πx^3
Diameter=x
Radius (r)=diameter/2
=x/2
V = r² π h
πx^3=(x/2)^2πh
πx^3=(x^2/4)πh
Divide both sides by π
x^3=(x^2/4)h
Make h the subject of the formula
h=x^3÷x^2/4
=x^3×4 / x^2
=4x^3 / x^2
=4*x*x*x / x*x
h=4x
Area of the base:
B = r² π
Recall, r=x/2
B=(x/2)^2 * π
=(x^2/4)π
=πx^2/4
=1/4(πx^2)
The area of the cylinder’s base is One-fourthπx2 square units.
Answer:
B & E
Step-by-step explanation:
Edge 2020
URGENT!! Please help me with this as soon as possible!!
The statement is valid because the measure of the vertices located in the center of the pentagon is the quotient of 360 and 5, and the sum of two base angles in the given isosceles triangle is 108.
==========================================================
Explanation:
Check out the diagram below. I have added x and y such that
x = base angle
y = vertex angle (located adjacent to center of polygon)
The pentagon is sliced up like a cake into 5 equal portions. Each vertex angle is y = 360/5 = 72 degrees.
The two base angles x must add with the vertex angle y to get 180
(angle1)+(angle2)+(angle3) = 180
x+x+y = 180
2x+y = 180
2x+72 = 180
2x = 180-72
2x = 108
This is true for any one of the five triangles. Notice that for angle LMN, we can divide it into LMQ and QMN where Q is the center of the polygon. Both of these angles are x. Since we've shown 2x = 108, we can see that LMN must also be 108 as well.
Choice A is close, but we wouldn't use the exterior angle theorem. Choice B is the better answer.
you toss a coin and roll a number cube.find p(heads and an even number) a)1 b)1/6 c)1/12 d)1/4
Answer:
1/4
Step-by-step explanation:
PROVE √(1-〖cos〗^2 θ)/cosθ=tanθ
Answer:
The answer is below.
Step-by-step explanation:
PROVE √(1-〖cos〗^2 θ)/cosθ = tanθ
Now 1 - cos^2 θ = sin^2θ
So √(1 - cos^2 θ) = sin θ
and √(1 - cos^2 θ) / cos θ
= sin θ / cos θ
= tan θ
Step-by-step explanation:
[tex]\dfrac{\sqrt{1-\cos^2\theta}}{\cos\theta}=\tan\theta\\\\\text{We know:}\\(1)\ \sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\\(2)\tan x=\dfrac{\sin x}{\cos x}\\\\\text{For}\ \sqrt{1-\cos^2\theta}\ \text{use}\ (1):\\\\L_S=\dfrac{\sqrt{1-\cos^2\theta}}{\cos\theta}=\dfrac{\sqrt{\sin^2\theta}}{\cos\theta}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta\ \ \ _{used (2)}\\\\R_S=\tan\theta\\\\L_S=R_S[/tex]
[tex]\text{Of course, this equality is not true for everyone values of}\ \theta.\\\\1^o.\ \cos\theta\neq0\to\theta\neq\dfrac{\pi}{2}+k\pi,\ k\in\mathbb{Z}\\\\2^o.\ \sqrt{\sin^2\theta}=|\sin\theta|,\ \text{therefore}\\\\\text{for}\ \theta\in[2k\pi;\ (2k+1)\pi],\ \sin\theta\geq0\to|\sin\theta|=\sin\theta\\\\\text{therefore}\ \dfrac{|\sin\theta|}{\cos\theta}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta[/tex]
[tex]\text{for}\ \theta\in\bigg((2k-1)\pi;\ 2k\pi\bigg),\ \sin\theta<0\to|\sin\theta|=-\sin\theta\\\\\text{therefore}\ \dfrac{|\sin\theta|}{\cos\theta}=\dfrac{-\sin\theta}{\cos\theta}=-\tan\theta\neq\tan\theta[/tex]
[tex]\text{Conclusion:}\\\\\text{This equality is true for}\ \theta\in\left[2k\pi;\ \dfrac{\pi}{2}+2k\pi\right)\cup\left(\dfrac{\pi}{2}+2k\pi;\ \pi+2k\pi\right],\ k\in\mathbb{Z}[/tex]
Congress regulates corporate fuel economy and sets an annual gas mileage for cars. A company with a large fleet of cars hoped to meet a 2018 goal of 30.2 mpg or better for their fleet of cars. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 32.12 mpg and a standard deviation of 4.83 mpg. Is this strong evidence that they have attained their fuel economy goal
Answer:?
Step-by-step explanation:
Which expression is equivalent to (2 Superscript one-half Baseline times 2 Superscript three-fourths Baseline) squared?
Answer:
Your answer is correct
Step-by-step explanation:
(2^5/4)² = 4^5/2 = √4^5
The correct answer is option B which is [tex]\sqrt{2^5}[/tex].
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The expression will be solved as follows:-
[tex]E = ([ 2^{\frac{1}{2}} \times 2^{\frac{3}{4}}])^2\\E = (2^{({\frac{1}{2}+\frac{3}{3}})})^2\\E = (( 2 )^ {\frac{5}{4})}^2 \\E = ( 2 ) ^{\frac{5}{2}}\\E = \sqrt{2^5}[/tex]
Therefore the correct answer is option B which is [tex]\sqrt{2^5}[/tex].
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Hello!! Plz ans with explanation.. Plz!! I need it ASAP!!! PLZ TYSM
Faaast!!
Answer:
1/4
1/2
3/4
Step-by-step explanation:
Given:
Types of colors in the spinner
Yellow 1
Red 2
Blue 1
Total:4
Successful outcome of Yellow:1
Successful outcome of Red:2
Successful outcome of Blue:1
Required:
Probability of the
blue sectorred sectornot on yellow sectorFormula:
Probability= successful outcome ÷ possible outcome
Solution
Blue sectorProbability=1 ÷ 4
Red sectorProbability= 2÷4
not on yellow sectorProbability= 3÷4
Hope this helps ;) ❤❤❤