Answer:
13 slices of cheese pizza
Step-by-step explanation:
Consider grouping the slices so there are 10 pepperoni and 1 cheese in each group of 11. Then 143 slices represents 143/11 = 13 groups. Since there is 1 cheese slice in each group, ...
13 slices of cheese pizza were sold
The scores on one portion of a standardized test are approximately Normally distributed, N(572, 51). a. Use the 68-95-99.7 rule to estimate the range of scores that includes the middle 95% of these test scores. b. Use technology to estimate the range of scores that includes the middle 90% of these test scores.
Answer:
a) The range of scores that includes the middle 95% of these test scores is between 470 and 674.
b) The range of scores that includes the middle 90% of these test scores is between 488.1 and 655.9.
Step-by-step explanation:
68-95-99.7 rule:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Z-score:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Mean [tex]\mu = 572[/tex], standard deviation [tex]\sigma = 51[/tex]
a. Use the 68-95-99.7 rule to estimate the range of scores that includes the middle 95% of these test scores.
By the 68-95-99.7 rule, within 2 standard deviations of the mean.
572 - 2*51 = 470
572 + 2*51 = 674
The range of scores that includes the middle 95% of these test scores is between 470 and 674.
b. Use technology to estimate the range of scores that includes the middle 90% of these test scores.
Using the z-score formula.
Between these following percentiles:
50 - (90/2) = 5th percentile
50 + (90/2) = 95th percentile.
5th percentile.
X when Z has a pvalue of 0.05. So when X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 572}{51}[/tex]
[tex]X - 572 = -1.645*51[/tex]
[tex]X = 488.1[/tex]
95th percentile.
X when Z has a pvalue of 0.95. So when X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 572}{51}[/tex]
[tex]X - 572 = 1.645*51[/tex]
[tex]X = 655.9[/tex]
The range of scores that includes the middle 90% of these test scores is between 488.1 and 655.9.
how do I simplify this
Answer:Use Distributive property
whats the answer for 45 meters every 5 seconds = meters per second
Answer:
9 meters every second
Step-by-step explanation:
45/5=9
5/5=1
9:1
Please help if you can
Answer:
4
Step-by-step explanation:
We just have to find the corresponding d(t) value when t=2. From the graph, we can see that when t = 2, d(2) = 4. Hope this helps!
A bedroom wall is to be painted around a window as shown below.
A rectangle with length 11 feet and width 10 feet. A smaller rectangle with length 3 feet and width 2 feet is cut out of the larger rectangle.
What is the area of the wall that will be painted?
A.6 feet squared
B.104 feet squared
C.110 feet squared
D.116 feet squared
Answer:B.104 feet squared
Step-by-step explanation:
First find the area of the rectangle 11×10=110 then find the area of the window 3×2=6 then subtract 110-6=104
Answer:
B
Step-by-step explanation:
Find an equation for the nth term of the arithmetic sequence.
a16 = 21, a17 = -1
Answer:nth term=a1 - 27n + 27
Step-by-step explanation:
first term =a1
common difference=d=-1-21
d=-27
Using the formula
Tn=a1 + d x (n-1)
nth term=a1 + (-27)(n-1)
nth term=a1 - 27n + 27
12 divided by 9 tenths and hundredths
Johanna wrote the system of equations.
4x-3y=1, 5x+4y=9
If the second equation is multiplied by 4, what should the first equation be multiplied by to eliminate the x-variable by addition?
Answer:
-5
Step-by-step explanation:
If the second equation is multiplied by 4, the coefficient of the x-variable will be 5·4 = 20. To eliminate the x-variable by addition, the first equation needs to be multiplied by a value that will result in an x-coefficient of -20. If that value is k, then we have ...
4k = -20
k = -20/4 = -5
The first equation should be multiplied by -5 to eliminate the x-variable by addition.
_____
Comment on general case
In general, if you have ...
ax +by = c
dx +ey = f
to eliminate the x-variable by addition, you can multiply the second equation by "a" and the first equation by "-d". In the problem above, those numbers are 4 and -5.
Answer:
-5
Step-by-step explanation:
The picture shows a cement bag of weight Fg hanging from a rope which itself is supported by two other ropes attached to a ceiling. The latter two ropes make an angle θ1 and θ2 with the ceiling. Determine the tension in each rope. Use the angle addition identity to simplify your result: sin(α ± β) = sin α cos β ± cos α sin β
Answer:
[tex]T_1= \dfrac{F_gcos \theta_2}{sin (\theta_1+\theta_2)}[/tex]
Step-by-step explanation:
From the free body diagram attached below; we will see that
T₃ = Fg ------ (1)
Thus; as the system is in equilibrium, the net force in the x and y direction shows to be zero
Then;
[tex]\sum F_x= 0 \to T_2 Cos \theta _2 - T_1 cos \theta _1[/tex]
[tex]T_2 Cos \theta _2 = T_1 cos \theta _1 \ \ \ \ \ - - - (2)[/tex]
Also;
[tex]\sum F_y =0 \to T_2sin \theta_2+T_1sin \theta_1 - T_3 = 0[/tex]
[tex]T_3 = T_2sin \theta_2+T_1sin \theta_1[/tex] ---- (3)
From equation (2):
[tex]T_2 = \dfrac{T_1cos \theta_1}{cos \theta_2}[/tex]
Replacing the above value for T₂ into equation 3; we have
[tex]T_3 = \dfrac{T_1cos \theta_1}{cos \theta_2}sin \theta_2+T_1sin \theta_1[/tex]
[tex]T_3 cos \theta_2 = {T_1cos \theta_1}{}sin \theta_2+T_1sin \theta_1 cos \theta_2[/tex]
[tex]T_3 cos \theta_2 = T_1(cos \theta_1 sin \theta_2+sin \theta_1 cos \theta_2)[/tex] ---- (4)
Using trigonometric identity Sin (A+B) = SIn A cos B + Cos A sin B
So ; equation 4 can now be:
[tex]T_3 cos \theta_2 = T_1sin(\theta _1 + \theta_2)[/tex] --- (5)
replacing equation (1) into equation (5) ; we have:
[tex]F_g}cos \theta_2 =T_1 sin (\theta_1+\theta_2)[/tex]
Hence; the tension in the string is:
[tex]T_1= \dfrac{F_gcos \theta_2}{sin (\theta_1+\theta_2)}[/tex]
The vertices of ΔDEF have coordinates D(–1, 2), E(3, 3), and F (2, –4).What are the coordinates of the vertices of r(90°, O)(ΔDEF)?
Answer:
D,E
Step-by-step explanation:
hope I helped
A child is laying on the ground relaxing and looking up at a plane that is passing by. If the plane’s altitude is 33,500 feet and the child’s eyes are located 8,200 feet away from a point on the ground directly beneath the plane, what is the angle of elevation for the child’s line of sight to the plane?
Answer:
about 76.2°
Step-by-step explanation:
The geometry can be modeled by a right triangle with the given dimensions being the side opposite the angle (height = 33,500 ft) and the side adjacent to the angle (8,200 ft). The fact that you know these two sides suggests the inverse of the tangent function may be useful.
Tan = Opposite/Adjacent
tan(angle) = (33,500/8,200)
angle = arctan (335/82) ≈ 76.246°
The angle of elevation is about 76.2°.
plzz help i hav a test after i need the answer quick plzz.
Answer:Oop
Step-by-step explanation:
PLS HELP ME!
Um doing venn digrams so u have to set one up for it to work... TWENTY POINTS
Answer:
Creating a diagram..
Step-by-step explanation:
Alrighty, I've made a diagram. I've even uploaded it so everyone can see how good at drawing I am (not)
a. 7 do not own anything.
b. the probability that someone owns a bone or a stick is 50%.
c. the probability that someone owns a rock and a bone is 14%.
d. the probability that someone owns at least 2 items is 42%.
e. the probability that someone owns only 1 of these items is 51%.
Please tell me if im wrong! im only a student .m.
The Senate in a certain state is comprised of 58 Republicans, 39 Democrats, and 3 Independents. How many committees can be formed if each committee must have 3 Republicans and 2 Democrats?
YuAnswer:
Step-by-step explanation:
I really don't know the answer sorry
The object below is a cubical lunch box having each edge as 10 cm.
Find its surface area.
A
600 cm2
B
360 cm2
C
300 cm2
D
36 cm2
Answer:
B
Step-by-step explanation:
The total surface area of a cubical lunch box having each edge as 10 cm is 600 square centimeter. Therefore, option A is the correct answer.
What is surface area of a cube?The surface area of the cube all six faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added six times to itself. The formula to find the surface area of a cube is 6a², where a is edge.
Given that, the cubical lunch box having each edge as 10 cm.
Here, surface area = 6×10²
= 600 square centimeter
Therefore, option A is the correct answer.
Learn more about the surface area of a cube here:
brainly.com/question/23273671.
#SPJ2
A bookstore had 60 copies of a magazine. Yesterday, it sold 1/3 of them. Today, it sold 1/4 of what remained. How many copies does the bookstore have left?
Answer:
30
Step-by-step explanation:
1/3 of 60 is 20
40 would be left
1/4 of 40 is 10 so 30 would be left
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 18, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B
One-half of the dogs in each shelter are between which weights?
between 8 and 30 pounds in shelter A; between 10 and 28 pounds in shelter B
between 8 and 17 pounds in shelter A; between 10 and 16 pounds in shelter B
between 21 and 30 pounds in shelter A; between 18 and 28 pounds in shelter B
between 28 and 30 pounds in shelter A; between 20 and 28 pounds in shelter B
Answer:
the 2nd one
i am pretty sure
Step-by-step explanation:
A polynomial function has a root of -5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the
function has a negative leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (-0, 5).
The graph of the function is negative on (-5, 3)
The graph of the function is positive on (-0, 1).
The graph of the function is negative on (3,co)
Mark this and return
Save and Exit
Sabem
Answer:
The graph of the function is negative on (3, ∞)
Step-by-step explanation:
The function starts negative at the left side of the graph, crosses the x-axis at x = -5, touches the x-axis at x = 1, again crosses into negative values at x = 3.
The function is positive on the open intervals (-5, 1) and (1, 3). It is negative on the open intervals (-∞, -5) and (3, ∞). The latter description matches the last answer choice:
the graph of the function is negative on (3, ∞).
What is the value of 5x+3 when x = 4?
Answer:
Step-by-step explanation:
5(4)+ 3
20+3
23
1.] What is the probability of choosing a king
from a standard deck of playing cards?
Answer:
1/13
Step-by-step explanation:
there are 4 kings in a deck of 52 cards.
4/52 = 1/13
if a cube measures 5.3 cm on each side and has a mass of 280 grams how much is its volume
Answer:
8.1 g/cm
Step-by-step explanation:
Identify two Pythagorean triples using the known triple 9, 40 , 41. *
Your answer
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {9}^{2} + {40}^{2} = {41}^{2} \\ 81 + 1600 = 1681 \\ 1681 = 1681[/tex]
What is the solution to the equation StartFraction m Over m + 4 EndFraction + StartFraction 4 Over 4 minus m EndFraction = StartFraction m squared Over m squared minus 16 EndFraction?
Answer: m = -2.
The given equation is: [tex]\frac{m}{m+4}+\frac{4}{4-m}=\frac{m^{2}}{m^{2}-16}[/tex].
The LCM of the denominators = [tex]m^{2}-16=(m+4)(m-4)[/tex].
We multiply both sides by LCM.
[tex]\left(m+4\right)\left(m-4\right)\left(\frac{m}{m+4}+\frac{4}{4-m}\right)=\left(m+4\right)\left(m-4\right)\cdot\frac{m^{2}}{m^{2}-16}[/tex]
[tex]m\left(m-4\right)-4\left(m+4\right)=m^{2}[/tex]
[tex]m^{2}-4m-4m-16=m^{2}[/tex]
[tex]8m=-16\\m=-2[/tex]
Learn more: https://brainly.com/question/13769924
Answer:
M=-2 B
Step-by-step explanation:
trust me i took the quiz
Find the compound interest on GHS 50,200 invested at 13% p.a. compounded annually for 3 years ( to the nearest
GHS).
Select one:
A. GHS 19,578
B. GHS 69,778
O
C. GHS 72,433
D. GHS 22.233
Answer:
D
Step-by-step explanation:
First found amount yielded
A = P(1+r)^nt
P is amount deposited 50,200
r is interest rate 13% = 13/100 = 0.13
t = 3
A = 50,200(1+0.13)^3
A = 50,200(1,13)^3
A = 72,433.42939999998
A is approximately 72,433.43
interest = A - P = 72,433.43-50,200 = 22,233.43= 22,233 to the nearest GHS
Daryl wishes to save money to provide for his retirement. He is now 30 years old and will be
retiring at age 64. Beginning one month from now, he will begin depositing a fixed amount into
a retirement savings account that will earn 12% compounded monthly. Then one year after
making his final deposit, he will withdraw $100,000 annually for 25 years. In addition, and after
he passes away (assuming he lives 25 years after retirement) he wishes to leave in the fund a sum
worth $1,000,000 to his nephew who is under his charge. The fund will continue to earn 12%
compounded monthly. How much should the monthly deposits be for his retirement plan?
Answer:
Step-by-step explanation:
Today's Age = 30
Retirement Age = 64
Total Monthly Deposits = ( 64 - 30 ) * 12 = 408
In case of 12% Compounded Monthly , Interest Rate per month = ( 12% / 12 ) = 1%
Effective Interest Rate per year = ( 1 + 0.12/12 )12 - 1 = 1.1268 - 1 = 0.1268 = 12.68%
Present value of Annual 25 Years withdrawal of $100,000 at time of Retirement = $100,000 * PVAF ( 12.68% , 25 )
= $100,000 * 7.4864
= $748,642.20
Present Value of Money for nephew at time of Retirement = $1,000,000 * PVF ( 12.68% , 25 )
= $1,000,000 * 0.050535
= $50,534.52
Now the Present Value of total Amount Required at time of Retirement = $748,642.20 + $50,534.52
= $799,176.70
Now the monthly deposit be X
= X * FVAF ( 408 , 1% ) = $799,176.70
= X * 5752.85 = $799,176.70
X = $138.918
Therefore Monthly Deposit = $138.92
The table shows the number of cups of water required when cooking different amounts of rice.
Amount of
Rice
(cups) Amount of
Water
(cups)
2 5
3 7.5
5 12.5
8 20
Which statements apply to the ratio of rice and water? Choose two options.
The amount of rice is the dependent value.
The amount of water is the dependent value.
The amount of rice is the independent value.
The amount of water is the independent value.
The values cannot be labeled as dependent or independent without a given equation
Answer:
The amount of water is the dependent value.The amount of rice is the independent value.Step-by-step explanation:
The wording "the amount of water required for different amounts of rice" suggests that the "output" value of the table is the amount of water, and the "input" value is the amount of rice.
That makes "water" the dependent variable, and "rice" the independent variable.
The amount of water is the dependent value.
The amount of rice is the independent value.
Answer:
The amount of water is the dependent value.
The amount of rice is the independent value.
Step-by-step explanation:
Trust me,I will give braineist. I swear to god.
Answer:
= 1696m^3
Step-by-step explanation:
V = πr²h
= 3.14 x 6 x 6 x 15
= 3.14 x 540
= 1695.6 m^3
= 1696m^3
the atlantic ocean is 2.78×10^4 feet deep at it's lowest point. If a scuba diver dives 1/50 of the total depth of the ocean, enter how many feets he dove down?
Answer:
556 feet
Step-by-step explanation:
What you have to do to get the answer is find out what 10^4 is, and then multiply that by 2.78. After that, you just need to divide it by 50.
10^4 = 10,000
2.78 × 10,000 = 27,800
27,800 ÷ 50 = 556
Answer:
556
Step-by-step explanation:
................................................
Answer:
V =108 ft^3
Step-by-step explanation:
The volume is found by
V = Bh where B is the area of the base
B = the area of the trapezoid
B = 1/2 (b1+b2)*h of the trapezoid
B = 1/2(4+6)*4 = 1/2(10)*4 = 20
Now we can find the volume
V = 20* 9
V =108 ft^3
Jessica bought the ingredients to make chicken soup, and wanted to make a double batch, which would be 18 cups of soup. A quick Google search told her that this was 259.9 cubic inches. She hoped the soup pot below would be big enough. The soup pot is 9 inches tall with a radius of 3.5 inches. What is the volume of the soup pot? Answer choices are rounded to the nearest tenth cubic inch. 169.6 cubic inches 890.6 cubic inches 197.9 cubic inches 346.4 cubic inches
Answer: 346.4 in^3
Step-by-step explanation:
The pot can be thinked as a cylinder:
The volume of a cylinder is equal to:
V = (pi*r^2)*h
where h is the height, r is the radius and pi = 3.1416
Here we have that: r = 3.5in, h = 9in.
Then the volume is:
V = 3.1416*(3.5in)^2*9in = 346.4in^3
